terça-feira, 9 de agosto de 2016

Claudio Costa: PHILOSOPHICAL TEXTS - TEXTOS DE FILOSOFIA



THIS "BLOG" IS THOUGHT AS A WAY TO MAKE MY WORK IN PHILOSOPHY ACCESSIBLE TO A WIDE PUBLICUM. THERE ARE MORE THAN 100 TEXTS, MOST OF THEM IN DRAFT FORM. MANY ARE INTRODUCTORY TEXTS. THE TEXTS MARKED WITH ONE OR MORE # ARE THOSE THAT CAN BE OF SOME INTEREST FOR THE SPECIALISTS. I HOPE IT IS USEFUL.

ESSE "BLOG" FOI PENSADO COMO UMA MANEIRA DE TORNAR MEU TRABALHO EM FILOSOFIA ACESSÍVEL A UM PÚBLICO MAIS AMPLO. SÃO MAIS DE 100 TEXTOS, A MAIORIA EM FORMA DE DRAFT. MUITOS SÃO TEXTOS INTRODUTÓRIOS. AQUELES MARCADOS COM UM OU MAIS # SÃO OS QUE PODEM SER DE ALGUM INTERESSE PARA A PESQUISA. ESPERO QUE SEJA ÚTIL.

On my curriculum:
After a study of medicine I made my M.S. in philosophy at the UFRJ (Rio de Janeiro) with prof. Raul Landin. My PhD I made at the University of Konstanz (Germany) with Gottfried Gabriel and Friedrich Kambartel. Afterwards there were very useful one year post-doctoral works in the Hochschule für Philosophie (with Friedo Ricken), at the University of Berkeley (with John Searle) at the University of Oxford (with Richard Swinburne), at the University of Konstanz (with Wolfgang Spohn) and now at the University of Göteborg (with Anna-Sofia Maurin). My main articles published in in international journals were collected and better developed in the book Lines of Thought: Rethinking Philosophical Assumptions (Cambridge Scholars Publishing, 2014). I also developed a theory on the nature of philosophy in the book The Philosophical Inquiry (UPA, 2002). Presently I am writting a book aiming to recuperate the credibility of the old orthodoxy in analytic philosophy of language. This book, to be called Philosophical Semantics, will be also published by CSP probably still in 2016.

Presently I am full professor of philosophy and (mainly) a CNPq researcher at the UFRN, in the Northeast of Brazil.

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### VERIFICATIONISM REDEEMED

Draft for th book Philosophical Semantics, to be published by Cambridge Scholars Publishing in 2016. (I already found several mistakes.)




– 5 –

VERIFICATIONISM REDEEMED



There is no distinction of meaning so fine as to consist in anything but a possible difference in practice.
C. S. Peirce

Verificationism is seen today as a relic of the the first half of the 20th century’s philosophy. Although initially advocated by members of the Vienna Circle, it soon proved incapable of resisting the increasing variety of opposing arguments, which came from both within and outside the Circle. My aim in this chapter is to show that we can find a version of the principle of verifiability that is both intuitively acceptable and resistant to the most widespread objections. The Vienna Circle failed to successfully defend verificationism because it used the wrong approach of beginning by formally clarifying the principle of verification as proposed by Wittgenstein without paying attention to the pragmatics. When their arguments in its favor were shown to be faulty, most of them, followed by their offspring, unwisely concluded that the principle itself should be false. In my view, they were reacting like the proverbial fox in Aesop’s fable: unable to reach the grapes, he consoled himself by imagining that they were anyway sour...
   Returning to the methodology and assumptions of the later Wittgenstein, my aim in this chapter is twofold: first to sketch a plausible version of what could be called semantic verificationism, which consists in the proposal that the epistemic (cognitive, factual…) content of declarative sentences is essentially constituted by their verifiability rules; second, to confirm and extend it by answering the main arguments against this view.

1. Origins of semantic verificationism
A first point to be remembered is that, contrary to mistaken popular belief, the idea that a sentence’s meaning is its method of verification is not attributable to the logical positivists. The first to propose the principle was actually Wittgenstein himself, as the Vienna Circle always acknowledged (cf. Glock, p. 354). Indeed, if we review his works, we see that he formulated the principle in 1929 conversations with Waismann and mentioned it repeatedly in texts over the course of the following years. Furthermore, there is no convincing evidence that he abandoned the principle later, replacing it with a purely performative conception of meaning as use. On the contrary, there is evidence that from the beginning his verificationism and his subsequent thesis that meaning is a function of use seemed mutually compatible to him. After all, Wittgenstein did not hesitate to conflate the concept of meaning as verification with meaning as use, and even with meaning as calculus. As he said:

If you want to know the meaning of a sentence, ask for its verification. I stress the point that the meaning of a symbol is its place in the calculus, the way it is used.[1] (Wittgenstein 2001, p. 29)

It is always advisable to consult what the original author of an idea really said. If we compare Wittgenstein’s verificationism with the Vienna Circle’s verificationism, we can see that there are some striking contrasts. A first one is that Wittgenstein’s main objective with the principle always seems to have been to achieve a grammatical overview (grammatische Übersicht), that is, to clarify central principles of our factual language, even if this clarification could be put at the service of therapeutic goals. On the other hand, he was against the positivist or scientistic spirit of the Vienna Circle, which in its insipient and precocious desire to develop a purely scientific philosophy had the strongest motivation to develop the verification principle as a powerful reductionist weapon, able to vanquish once and for all the fantasies of metaphysicians. Wittgenstein, for his part, didn’t reject metaphysics in this way. For him the metaphysical urge was a kind of unavoidable dialectical condition of philosophical inquiry, and metaphysical mistakes have the character of deepness (Wittgenstein 1984c sec. 111, 119). It was this rejection of scientistic reductionism that gradually estranged him from the Logical Positivists. For him metaphysical errors were intrinsically necessary for the practice of philosophy as a whole:

The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; their roots are as deep in us as the forms of our language and their significance is as great as the importance of our language. (1984c, sec. 111)

In these aspects, Wittgenstein was much closer to that great American philosopher C. S. Peirce. According to Peirce’s pragmatic maxim, metaphysical deception can be avoided when we have a clearer understanding of our beliefs. This clarity can be reached by understanding how these beliefs are related to our experiences, expectations and their consequences. Moreover, the meaning of a concept, which can be expressed in its definition, was for Peirce the totality of its practical effects, the totality of its inferential relations with other concepts and praxis. So, for instance, a diamond, as the hardest material object, can be partially defined as something that scratches all other things, but cannot be scratched by anything.
   Moreover, in contrast to the positivists, Peirce was aiming to extend science to metaphysics, instead of reducing metaphysics to science.[2] So, he was of the opinion that verifiability – far from being a weapon against metaphysics – should be elaborated in order to be applicable to it, since the aim of metaphysics is to say extremely general things about our empirical world. As Peirce wrote:

But metaphysics, even bad metaphysics, really rests on observations, whether consciously or not; and the only reason that this is not universally recognized is that it rests upon kinds of phenomena with which every man’s experience is so saturated that he usually pays no particular attention to them. The data of metaphysics are not less open to observation, but immeasurably more so, than the data, say, of the very highly observational science of astronomy… (Peirce 1931, 6.2)[3]
                                          
Although overall Peirce’s views were as close to Wittgenstein’s as those of both were distant from the logical positivists’, there is an important difference between both philosophers concerning the analysis of meaning. Peirce was generally interested in the connection between our concepts and praxis, including their practical effects, as a key to their clarification and a better understanding of their meaning. But by proceeding in this way he was in my view extending the concept of meaning too far; he took a path that can easily lead us to confuse the cognitive and practical effects of meaning with meaning itself. For as we already saw, the cognitive meaning of a declarative sentence, seen as a combination of semantic-cognitive rules, works as a condition for the production of inferential awareness, which consists in the kind of systemic openness (the ‘propagation of content’) that can produce an indeterminate number of subsequent mental states and actions.[4] Meaning as a verifiability rule is one thing; awareness of meaning, the inferences that may result from this awareness, together with the practical effects of such inferences, may be a very different thing. Though they can be intermingled, they need to be distinguished. Hence, within our narrow form of inferentialism, we first have the inferences that construct meanings (like those of the identification rules of singular terms, the ascription rules of predicates, and the verifiability rules of sentences). Then we have the multiple inferences that enable us to gain something from our knowledge of meaning, along with the multiplicity of behavioral and practical effects that may result from them. Without this separation, we may even have a method that helps us clarify our ideas, but we will lack a boundary that can prevent us from extending our concept of meaning beyond any reasonable limit. This is why Wittgenstein, restricting cognitive meaning to a method of verification, that is, to the combination of rules that make a proposition true, proposed a more adequate view of cognitive truth or cognitive meaning. For instance: the fact that something cannot be scratched helps to verify the sentence ‘This is a diamond’, whereas the use of diamonds as abrasives will probably not serve as a proof.
   Looking for a better example, consider the statement: (i) ‘In October 1942 Chil Rajchman was arrested, put on a train, and deported to Treblinka’. This promptly leads us to the conclusion: (ii) ‘Chil Rajchman was sent to be killed in a death camp’. However, his probable fate isn’t part of the verifiability procedure of (i), but rather of statement (ii). Consequently, although (ii) is a consequence of (i), it isn’t a true constituent of the cognitive meaning, the thought-content expressed by (i). Statement (ii) has its own verifiability rule, even if its meaning is strongly associated with that of statement (i), since it is our main reason for being interested in this last statement. So, we could say that there is a cloud of meaning surrounding the cognitive meaning of our statements, which is formed by inferentially associated cognitive meanings of other statements with their own verifiability rules. But it is clear that this cloud of meaning does not properly belong to the cognitive meaning of S and should not be confused with it. In short: only by restricting ourselves to the constitutive verifiability procedures of a chosen statement are we able to restrict ourselves to the limits of its meaning.
   Opposition to a reductionistic replacement of metaphysics by science was also one reason why Wittgenstein didn’t bother to make his principle formally precise, unlike positivists from A. J. Ayer to Rudolph Carnap. In saying this, I do not object to this possibility. I am only warning that such efforts, if not well supported by a sufficiently careful pragmatic consideration of how language really works, tend to put the logical cart before the linguistic horse. I want to show that unwisely neglecting the most natural linguistic intuitions defeated the attempts of positivist philosophers to advocate their own principle.
   Having considered these differences, I want to start by examining some of Wittgenstein’s remarks regarding the verifiability principle, in order to find the most adequate formulation and its justification. Afterwards, I will answer the main objections against the principle, demonstrating that they are much weaker than they seem at first glance.


2. Wittgensteinian verificationism
Here are some of Wittgenstein’s statements presenting the verifiability principle:

Each sentence (Satz) is a signpost for its verification. (Wittgenstein 1984e, p. 150)
A sentence (Satz) without any way of verification has no sense (Sinn). (Wittgenstein 1984f, p. 245)
If two sentences are true or false under the same conditions, they have the same sense (even if they look different). (Wittgenstein 1984f, p. 244)
To understand the sense of a sentence is to know how the issue of its truth or falsity is to be decided. (Wittgenstein 1984e, sec. 43)
Determine under what conditions a sentence can be true or false, then determine thereby the sense of the sentence. (This is the foundation of our truth-functions.) (Wittgenstein 1984f, p. 47)
To know the meaning of a sentence, we need to find a well-defined procedure to see if the sentence is true. (Wittgenstein 1984f, p. 244)  
The method of verification is not a means, a vehicle, but the sense itself. Determine under what conditions a sentence must be true or false, thus determine the meaning of the sentence. (Wittgenstein 1984f, pp. 226-7)
The meaning of a sentence is its method of verification. (Wittgenstein 1980, p. 29)[5]

What calls attention to statements like these is their strongly intuitive appeal: they seem to be true. They satisfy our methodological parti pris of clinging to our common knowledge beliefs. To some extent they even seem to corroborate Wittgenstein’s suspect view that philosophical theses are ‘trivial’ because they do no more than make explicit what we already know. They are what he would call ‘grammatical sentences’ expressing the rules grounding the linguistic practices that constitute our factual language. In the end the appeal to meaning verificationism involves what may be called a ‘transcendental argument’: we cannot reasonably conceive a different way to analyze the cognitive meaning of a declarative sentence except by appealing to verifiability; hence, assuming that meaning is analyzable, some form of semantic verificationism must be right.
   There are some points to be added here. The first is terminological and already well explained in this book: we should not forget that the verifiability rule must be identified with the cognitive content of a declarative sentence. This cognitive content is what I called in my discussion of Frege’s semantic the thought-content (s-thought) expressed by the sentence, being called by others the descriptive, informative or factual content of the sentence, if not its proposition or propositional content. A complementary point is that we should never confuse cognitive content with grammatical meaning. If you do not know who Tito and Baby are, you cannot understand the cognitive meaning of the sentence ‘Tito loves Baby’, though you are still able to understand its gram­matical meaning.
   Another point to be noted is that the verifiability rule includes both the verification and the falsification of the statement. The reason is that this rule either applies to the verifier as such – the truthmaker that in the last chapter we unequivocally identified with some cognitively independent fact in the world – or it does not apply to any expected verifier or fact in the world. Consider, for example, the statement ‘Frege was bearded’. Here the rule of verification applies to a circumstantial fact intended in the world that makes the rule effectively applicable, which means that the thought-content expressed by the statement is true. Consider, by contrast, the statement ‘Wittgenstein was bearded’: here the rule of verification does not apply to the intended fact in the world, since this fact does not exist. So the thought-content expressed by this sentence is false.
   These remarks also lead us to conclude against the existence of negative facts: a negative statement never states this phantasmagoric thing called a negative fact; what it really does is to deny the existence of a positive fact. The true thought expressed by the sentence ‘Teetetus isn’t flying’ does not properly apply to a negative fact – the fact that he is not flying – but rather to no fact at all. It is so because ‘Teetetus isn’t flying’ means the same as ‘It is not the case that Teetetus is flying’, which in turn has the same sense as ‘It is false that Teetetus is flying’; but this means only that the here expressed thought-content, that is, the verifiability rule, does not effectively apply to any real fact in the world. This real fact, the truthmaker, should be the fact of Teetetus flying. But after identifying Teetetus we see that he is in fact sitting and that the ascription rule for ‘…is flying’ does not apply to him. (You can say ‘It is a fact that Teetetus isn’t flying’, but here you use the word ‘fact’ derivatively in the sense of ‘true’.)
   It is also true that we can imagine or conceive the application of the verifying rule of a false statement to a possible fact, knowing in this way that it could be satisfied, proving its meaningfulness: Plato could imagine his friend Teetetus flying. But this possible fact isn’t a negative fact. Consider now the universal negative statement ‘There are no yetis’. Here as well there is no negative fact to consider. For calling ‘yeti’ Y, we can formalize ‘There are no yetis’ as ~Ǝx (Yx) or (x) (~Yx). This is the same as {~Ya1 & ~Ya2… & ~Yan}, where each negative singular statement is equivalent to the falsity of its affirmation, namely, to the non-application of its ascription rule for yetis to the objects {a1, a2… an}, since the expected positive fact of the existence of at least one yeti does not exist. The false statement ‘There are yetis’ remains only a conceivable, empirically possible fact.
   A final point concerns my reading of Wittgenstein’s distinction between the verification of a sentence (Satz) and of a hypothesis (Hypothese) in the obscure last chapter of his Philosophical Remarks. As he writes:

A hypothesis is a law for the building of sentences.
One could say: a hypothesis is a law for the building of expectations.
A sentence is, so to speak, a cut in our hypothesis in a certain place.  (Wittgenstein 1984e ch. xxii, sec. 228)

 In my understanding, the hypothesis is distinguished here by being more distant from sensory-perceptual experience than what he calls a sentence. As a consequence, only the verification of a statement is made with certainty (for instance, ‘I am seeing a chair now’). However, this does not mean that the verification of this statement is infallible. So, when Wittgenstein writes that we verify the truth of the sentence ‘Here is a chair’ by looking only at a side of the chair (1984e, ch. xxii sec. 225), it is clear that we can increase our degree of certainty by adding new facets, aspects, modes of presentation and subfacts.
   Thus, my view is that what he calls the certainty of a sentence is only postulated as such after what we consider sufficient verification in the context of some linguistic practice. This is why things can be seen as certain and yet remain fallible. By contrast, the verification of hypotheses, like those stating scientific laws, being reached only derivatively, gives us comparatively lower degrees of probability, but even so is also assumed to be true.

3. Verifiability rule as a criterial rule
A more important point noted by Wittgenstein and ignored by others is that usually we have a variety of ways to verify a statement, each way constituting some different, more or less central aspect of its meaning. As he noted:

Consideration of how the meaning of a sentence is explained makes clear the connection between meaning and verification. Reading that Cambridge won the boat race, which confirms that ‘Cambridge won’, is obviously not the meaning, but is connected with it. ‘Cambridge won’ isn’t the disjunction ‘I saw the race or I read the result or...’ It’s more complicated. But if we exclude any of the means to check the sentence, we change its meaning. It would be a violation of grammatical rules if we disregarded something that always accompanied a meaning. And if you dropped all the means of verification, it would destroy the meaning. Of course, not every kind of check is actually used to verify ‘Cambridge won’, nor does any verification give the meaning. The different checks of winning the boat race have different places in the grammar of ‘winning the boat race’. (Wittgenstein 2001, p. 29)

Moreover:

All that is necessary for our sentences to have meaning is that in some sense our experience would agree with them or not. That is: the immediate experience should prove only something of them, a facet. (Wittgenstein 1984f, p. 282, my italics)

In other words: one can verify through the direct observation of relational facts, i.e., by seeing the Cambridge boat winning the race or by hearing the judge’s confirmation, or both. These forms of verification are central to the meaning of ‘Cambridge won the boat race’. Here it is worth remembering that even this direct observation of the fact is aspectual: each person at the boat race saw the fact from a different perspective, they saw different subfacts: different aspects (facets) of the same event. However, we also say that they did see the grounding fact in the sense that they inferred its totality in the most direct way possible; this is why we can say that the fact-event of Cambridge winning was directly experienced. In the same way, we are allowed to say that we see a sheep in the field (the inferred grounding fact), while in fact we see the only one side of a sheep (a given aspectual subfact).
   However, often enough the way we can know the truth-value of a thought-content like that expressed by the sentence ‘Cambridge won the boat race’ is more indirect: someone can tell you, you can read this in the internet or in a magazine, or you can see a trophy in the clubhouse… These ways are secondary, and for Wittgenstein they participate only secondarily in the sentence’s meaning. Finally, they are causally dependent on the first ones. If the first form of verification did not exist, these dependent forms would lose their reliability.
   Using Wittgensteinian terms, we can say that the verifiability rule applies when we reach an awareness of a fact, that is, when we are in a position to make the relevant inferences from this awareness. This awareness is the most direct when the criterial configuration (a configuration of singularized s-properties or tropes) that satisfies the verifiability rule is constitutive of the fact, that is, when we observe the competition being won. But more often the verification is indirect, namely, by means of symptoms, or of a sum total of symptoms making the thought-content more or less probably true.
   Criteria tend to be displayed in the form of criterial configurations. Thus, the verifiability rule applies when the criterial configurations demanded by the rule are objectively given as belonging to the objective facts as their s-properties. Furthermore, the satisfaction of the criterial rule seems to have as a minimum condition of satisfaction a structural isomorphism between, on the one hand, the interrelated internal elements that make up the thought-content, and, on the other hand, the interrelated objective elements (combinations of s-properties) that make up the fact in the world – this would be the grounding fact isomorphism. Since experience is always aspectual and often indirect, this also means that the internal criterial configurations demanded by the rule must also show a structural isomorphism with derived configurations of s-properties or tropes (given in the world and experienced by the epistemic subject) generating what we could call isomorphism with a subfact. I will try to say more about this complicated issue in the last chapter.
   As my reconstruction of Wittgenstein’s views shows, a sentence’s meaning should be constituted by verifiability rules that require the fulfillment of criterial configurations, allowing us to infer facts in more or less direct ways. Hence, there are definitional criterial configurations (primary criteria) such as, in Wittgenstein’s example, those created from direct observation by a spectator at the boat race. But there is also an indefinite number of secondary criterial configurations depending on the first ones. They are symptoms (secondary criteria) allowing us to infer that Cambridge (more or less probably) won the boat race, etc. Here too, we can say that the primary criteria have a definitional character: once we accept them as really given and we can agree on this, our verifiability rule should apply with practical certainty. On the other hand, symptoms (secondary criteria) make the application of a verifiability rule only probable. Thus, if someone tells me this, it is very probable that Cambridge won. However, this probability must be backed by primary criterial observation of the fact by judges and eye-witnesses.
   Investigating the structure of verifiability rules has some consequences for the traditional concept of truth conditions. The truth condition of a statement caan be defined as the condition that a thought-content S actually is the case. The truth condition for the statement ‘Frege had a beard’ is the condition that he actually did have a beard. This means that the truth-condition of S is the condition that a fact is given as S’s truthmaker. Thus the philosophical belief that a true condition could exist without at least the conception of criterial configurations (s-properties that could possibly warrant its existence) is a misconception.
   Now, considering our analysis of the identification rules of proper names (appendix of chapter 1) and of the application rules of predicative expressions (e.g., chap. 2, sec. 6), we must consider the verifiability rule of a singular predicative statement to be a combination of both. We can see this by examining a very simple predicative statement: ‘Aristotle was bearded’. For this we use as a definitional identification rule for Aristotle the rule presented in appendix 1, sec. 1:

IR-Aristotle: In any possible world where there is a bearer of the name ‘Aristotle’, this object is the human being who sufficiently and more than any other person satisfies the conditions of having been born in Stagira in 384 BC, lived the main part of his life in Athens and died in Chalcis in 322 BC and/or having been the philosopher who developed the main ideas of the Aristotelian opus. (With the possible helpful addition of auxiliary descriptions...)

And for the predicative expression ‘…was bearded’ we may formulate the following definitional ascription rule:

AR-bearded = a human being who has natural hair growth on the chin and/or cheek(s) and/or neck.

Now, as we already know, we usually first apply the identification rule of the singular term in order to identify the object, subsequently applying the ascription rule of the general term by means of which we select the s-property of the object identified by the first rule. Not only are there many possible ways in which the identification rule and the ascription rule can be satisfied, there are still more ways of verification for the thought-content stated by ‘Aristotle was bearded’. One of them is by examining the famous marble bust of Aristotle found in Athens, another is by accepting the testimony of contemporaries, and still another is by learning that most ancient Greeks (particularly among the peripatetics) customarily wore beards as a badge of manhood, which allows the satisfaction of AR-Aristotle in addition to the satisfaction of IR-Aristotle. As we noted, we postulate this criteriologically based verification as practically certain, so that we can say we know that Aristotle was bearded, even if we are aware that in an absolute sense this is only highly probable.
   These brief comments on verificationism à la Wittgenstein suggest the need for more intensive pragmatic research on ways of verification. The structure of verifiability rules is usually ramified, and this must vary in accordance with the kinds of sentences expressing them. A detailed pragmatic investigation of the structure of verifying rules seems to me an important task that until now was neither sufficiently nor adequately attempted. In what follows, I will not attempt to rectify this situation. I will limit myself to answering the main objections to the verifiability principle as explained above.

4. Objection 1: The principle is self-refuting
The first and most notorious objection to the principle of verifiability is that it is self-defeating. The argument is as follows. The principle of verifiability must be either analytic or synthetic. If it is analytic it must be tautological, i.e., non-informative, but it seems clearly informative in its task of elucidating cognitive meaning. Furthermore, analytic statements are self-evident, and denying them is contradictory or inconsistent, which is not the case with the principle of verifiability. Therefore, the principle is synthetic. But if it is synthetic, it needs to be verifiable in order to have meaning. Yet, when we try to apply the principle of verifiability to itself we find that it is unverifiable. Therefore, the principle is devoid of meaning. The principle is meaningless by its own standards. And one cannot decide meaningfulness by means of what is meaningless.
   Logical positivists tried to circumvent such objections by responding that the principle of verifiability has no truth-value, for it is nothing more than a proposal, a recommendation, a methodological requirement.[6] A. J. Ayer advocated this idea by challenging his readers to suggest a more compelling option. However, a reader with very different convictions could respond that he simply doesn’t feel the need to accept or to opt for anything of the kind... In effect, the thesis that the principle is a proposal appears to be ad hoc. It goes against the Wittgensteinian assumption that what we are doing is just to expose the already given intuitions underlying our natural language, the general principles embedded in it. Hence, to impose on our language a methodological rule that does not belong to it would be arbitrary and misleading as a means of clarifying meaning.[7]
   My suggestion is simply to keep Wittgenstein’s original insight, according to which a principle of verifiability is nothing but a very general grammatical sentence stating the way our factual language must work to provide cognitive content with truth-value. Once we understand that the principle should make explicit our pre-existing linguistic dispositions, we are entitled to think that it must be seen as an analytic-conceptual principle. More precisely, this principle would consist in the affirmation of a synonymy between the expressions ‘meaning as the cognitive content expressed by a declarative sentence’ and ‘the procedures (combinations of rules) by which we may establish the truth-value of this same cognitive content.’ Thus, taking X to be any declarative sentence, we can define the epistemic value (meaning) of X with the following analytic-conceptual sentence:

(Df.) Cognitive meaning of the declarative sentence X = the verifiability rule for X.

Against this, a critic can react by saying that this claim to analytical identity isn’t transparent. Moreover, if the principle of verifiability were analytic, it would be non-informative, its denial being incoherent. However, it appears that we can deny the principle: It seems possible that the meaning of the statement X isn’t a verifiability rule.
   My first reaction to this objection is to remember that an analytic sentence does not need to be transparent; it does not need to be immediately seen as necessarily true, and its negation does not need to be clearly seen as contradictory or incoherent. Assuming that mathematics is analytic, consider the case of the following sentence: ‘3,250 + (3 × 896) = 11,276 ÷ 2’. At first glance, this identity neither seems to be necessarily true nor does its negation seem incoherent; but a detailed presentation of the calculation shows that it must be the case. This can be seen as a hidden analytic truth, hard to grasp at first because of its derivative character and our inability to see its truth at first glance.
   There is even a thought-experiment to demonstrate this. We can imagine a person with a better grasp of arithmetic than ours. For a child, 2 + 3 = 5 can be analytically transparent, as it is for me. For me, 12 × 12 = 144 is also transparently analytic (or intuitively true), though not to a child who has just started to learn arithmetic. But 124 × 124 = 20,736 isn’t transparently analytic for me, although it may be so for a person with greater arithmetical skill. Indeed, a person with great arithmetical skill (as in the case of some savants) can see at a glance the truth of the identity ‘3,250 + (3 × 896) = 11,276 ÷ 2’. This means that the boundary line between transparent and derived or non-transparent analytic truths is moveable, depending on our cognitive capacities and to some extension affected by training. Thus, from a cognitively neutral point of view the two types are on the same level, since for God (the only epistemic subject able to see all truths at a glance) analytic truths would all be transparent.
   In searching for a better-supported answer, we could distinguish between transparent and non-transparent analytic-conceptual knowledge.[8] The sentences ‘A triangle has three sides’, ‘Red is not green’ and ‘Three is greater than two’ express transparent analytic knowledge, since these relations are self-evident and their negation clearly contradictory. But not all analytic sentences are so. Sentences about geometry such as the one stating the Pythagorean Theorem express (I assume) an analytic truth in Euclidean geometry, although it isn’t transparent for me. Non-transparent analytic knowledge is based on demonstrations whose premises are usually made up of transparent analytical knowledge, namely, intuitive analytical truths. Hence, this kind of knowledge is only clarifying, which can mislead us to think that it really is informative. It also seems very possible that the principle of verifiability is a non-transparent, hidden analytic statement.
   Against this suggestion, one could object that the principle of verifiability cannot be stated along the same lines as a mathematical or geometrical demonstration. After all, in the case of a proved theorem it is easy to retrace the path that leads to its demonstration; but there is no similar way to demonstrate the principle of verifiability.
   More plausibly, the key to an answer may be found if we compare the principle of verifiability with statements that at first glance do not seem to be either analytic or demonstrable. Close examination reveals that they are in fact only non-transparent analytic truths. A famous statement of this kind is the following:

The same surface cannot be simultaneously red all over and green all over (under the same conditions of observation).

   This statement isn’t analytically transparent. In fact, it has been regarded by logical positivists and even contemporary philosophers as a serious candidate for what might be called a synthetic a priori judgment (Bonjour 1998, p. 100 ff.). Nevertheless, I think it isn’t difficult to show that it is actually a hidden analytic statement. We begin to see this when we consider that it seems transparently analytic that (i) visible colors can occupy surfaces, (ii) different colors are things that cannot simultaneously occupy the same surface all over, and (iii) red and green are different colors. From this it seems to follow that the statement (iv) ‘The same surface cannot be both red and green all over’ must be true. Now, since (i), (ii) and (iii) are intuitively analytic, (iv) should be analytic too, even if not so intuitively. Here’s how a similar argument can be better formulated:

(1)  Two different things cannot occupy the same place all over at the same time.
(2)  A surface constitutes a place.
(3)  (1, 2) Two different things cannot occupy the same surface all over at the same time.
(4)  Colors are things that can occupy surfaces.
(5)  (3, 4) Two different colors cannot occupy the same surface all over at the same time.
(6)  Red and green are different colors.
(7)  (5,6) Red and green cannot occupy the same surface all over at the same time.

To most people, premises (1), (2), (4) and (6) can be clearly seen (preserving the intended context) as definitely analytical. Therefore, conclusion (7) must also be analytic, even if it does not appear to be so.
   The suggestion that I want to make is that the principle of verifiability is also a true, non-trivial and non-transparent analytic sentence, and its self-evident character may be demonstrated through an elucidation of its transparent assumptions in a way similar to that of the above argument. Here is my argument on how to make it plausible:

(1)  Semantic-cognitive rules are criterial rules applicable to objective criterial configurations or configurations of s-properties.
(2)  Cognitive (descriptive, representational, factual…) meanings (or contents) of statements are constituted by combinations of (referential) semantic-cognitive rules applicable to arrangements of s-properties called facts.
(3)  The cognitive meanings of statements depend on ways of determining their truth by means of facts.
(4)  (1, 2, 3) The truth-determination of cognitive meanings of statements lies in the effective application of their combinations of semantic-cognitive criterial rules to the arrangements of s-properties called facts.
(5)  Combinations of semantic-cognitive criterial rules determining the truth of statements by their effective application to facts constitute what we have decided to call their verifiability rules (Df).
(6)  (4, 5) The cognitive meanings or contents of statements consist in their verifiability rules.

 For me, at least, premises (1), (2), (3), and (5) (which is definitional) sound clearly analytic, although not the conclusion (6). I admit that my view of these premises as analytic derives from a background of assumptions gradually reached in the earlier chapters of this book: it is analytically clear to me that contents, meanings or senses are constituted by the application of rules or combinations of rules; and it is also analytically clear to me that the relevant rules are semantic-cognitive rules that can combine to form cognitive meanings or contents of statements, with the result that once they are satisfied by the adequate criterial configurations formed by arrangements of s-properties called facts, they allow us to see them as effectively applicable, that is, as able to have a verifying fact as their referent. These semantic-criterial combinations of rules, when judged as effectively applicable, are called true, otherwise they are called false. And these semantic-criterial combinations of rules can be also called s-thoughts, thought-contents, propositional contents or simply verifiability rules.
   Some philosophers of language would still vehemently disagree, saying that they have different intuitions originated from a different parti pris. But since I cannot extend this argument further, I prefer to avoid discussion, invoking as excuse the words of Hákim de Merv: ‘Their impurities forbid them to recognize the splendor of truth.’[9]

5. Objection 2: A formalist illusion
Logic can be illuminating but also delusive. An example is offered by A. J. Ayer’s attempt to formulate a precise version of the principle of verifiability in the form of a criterion of factual meaningfulness. In his first attempt to develop this kind of verifiability principle, he suggested that:

…it is the mark of a genuine factual proposition… that some experiential propositions can be deduced from it in conjunction with certain other premises without being deducible from these other premises alone. (Ayer 1952, pp. 38-39)

Soon, unfortunately, it was noted that this criterion of verifiability was faulty. As Ayer later recognized, his formulation was ‘too liberal, allowing meaning to any statement whatsoever.’ (Ayer 1952, p. 11)[10] Why? Suppose that S is the senseless sentence ‘The absolute is lazy’. Conjoining it with the auxiliary premise ‘If the absolute is lazy, then snow is white’, we can – considering that the observation that snow is white is true and that this truth cannot be derived from the auxiliary premise alone – verify the laziness of the absolute.
   Now, the core problem with Ayer’s suggestion (which has not been solved by his attempt to remedy it) is this: In order to derive the observation that snow is white, he assumes that an indicative sentence (which he mistakenly called a ‘proposition’) whose meaningfulness is questioned is already able to attain some truth-value. But meaningless sentences cannot attain any truth-value; and if a sentence has a truth-value, then it must also have a meaning, it must also express a thought-content, a proposition. By assuming a truth-value for a sentence under consideration, Ayer’s principle simply does not allow the empirical statement to reveal if it has a proper way of verification or, if it has one, to show what this way is.
   Indeed, we cannot imagine any way to give a truth-value to the sentence ‘The absolute is lazy’, even a false one, simply because it is a grammatically correct but epistemically senseless word combination. As a consequence, the sentence ‘If the absolute is lazy, then snow is white’ cannot imply that the conclusion ‘Snow is white’ is true in conjunction with the sentence ‘The absolute is lazy’. Suppose we replace ‘The absolute is lazy’ with the symbols @#$, producing the conjunction ‘@#$ & (@#$  Snow is white)’. We cannot apply a truth-table to show the result of this. Even if the sentence ‘Snow is white’ is a meaningful sentence, we cannot say that this formula allows us to derive the truth of ‘Snow is white’ from ‘The absolute is lazy’, because @#$, being a senseless combination of signs, cannot even be false in order to imply the truth of ‘Snow is white’. My conclusion is that Ayer’s solution begs the question regarding the verifiability principle, since it works as if sentences like ‘The absolute is lazy’ had the status of meaningful sentences before he applies his criterion to them.[11]
   I can develop my point further by giving a contrasting suggestion as a criterion of meaningfulness, more akin to Wittgenstein’s views. Consider the sentence ‘This piece of metal is magnetized.’ Question: Does the sentence ‘This piece of metal is magnetized’ have any meaning? This question suggests a verifiability procedure. Suppose an affirmative answer results from the application of the following verification procedure that naturally follows (flows) from the statement ‘This piece of metal is magnetized’ and some additional information. Here it goes:

(1)  This is a piece of metal (observational sentence).
(2)   If a piece of metal is magnetized, it will attract other objects made of iron (criterion for being magnetized),
(3)  This piece of metal has attracted iron coins, which remained stuck to it (observational application of the criterion).
(4)  (From 1 to 3): It is (certainly) true that this piece of metal is magnetized.
(5)  If we have a reliable procedure to show the truth of an empirical statement, then the sentence has cognitive meaning (a principle of verification).
(6)  The procedure bringing us from (1) to (4) is reliable.
(7)  (From 4 to 6): The sentence ‘This piece of metal is magnetized’ is epistemically meaningful.

Notice that here the verifying procedure follows naturally from the sentence that we intend to verify, giving the conditions for its verification. However, in the case of senseless sentences like ‘The absolute is lazy’ or ‘The nothing nothings’, we can find no verification procedure following naturally from them, and this is the real sign of their lack of cognitive content. Also Ayer’s statement ‘If the absolute is lazy, then snow is white’ does not follow naturally from the sentence ‘The absolute is lazy.’ In other words: the many ways of verification of a statement, themselves consisting in other statements, contribute, in different measures, to make it fully meaningful; but they contribute by building its epistemic sense and not by being arbitrarily attached to it, as we saw in Ayer’s proposal. They must be given to us intuitively as the declarative sentence’s proper way of verification. The lack of any consideration of the ways of verification built into the declarative sentence is the central fault in Ayer’s criterion.

6. Objection 3: Verificational holism
A sophisticated objection to semantic verificationism is found in W. V-O. Quine’s generalization of Duheim’s thesis, according to which it is impossible to confirm a scientific hypothesis in isolation, that is, apart from the assumptions constitutive of the theory to which it belongs. In Quine’s compressed sentence: ‘our statements about the external world face the tribunal of sense experience not individually but only as a corporate body.’ (Quine, 1951 p. 9)[12] The result is Quine’s semantic holism: our language forms a so interdependent network of meanings that it cannot be divided up into verifiability procedures explicative of the meaning of any isolated statement. The implication for semantic verificationism is clear: since what is verified must be our whole system of statements and not any statement alone, it makes no sense to think that each statement has an intrinsic verifiability rule that can be identified with a particular cognitive meaning. If two statements S1 and S2 can only be verified together with the system composed by {S1, S2, S3Sn}, their verification must always be the same, and if the verifying rule is the meaning, all the statements should have the same meaning, which is so absurd that it leaves room for skepticism, if not about meaning, as Quine would like, at least about his own argument.
   In my view, if taken on a sufficiently abstract level, on which the concrete spatio-temporal confrontations with reality to be made by each statement are left out of consideration, the idea that the verification of any statement in some way depends on the verification of a whole system of statements – or, more plausibly, of a whole molecular sub-system – is very plausible. This is what I call abstract or formal confirmational holism, and this is what can be meant in Quine’s statement. However, his conclusion, according to which the admission of structural holism destroys semantic verificationism, does not follow. It requires admitting that structural holism implies what could be called a concrete or performative verificational holism, i.e., a holism regarding the concrete spatio-temporal verification procedures of individual statements, which are constitutive of the cognitive meaning. But this just never happens.
   Putting things in a somewhat different way: Quine’s holism has its seeds in the fact, well known by philosophers of science, that in order to be true the verification of an observational statement always depends on the truth of an undetermined quantity of assumed auxiliary hypotheses and background knowledge. Considered in abstraction from what we really do when we verify a statement, at least some form of molecularism is true: verifications are interdependent. After all, our beliefs regarding any domain of knowledge are more or less interdependent, building a complex network. But it is a different matter if we claim that from formal or abstract confirmational holism, a procedural or verificational holism follows on a more concrete level. Quine’s thesis is fallacious because, although in the end a system of statements really needs to confront reality as a whole, its individual statements do not confront reality, either conjunctively or simultaneously.
   I can clarify what I mean with the help of a well-known example. We all know that by telescopic observation Galileo discovered the truth of the statement: (i) ‘The planet Jupiter has at least four moons’. He verified this by seeing and drawing, day after day, four luminous points near Jupiter, and observing that these points were constantly changing their locations in a way that seemed to keep them close to the planet, crossing it, moving away and then approaching it again, repeating these same movements in a regular way. His obvious conclusion was that these luminous points could be nothing other than moons orbiting the planet. His contemporaries, however, were suspicious of the results of his telescopic observation. How could two lenses magnify images without deforming them? Some even refused to look: the device could be bewitched… Philosophers of science today have realized that Galileo’s contemporaries were not as scientifically naive as it often seems to us.[13] As was noted (Salmon 2002, p. 260), one reason for accepting the truth of the statement ‘Jupiter has four moons’ is the assumption that the telescope is a reliable instrument. But the reliability of telescopes was not sufficiently confirmed at that time. To improve the telescope as he did, Galileo certainly knew the law of telescopic magnification, whereby its power of magnification results from the focal length of the telescope divided by the focal length of the eyepiece. But in order to guarantee this auxiliary assumption, one would need to prove it using the laws of optics, still unknown when Galileo constructed his telescope. Consider, for instance, the fundamental law of refraction, whereby n1·senθ1= n2·senθ2. This law was established by Snell in 1626, while Galileo’s telescopic observations were made in 1610. With this addition, we can state in an abbreviated form the formal procedure of confirmation as it is known today and which I claim was unwittingly confused by Quine with the concrete verification procedure. Here it is:

      (I) 
1.  Repeated telescopic observation of four points of light orbiting Jupiter.
2.  Law of magnification of telescopes.
3. Snell’s law: n1·senθ1= n2·senθ2.
4. A telescope cannot be bewitched.
5. Jupiter is a planet.
6. The earth is a planet.
7. The earth is orbited by a moon.
8. (all other auxiliary and background hypotheses...)
9. Conclusion: the planet Jupiter has at least four moons.

Even if Galileo did not have knowledge of premise 3, this only weakens the inductive argument, which was still strong enough to his lucid mind. From a Quinean verificationist holism, the conclusion, considering all the other constitutive assumptions, would be that statement 9 does not have a verification method, since it depends not only on observation 1, but also on the laws expressed in premises 2 and 3, well-known premises from 4 to 7, and an undetermined number of other premises constitutive of our system of beliefs, all of them having their own verifiability procedures. As he wrote: ‘our statements should face the tribunal of experience as a corporate body’. Indeed.
    In this example, the problem with Quine’s reasoning becomes clear. First, we need to note that the premises belonging to confirmation procedure (I) are not simultaneously checked. The conclusion expressed by statement 9 was actually verified only as a direct consequence of statement 1, resulting from the daily drawings made by Galileo of his observations of variations in the positions of the four ‘points of light’ aligned around Jupiter. However, Galileo did not simultaneously verify statement 2 when he made these observations, nor the remaining ones. In fact, as he inferred conclusion 9 from premise 1, he only assumed a previous verification of premises like 2, which he verified as he learned how to build a telescope. Although he didn’t have premise 3 as a presupposition, he had already verified or assumed as verified premises 2, 4, 5, 6, 7… Now, because the verifications of 2 to 7… are already presupposed in the verification of 9, it becomes clear that these verifications are independent of the verification of 9 by means of 1. The true form of Galileo’s concrete verification procedure was much simpler than the abstract (holistic or molecularist) procedure of confirmation presented above. It was:

1. Repeated telescopic observation of four points of light orbiting Jupiter.
2. Conclusion: the planet Jupiter has at least four moons.

Generalizing: If we call the statement to be verified S, and the statements of the observational and auxiliary hypotheses O and A respectively, the structure of the concrete verifiability procedure of S is not

     O
     A1 & A2… & An
     S

But simply:

     O
     (Assuming the prior verification of A1 & A2... & An)
     S

This assumption of an anterior verification of auxiliary hypotheses in a way that may hierarchically presuppose that sufficient background knowledge is what in fact makes all the difference, as it allows us to separate the verifiability procedure of S from the verifiability procedures of the involved auxiliary hypotheses and the many background beliefs which are already assumed to have been successfully verified.
   The conclusion is that we can now clearly distinguish what verifies each auxiliary hypothesis. For example: the telescope’s law of magnification can be verified by very simple empirical measurements; and the law of refraction has been established based on empirical measurements of the relationship between variations in the angle of incidence of light and the density of the medium. Thus, while it is true that on a formal, abstract level a statement’s verification depends on the verification of other statements of a system, on the level of its proper cognitive and practical procedures the verification of auxiliary statements is already assumed, which allows us to isolate the verifiability procedure proper of our statement as what is actually being verified, identifying it with what we mean with the statement, with its true cognitive meaning.
   In the same way, we are able to distinguish the specific modes of verification of each distinctive auxiliary or background statement whose truth is assumed as verified before employing the verification procedure that leads us to accept S as true. This allows us to distinguish and identify the concrete procedure whereby each statement of our system is cognitively verified, making the truth of formal or structural holism irrelevant to the performative structure of semantic verificationism.
   By considering all that is formally involved in confirmation, and by simultaneously disregarding the difference between what is presupposed and what is performed in the concrete spatio-temporal verification procedures, Quine’s argument gives us the illusory impression that verification as such should be a holistic procedure. This seems to imply that the meaning of the statement cannot be identified with a verifiability procedure, since the meanings of statements are diverse and differentiated, while the holistic confrontation of a system of beliefs with reality is unique and as such undifferentiated.
   Finally, if we remember that each different statement must have a meaning of its own, it again becomes perfectly reasonable to identify the cognitive meaning of a statement with its verifying rule. For both the verifying rule and the meaning are again individuated together as belonging to each statement, and not to the system of statements or beliefs assumed in the verification. If true, this would be good regarding the form of confirmation and bad regarding the meaning, since it would dissolve all meanings into one big, meaningless mush.
   The inescapable conclusion is that Quine’s verificational holism is false. It is false because the mere admission of formal holism, i.e., of the fact that statements are always in some measure inferentially intertwined with each other is not sufficient to lead us to conclude that the verifiability rules belonging to these statements cannot be identified with their meanings, because these rules cannot be isolated from the others. Finally, one should not forget that in my example I gave only one way of verification for the statement ‘The planet Jupiter has at least four moons’. Other ways of verification can be added, also belonging to the meaning and enriching it.
    Summarizing my argument: an examination of what happens when a particular statement is verified shows us that even assuming formal holism (which I think is generally correct at least in the form of a molecularism of linguistic practices), the rules of verifiability are distinguishable from each other in the same measure as the meanings of the corresponding statements – a conclusion that only reaffirms the expected correlation between the cognitive meaning or content of a statement and its method of verification.

7. Objection 4: The existential-universal asymmetry
The next objection is that the principle of verifiability only applies conclusively to existential sentences, but not to universal ones. To verify an existential sentence such as ‘At least one piece of copper expands when heated’, we need only observe a piece of copper that expands when heated. To conclusively verify a universal claim like ‘All pieces of copper expand when heated’ we would need to observe all the pieces of copper in the entire universe, including its future and past, which is impossible. It is a truth that absolute universality is a fiction and that, when we talk about universal statements, we are always considering some limited domain of entities. But even in this case the problem remains. In the case of metal expanding when heated, for instance, the domain of application tends to be much broader than anything we can effectively observe, making conclusive verification practically impossible. Therefore – mainly because scientific laws usually take the form of universal statements – some would ask whether it wouldn’t be better to admit that the epistemic sense of universal statements is composed of falsifiability rules instead of verifiability rules. Wouldn’t this be the correct answer? (See Hempel 1959)
   Well, I don’t think so. We can, for example, falsify the statement ‘All ravens are black’ simply by finding a single white raven. In this case we verify the statement ‘This raven is white’. In this way we see that the verifiability rule of this last statement is such that, if applied, it falsifies the statement ‘All ravens are black’. But if the meaning of the utterance may be a falsification rule, a rule able to falsify it, and the verifiability rule of the utterance ‘That raven is white’ is the same rule that when applied falsifies the statement ‘All ravens are black’, then it seems that we should admit that the statement ‘All ravens are black’ is synonymous with ‘That raven is white’ (or that the latter expresses at least part of the meaning of the former). However, this would be absurd: the meaning of ‘This raven is white’ has almost nothing to do with the meaning of ‘All ravens are black’, insofar as their verifiability rules have almost nothing to do with each other.
   The real problem, as already noted, is that there seems to be no rule of falsifiability for a statement, as there certainly is no counter-assertive force (a force proper to negative judgments, as was once believed), no rule of de-identification of a name, and no rule for the de-ascription or de-application of a predicate. This is because what satisfies a rule is a criterion and not its absence, even when the criterion is the absence of something normally expected, as in the case of a hole when someone says: ‘Your shirt has a hole in it’.[14]
   It seems, therefore, that we must admit that the cognitive meaning of a statement can only be its verifiability rule. But in this case it seems inevitable to return to the problem of the inconclusivity of the verification of universal propositions, leading us to the admission of a ‘weak’ form of verificationism (Ayer 1952, p. 37). However, according to my reading of Wittgenstein, this does not seem to be the right path to reaching an answer. My suggestion is that the inconclusivity objection is simply faulty, since it emerges from a wrong understanding of the true logical form of universal statements; a brief examination shows that these statements are in fact both probabilistic and conclusive. Consider again the statement:

Copper expands when heated.

It is clear that its true logical form is not, as it seems:

I state that it is absolutely certain that all pieces of copper expand when heated,

where ‘absolutely certain’ means ‘without possibility of error’. This form would be suitable for formal truths such as

I state that it is absolutely certain that 2 + 3 = 5,

because here there can be no error (except procedural error, which we are leaving out of consideration). However, this form is not suitable for empirical truths, since we cannot be absolutely sure about their truth. The logical form of what we mean with statement (1) is a different one. This form is that of practical certainty, which can be expressed by

I affirm that it is practically certain that every piece of copper expands when heated,

where ‘practically certain’ means ‘with a probability that appears to be sufficiently high to disregard the possibility of error’. In fact, we couldn’t rationally mean anything different from this. Now, if we accept this paraphrase, a statement such as ‘copper expands when heated’ becomes conclusively verifiable, because we can clearly find inductive evidence protected by theoretical reasons that become so conclusive that we can be practically certain, namely, that we can assign a very high probability to the truth of the statement that all pieces of copper expand when heated. In short: the logical form of an empirical universal utterance, assuming a domain of application, is not that of a universal statement like ‘├ All S are P’, but usually:

    I affirm that it is practically certain that all S are P.

Or (using the Fregean sign of assertion):

    ├ It is practically certain that all S are P.

The objection of asymmetry was based on the assimilation of the logical form of formal universal statements in the logical form of empirical universal statements. The empirical universal statement is shown to be conclusively verifiable, since what it claims is nothing but sufficiently high probability. Hence, the cognitive meaning of an empirical universal statement can still be seen as its verifiability rule. Verification allows judgment; judgment must be treated as conclusive; verification too.

8. Objection 5: Arbitrary indirectness
Another common objection is that the rule of verifiability of statements with empirical content requires taking as a starting point at least the direct observation of possibly inter-subjective states of affairs. However, many statements do not depend on direct observation to be true, as is the case with ‘The mass of an electron is 9.109 x 10 kg raised to the thirty-first negative power’. Cases like this force us to admit that many verifiability rules are indirect. As has been noted, if we don’t accept this, we will be driven to a grotesque form of instrumentalism, in which what is real must be reduced to what can be inter-subjectively observed and in which things like electrons and their masses do not exist anymore. But if we accept this – admitting that many verifiability rules are indirect – how do we decide what the direct and indirect observations are? Is this not one of those desperately confusing distinctions? (Lycan, 2000, p. 121 f.)
   Here again, problems only emerge if we embark in the narrow formalist canoe of logical positivism and, paddling straight away, trample on natural language with inappropriate requirements. Our assertive sentences are uttered or thought of in linguistic practices, circumstances, language games, speech acts. The verification procedure must be adapted to the linguistic practice in which the statement is uttered. Consequently, the criterion to distinguish direct observation from indirect observation should always be relative to the linguistic practice that we take as a model. We can be misled by the fact that the most common linguistic practices are (a): our linguistic practices of everyday direct observational verification. The standard conditions defining these practices are:

Virtually interpersonal observation by observers under normal internal conditions and with unbiased senses of solid, opaque and medium sized objects, which are close enough and under adequate lighting…

This is how the presence of my laptop, my table and my chair are typically checked. For being the most usual form of observation, this practice is seen as the first candidate for the title of direct observation, to be contrasted with, say, indirect observation through perceptually accessible secondary criteria like use of mirrors, optical instruments, etc. However, it may be an unfortunate mistake that we tend to use model (a) to evaluate what happens in other, sometimes very different, linguistic practices. Let us consider some of them.
   I begin with (b): the bacteriologist’s linguistic practice. Usually the bacteriologist is concerned with the description of the microorganisms visible under his microscope. In this practice, seeing a bacterium under a microscope is called by him a direct observation and set as the model for verification. But the bacteriologist can also say, for example, that he has verified the presence of a virus indirectly, due to changes he found in the form of the cells he saw under a microscope, even though viruses are for him not directly observable except under an electron microscope that he does not possess. Nobody would say that a bacteriologist’s checks are all indirect, unless when having in mind a comparison with our everyday linguistic practices (a). This would be unusual, though possible. In any case, the context can show clearly what the speaker has in mind.
   Let us consider now (c) the linguistic practice of paleontology. The discovery of fossils is seen here as a direct way to verify the real existence of extinct prehistoric creatures in the remote past, since live observation is impossible (unless we had a time machine, which seems something impossible). But the paleontologist can also speak of indirect verification by comparison and contrast within his practice. So, consider the suggestion that hominids once lived in a certain place based only on damage caused by stone tools to the fossil bones of animals that early hominids once killed. This finding may be regarded as resulting from an indirect verification in paleontological practice, in contrast to the finding of fossilized remains of early hominids, which would be considered the direct form of verification. Of course, here again any of these verifications will be considered indirect when compared with verification produced by the most common linguistic practice of everyday life, that is (a). However, the context will readily show what kind of comparison we have in mind; a problem would arise only when the language used raises doubts about the model of comparison being used.
   If the practice is (d) of pointing to linguistically describable feelings, the verification of a sentence will be called direct when made by the speaker himself, albeit subjective, while the determination of feelings by a third person, based on behavior or verbal testimony, will generally be taken (by non-behaviorists and those who have read my objections to the private-language argument) as indirect. There isn’t any easy way to compare practice (d) with the everyday practice (a) of observing medium-sized physical objects in order to say what is more direct, since they belong to very different domains of verification.
   The conclusion is that there is no real difficulty in distinguishing between direct and indirect verification, insofar as we have clarity about the linguistic practice with which the verification is being made, that is, about the model of comparison we have chosen. Contrasted with philosophers, speakers share the contextually bounded linguistic assumptions needed for the applicability and truth-making of verifiability rules. To become capable of reaching agreement on whether an observation/verification is direct or indirect, they merely need to be aware of the contextually established model of comparison. 

9. Objection 6: Empirical counterexamples
Another kind of objection relates to statements that seem to have meaning, but lack any apparent verifiability rule. In my judgment, this type of objection demands consideration on a case-by-case basis.
   Consider, to begin with, the statement ‘John was courageous,’ in circumstances in which John died without having had any opportunity to demonstrate courage, say, shortly after birth (see Dummett 1978, p. 148 f.). If we add the stipulation that the only way to verify that John was courageous would be by observing his behavior, the verification of this statement becomes practically impossible. Therefore, in accordance with the verifiability principle, this statement has no cognitive meaning. However, it seems to be not only grammatically meaningful.
   The solution is that in the circumstances portrayed, the statement ‘John was courageous’ only appears to have meaning. It belongs to the set of statements whose cognitive meaning is only apparent. Although the sentence has an obvious grammatical sense, given by the combination of a non-empty name with a predicate, we are left without any criterion for the application or non-application of the predicate. Thus, such a statement has no function in language and is not able to tell us anything. It is part of a set of statements such as ‘The universe doubled in size last night’ and ‘My brother died the day after tomorrow’, ‘Saturday is in bed…’  Although these statements appear to make some sense, what they possess is only the expressive force of suggesting images in our minds. But they are devoid of cognitive meaning, since we cannot test or verify them.
   Wittgenstein considered a parallel case in his work On Certainty. Consider the statement ‘You are in front of me right now,’ said by someone under normal circumstances to a person standing before him. He notes that this statement just seems to make sense, given that we are able to imagine situations in which it would have some use, for example, when a room is completely dark, so that it is hard for one person to identify another (Wittgenstein 1984a, sec. 10). John’s case is similar. We are inclined to imagine counterfactual situations in which he would or wouldn’t have demonstrated courage, and we could think of them as possible situations. This invites us to project them into the situation and get the mistaken impression that the statement has a workable epistemic sense. Finally, we should not forget that what is contextually assumed as truth conditions affects the semantic status of the statement by affecting its verifiability conditions.
   What can we say of statements about the past or the future? Here too, it is necessary to examine them on a case by case basis. Suppose that someone says: ‘Java man lived about 1.8 million years ago’. This statement was fully verified by a fossilized skull and a reliable carbon dating procedure. The direct verification of past events in the same way that we observe present events is practically and probably physically impossible, but it is not part of the verifiability rule, whose application warrants the truth of the statement on the basis of a standard adopted in practice (a). Here direct verification is made on the basis of verifiable empirical traces let by past events.
   There are other, more indirect verifications of past events. The sentence ‘Neptune existed before it was discovered’ can be accepted as certainly true. Why? Because our knowledge of physical laws (which we trust as sufficiently verified) combined with data about the origins of our solar system allow us to conclude that Neptune certainly existed a long time before it was discovered, and this inferential procedure is suitable for verification.
   Very different is the case of statements about the past such as:

1. On that rock an eagle landed exactly ten-thousand years ago.
2. Napoleon sneezed more than 50 times while he was in Russia.
3. The number of human beings alive exactly 2,000 years ago was odd.

For such supposed thought-contents there is no empirical means of verification. Here we must turn to the old distinction between practical, physical and logical verifiability. Such verifications are not practically achiev­able, and as far as I know, they are not even physically realizable (it seems rather improbable that we can ever visit the past in a time-machine or through a worm-hole in space). The possibility of verification of such statements seems to be only logical. But it is hard to admit that an empirical statement whose verifiability is only logical can be considered as having a useful cognitive sense.
   To explain this point better: it seems to me that the distinction between logical, physical and practical verifiability influences meaning according to the respective fields of verifiability to which the statements in question belong. Statements belonging to a formal field need only be logically verifiable to be fully meaningful: ‘A → B’, for instance, is verified by the truth-table for material implication, which says that it is false only when A is true and B is false. But statements belonging to the empirical field (physical and practical) must be not only logically, but also at least empirically verifiable in order to really have cognitive meaning. As a consequence, an empirical statement that is only logically verifiable must be devoid of cognitive meaning. Here, if empirical verification is inconceiv­able, as it seems to be in cases (1), (2) and (3), the conclusion is that such statements, though having grammatical and logical meaning and invoking images in our minds, lack any relevant cognitive meaning, for we don't know what to make of them. Such statements aren’t able to perform the specific function of an empirical statement, which is to truly represent an actual state of affairs. We do not even know how to begin the construction of their verifiability rules; this is why they lack cognitive meaning; and this is why we do not need to abandon realism because of them.
   Something similar can be said of statements about the future, with the difference that here direct verification is in many cases physically possible. Consider the sentence (i) ‘It will rain in this place seven days from now.’ When a person seriously says something of this sort, what she usually means is (ii) ‘[Probably] it will rain in Caicó seven days from now’. And this sentence is conclusively verifiable, albeit indirectly, by a weather forecast. Thus, we have a verifiability rule, a cognitive meaning, and this rule was already applied in a way that has given the speaker a real degree of probability. However, one could not affirm that it certainly will rain in seven days. Although there is a direct verifiability rule (to look at the sky for seven days), it has the disadvantage that we will only be able to apply if we wait out the seven days, and we will only be able to affirm its truth (or deny it) afterward the event. It is true that one could use this sentence in some situations, for example, when making a bet about the future. But in this case we would not affirm (i) from the start, since we cannot apply the rule in anticipation. In this case, what we mean with sentence (i) is in fact (iii) ‘[I bet that] it will rain in Caicó seven days from now.’
    A similar statement is (i) ‘The first baby to be born on Madeira Island in 2050 will be female,’ which has a verifiability rule that can only be applied in the future. This sentence lacks any practical sense, since we are unable to verify and really state it now. Nonetheless, in a proper context the sentence may have the meaning of (ii) ‘[We are guessing that] the first baby to be born…’ or (iii) ‘[It is possible that] the first baby to be born…’ In these cases, we are admitting that the sentence has a cognitive meaning, since all it says is that it has an observational verifiability rule that can be applied (or not) in the future. But as an affirmation of something that will be the case in the year 2050, this sentence has no cognitive meaning, for in order to be true this affirmation requires awareness of the effective applicability of the verifiability rule. When we consider what is really meant in statements regarding future occurrences, we see that even in these cases verifiability and meaning go together.
   Now consider now the statement: ‘In about eleven billion years the Sun will expand and engulf Mercury’. This statement in fact means ‘[Very probably] in about eleven billion years the Sun will expand and engulf Mercury’; this prediction can be inferentially verified today, based on what we know of the fate of other stars in the universe that resemble our Sun but are much older.
    We conclude that there is no general formula detailing the structure of any verifiability procedure. Sentences about the future can be physically and to some extent practically verifiable. They cannot make sense as warranted actual assertions, since such affirmations require possible verification in the present. Most of them are concealed probability statements. The kind of verifiability rule required varies with the utterance and its insertion in the linguistic practice in which it is made, showing what it can really mean. This may lead us to mistakenly believe that there are unverifiable statements with cognitive content.
   Finally, a word about ethical statements: Positivist philosophers have maintained that they are unverifiable, which has led some to adopt implausible emotivist theories. Once again we find the wrong attitude! I would suggest that ethical statements are scarcely verifiable, like metaphysical statements and indeed like most philosophical statements. They aren’t decisively verifiable because we are still unable to state them in adequate ways, making them sufficiently precise, since we lack consensual agreement regarding the adequate verifiability rules about these matters. Anyway, I can give an imaginary example. Consider the utilitarian principle: ‘The morally correct action is that action that brings more happiness to all’ applied to a chosen community of individuals. Try to view this principle in the most general and flexible way.[15] If the application of this principle increases community well-being, this counts towards its verification.

10. Objection 7: Formal counterexamples
It is possible to extend the application of the verificationist thesis to the formal statements of logic, mathematics and geometry. In this case, the verifiability rules or procedures (combinations of rules) that demonstrate their formal truth add cognitive content deductively within the formal system in which they are considered. A fundamental difference with respect to empirical verification is that in the case of formal verification, to have a verifiability rule is the same as being able to effectively apply it, since the criteria to be ultimately satisfied are the own axioms already assumed as such by the system.
   A much discussed counterexample is Goldbach’s conjecture. This conjecture is usually stated as:

g = every even number greater than 2 can be expressed as the sum of two prime numbers.

The usual objection is that this conjecture has meaning even if we never manage to prove it, and even if the procedure for formal verification of g has not yet been found. Hence, its significance cannot be equated with a verifiability rule.
   The answer to this argument is too simple and stems from the perception that Goldbach’s conjecture is nothing more than a mere conjecture. Well, what is a conjecture? It’s not an affirmation, a proven theorem, but rather the recognition that a thought-content has enough plausibility to be taken seriously. One would not make a conjecture if it seemed fundamentally improbable. Thus, the true form of Goldbach’s conjecture is:

It is plausible that g.

But ‘It is plausible that g’, i.e., ‘[I state that] it is plausible that g’, or (using the Fregean sign of assertion) ‘├It is plausible that g’, is something other than

 I state that g,

 or ‘├g’, which is what we would be allowed to say if we wanted to enunciate Goldbach’s proved theorem. If our case were to uphold the statement ‘I state that g’, namely, a statement of Goldbach’s theorem as something epistemically meaningful, the required verifiability rule would be the procedure for proving the theorem, and this we do not have; in this sense g is meaningless. However, the verifiability rule for ascribing mere plausibility is far less demanding than the verifiability rule able to demonstrate or prove g. This is the case of:

[I state that] it is plausible that g.

whereby the verifiability rule consists in something very different, namely, in a verification procedure able to suggest that g can be proved. Now this verification procedure, this rule does in fact exist. It consists simply in considering random examples, such as the numbers 4, 8, 12, 124, etc., and showing that they are always the sum of two prime numbers. This verifiability rule not only exists; it has been applied up until today without exception to every even natural number already considered! This is the reason why we really do have enough support for Goldbach’s conjecture: it was verified as a true conjecture. If an exception had been found, the conjecture would have been proved false, for this would be incompatible with the truth of ‘[I state that] it is plausible that g.’
   Thus, in itself the conjecture is verifiable and – as a conjecture – has been effectively verified: It is true that it is really plausible that g can be true. And this explains its cognitive meaningfulness. What remains beyond verification is the statement affirming the necessary truth of g. And indeed, this statement doesn’t really make sense; it has no cognitive content, since we still do not have a proof, a mathematical procedure to verify it. The error consists in the confusion of the statement of a mere conjecture, which is true, with the ‘statement’ of a theorem that does not exist.
   It should not be forgotten that Goldbach’s conjecture can be demonstrated to be both a true conjecture and a false one. It has been considered to be a true conjecture, because all examples considered until now have confirmed it. It will be proved false if someone finds a counterexample to which the rule expressed by g is inapplicable.
   A contrasting case is Fermat’s last theorem. Here is how this theorem is usually formulated:

 f = there are no three positive numbers x, y and z that satisfy the equation xⁿ + yⁿ = zⁿ if n is greater than 2.

This theorem had been only partially demonstrated up until 1995, when Andrew Wiles succeeded in making a full demonstration.  Now, someone could object here that even before Wiles’ demonstration f was already called ‘Fermat’s theorem’. Hence, it is obvious that a theorem can make sense even without being proved.
   There are, however, two confusions in this objection. The first is easy to spot. Of course, Fermat’s last theorem has a grammatical sense: it is syntactically correct. But it would be an obvious mistake to confuse the grammatical meaning of f with its cognitive meaning. An absurd identity, for example, ‘Napoleon is the number 7’, has a grammatical sense.
   The second confusion concerns the fact that the phrase ‘Fermat’s theorem’ isn’t appropriate at all. We equivocally call f a ‘theorem’ because before his death Fermat wrote that he had proved it, but couldn’t put this proof on paper, since the margins of his notebook were too narrow for this…[16] For these reasons we here have a misnamed opposite of ‘Goldbach’s theorem’. Although f was called a theorem, it was in fact only a conjecture of the form:

   [I state that] it is plausible that f.

It was a mere conjecture until Wiles demonstrated f, only then effectively making it a theorem. Hence, before 1995 the cognitive content that could be given to f was actually ‘[I state that] it is plausible that f’, a conjecture that was demonstrated by the fact that no one had ever found numbers x, y and z that could satisfy the equation. Indeed, the cognitive meaning of the real theorem f, better expressed as ‘I state that f’ or ‘├ f’ (which very few really know), should include the demonstration or verification found by Wiles, which is no more than the application of an extremely complicated combination of mathe­matical rules.
   Some would complain that if this is the case, then only very few people really know the cognitive meaning of Fermat’s last theorem. I agree with this: The cognitive content of this theorem is known by very few people indeed. What most of us know is only the poor conjecture.
   Finally, there are phrases like (i) ‘the lesser convergent series’. For Frege, this definite description has sense but not reference. We can add that there is a rule that allows us to always find series that are less convergent than any given one, making them potentially infinite. We can spell it as IS: ‘For any given convergent series, we can always obtain a less convergent one’. Since IS implies the truth of statement (ii) ‘There is no less convergent series’, we conclude that (i) has no referent. The definite description (i) has no referent because it is derived from statement (ii). Now, what is the identification rule of (i)? The conclusion is that the identification rule for (i) is shown to be threatened by the reasons given above. Then, what is the meaning of (i)? The answer is that it is given by the erroneous attempt to devise the series (i) ignoring IS. It is like the meaning of any mathematical falsity. For instance, 121 + 384 = 515 is false and its cognitive meaning (if we concede that it has something of the kind) is derived from a failed attempt to apply a verification rule, which rightly applied should give 505 as result and not 515. (As I said in the beginning, in formal sciences to find a verificational procedure is to prove the statement. So, a false formal identity cannot have a verifiability procedure that does not apply. So it seems to me that a false formal identity either has no sense or, if it has it, it is a sense derived from its comparison with the identity reached by the corresponding rightly applied verifiability procedure that confirms its falsity.)

11. Objection 7: Skepticism about rules
One could still say that Wittgenstein created a skeptical thought-experiment that endangers the possibility of an ongoing common interpretation of rules and, consequently, the idea that our language may work as a system of rules (Wittgenstein 1984c, sec. 185, 198, 201…). His skeptical thought-experiment was formulated with more imagination by Kripke, followed by his own attempted skeptical answer (Kripke 1982).
   Here I will limit myself to explaining Wittgenstein’s short argument and to my own non-skeptical answer to it, which can easily be extended to Kripke’s similar skeptical argument. Answering this riddle interests us here because if the argument were correct, it might imply that it would be a mistake to admit that verifiability rules are responsible for the cognitive meanings of sentences.
   Wittgenstein introduced his riddle through the following example. Let’s say that a person learns a rule to add 2 to the natural numbers. If you give her the number 6, she adds 2 and writes the number 8. If you give her the number 73, she adds 2, writing the number 75... But let’s say she is for the first time presented with a larger number, the number 1,000, and that she then writes the number 2,004. If you ask why she did this, she responds that she had understood that she should add 2 to 1,000, 4 to 2,000, 6 to 3,000, etc.
   What the example demonstrates is that a rule can always be interpreted differently from the way we intended it, for misunderstandings can always occur in the application of rules, no matter the number of specifications we give in our instructions. The consequence is that we cannot be assured that we will follow our rules in a similar way in the future, that we can, for instance, continue to coordinate our actions based on them. And as meaning depends upon following rules, we cannot be certain about the meanings of expressions we choose to use. How could we be certain, for instance, of the meaning of ‘add two’?
   In my view, neither Kripke nor Wittgenstein gives a satisfactory answer to the riddle. Both assume some non-solution of the Humean kind. Wittgenstein writes that following a rule is a practice and that we follow rules blindly. And Kripke suggests that we follow rules as a fact resulting from our social dispositions, suggesting that Wittgenstein realized that in our statements we follow rules of assertion without regard to truth-conditions... However, against this we could say that the simple fact that we have so far coordinated our practices according to rules does not imply that these co-ordinations need to be like that, and does not even imply that they should continue to be like that, which shows that the point in question remains insufficiently answered.
   For my part, I think that the ‘paradox’ wasn’t seen from the right, more banal perspective. The crucial point is that we learn rules in a similar way simply because we share a similar human nature that makes us interpret the rules that we are taught in a manner that is very similar, if not identical, and that we must also be naturally provided with mechanisms of correction able to reinforce agreement.
   One might ask: what guarantees this similarity of nature? The obvious answer is Darwinian, namely, that it results from a process of natural selection that has long harmonized our learning capacities, eliminating by natural selection those individuals endowed with very different dispositions to interpret the rules that we usually share. Similarity of human nature, combined with a common form of life, leads us to understand semantic rules in the shared ways in which we think we understand them. If we add to this the assumption that our human nature and recurring patterns in the world will not change in the future, we may be confident that people will not show unexpected variations in their interpretation of the semantic rules they are taught. Of course, underlying all this is Hume’s much more defiant criticism of induction, which is the hidden cause of uneasiness. But this is a further issue that goes beyond our present worries (for a tentative answer see the appendix of this chapter).
   Summarizing: The shared interpretation of our learnt rules just seems puzzling when we insist on ignoring the scientific implications of the theory of evolution, along with implicit Humean doubts about the assumption of a deep permanent order in the world. By ignoring or questioning these things, we tend to ask ourselves (as did Wittgenstein and Kripke) how it is possible that these rules are and continue to be interpreted and applied in a similar manner by other human beings. For the same reason, modern pre-Darwinian philosophers – from Leibniz to Fichte – were impressed by the fact that our minds are such that we are able to understand each other, appealing to the Creator as producing the necessary harmony between human minds in our understanding of things. The puzzle about interpreting how to follow a rule is generated by this same old perplexity reformulated under a new guise.

12. Defending analyticity
Since I am assuming the concept of analyticity, I wish to say a word in its defense before finishing. I am satisfied with the definition of an analytic proposition as the thought-content expressed by a statement whose truth derives from the combination of its constitutive unities of sense. This is certainly the most common and intuitively acceptable formulation. W. V-O. Quine would reject it because he finds that it is based on a too vague concept, namely, the concept of meaning. However, as some have noted, there is nothing too vague in the concept of meaning used in our definiens, except from Quine’s own scientistic-reductionist perspective, which tends to see vagueness as synonymous with a lack of precision (Grice & Strawson 1956, pp. 141-158; Swinburne 1975, pp. 225-243). Philosophy works with concepts such as meaning, truth, good, beauty, which are felt as inevitably vague, as much as the concepts used in countless attempts to define them. In my view, the effort to explain away such concepts only by reason of their vagueness betrays an impatient positivist and in the case also pragmatic disposition of mind.
   I will begin by summarizing Quine’s influential refutation of analyticity. Dissatisfied with the usual definition, he tried to define an analytical sentence in the Fregean way, as a sentence that is either tautological or can be shown to be tautological by replacing its non-logical terms with synonyms. So, the statement (i) ‘Bachelors are unmarried males’ is analytic because ‘bachelor’ is a synonym of the phrase ‘unmarried male’, which allows us by the substitution of synonyms to show that (i) means the same thing as (ii): ‘Unmarried males are unmarried’, which is a tautology. However, he finds the word ‘synonym’ not precise enough. What is a synonym? One answer would be that a synonym of an expression is another expression that can replace the first in all contexts salva veritate. This answer does not work, however, because a sentence such as ‘Bachelor has 8 letters’ cannot be replaced by ‘An unmarried male has 8 letters’… Moreover, phrases such as a ‘creature with a heart’ and a ‘creature with kidneys’ are also interchangeable salva veritate, since they have the same extension, though they are not synonyms… In a last attempt to define analyticity, Quine makes an interesting appeal to the modal notion of necessity: ‘Bachelors are unmarried males’ is analytic if and only if ‘Necessarily, bachelors are unmarried males’. But he thinks that the notion of necessity does not help here, for we define ‘necessary’ as what holds in all possible circumstances because… it is analytic. As Quine puts it, the argument to explain synonymy, though not flatly circular, ‘has the form, figuratively speaking, of a closed curve in space.’ (Quine 1951, p. 8)
   Quine’s argument is ingenious but arguably equivocal. The error in the argument rests on the false assumption that a word should be defined with the help of conceptual words that do not belong to its specific field. Thus, for Quine the word ‘analyticity’ should not be defined by means of words like ‘meaning’, ‘synonymy’, ‘necessity’… which he considers too approximate in meaning to allow for an adequate definition. However, when we consider the point more carefully, we see that the words belonging to a definiens are not excessively close in their meanings to the definiendum, simply because their proximity derives from the requirement that the terms of a definiens belong to the same semantic field of its definiendum. For example, in order to define a conceptual word from ornithology, we would not use concepts from quantum physics, and vice versa. These conceptual fields are too distant one from the other. For instance, we define an ‘arthropod’ as an invertebrate animal having an exoskeleton, all these terms being biological, which does not make this definition circular. Hence, it may be perfectly adequate to define analyticity using words like ‘meaning’, ‘synonymy’ and ‘necessity’, as Quine tries to do. To say that a proposition is necessary is (by definition) to say that it is true in all possible worlds. But to say that a proposition is analytical iff by means of the inter-substitution of its synonymous expressions in order to make it tautological it remains true in all possible worlds (real and non-real ones) is not the same thing as to say that the proposition is necessary.
   Besides this, if we (concerned with formal sciences) decide to identify any proposition, any thought-content with a verifiability rule, it seems that we should say that an analytic proposition is a verifiability rule that is self-verifying. Or, somewhat better: It seems that the combination of rules that constitutes the verifiability rule of an analytical statement verifies not by its application to the world, but by means of some kind of self-application. This suggestion, of course, demands a better explanation that I will try to give later when discussing the concept of truth.
   A complementary point sustained by Quine is that, contrary to what is usually maintained, he does not see any definite distinction between empirical and formal knowledge. What we regard as analytic sentences can always be falsified by greater changes in our more comprehensive system of beliefs. Even sentences of logic like the excluded middle can be rejected, as occurs in some interpretations of quantum physics…
   Regarding this complementary point, it seems to me that it would not be correct to say that an analytic proposition loses its truth as a result of new experiences. What occurs is that its domain of application can be restricted or even lost. For example: since the development of non-Euclidean geometries, the Pythagorean theorem has lost part of its theoretical applicability; and since the theory of relativity has proved that physical space is non-Euclidean, this theorem has lost its integral applicability to the physical world. However, this is not the same as to say that the Pythagorean Theorem has been in a literal sense falsified. This theorem remains perfectly true within the framework of Euclidean geometry, where we can prove it. We can prove it as a result of the assumption of the system of rules that constitutes this geometry. This is so even if its application of Euclidean geometry has been theoretically restricted with the rise of non-Euclidean geometries and even if it has lost its absolute application to real physical space after the development of general relativity theory. It is not the same when a theory belonging to an empirical science is falsified. In this case, the theory definitely loses its truth, since its truth depends directly on its empirical application. Newtonian gravitational theory was falsified by general relativity. The best we could say in its favor is that it has lost some of its truth and try to make this idea clear by appealing to multi-valued logic.

13. Conclusion
There is much more to be considered on these issues. I hope, however, that the few but central considerations that were offered here are sufficient to convince you that semantic verificationism, far from being a hopeless hypothesis, comes close to being rehabilitated when investigated with a methodology that does not overlook and therefore does not violate the subtle tissue of natural language.







[1] As the best reader of Wittgenstein at the time, Moritz Schlick, also wrote: ‘Stating the meaning of a sentence amounts to stating the rules according to which the sentence is to be used, and this is the same as stating the way in which it can be verified. The meaning of a proposition is the method of its verification.’ (Schlick 1938, p. 340)
[2] See, for contrast, Carnap’s definition of scientific philosophy as ‘the logic of science’ in his 1937, § 72.
[3] C. S. Peirce’s view of metaphysics coincides with what is today the most accepted one (see Loux 2001, ix). On Peirce’s verificationism see also Misak 1995, ch. 3. As I do, and following Peirce, Misak favors a liberalized form of verificationism, opposed to the narrow forms advocated by the Vienna Circle.
[4]  See my analysis of the form of the semantic-cognitive rules in chapter 3, sec. 12, and of the nature of consciousness in chapter 2, sec. 10.
[5] I believe that the germ of the verifiability principle is already present in aphorism 3.11 of the Tractatus Logico-Philosophicus under the title of ‘method of projection’. There he writes: ‘We use the perceptible sign of a sentence (spoken or written) as a projection of a possible state of affairs. The method of projection is the thinking of the sentence’s sense.’
[6] This position was supported by A. J. Ayer, Rudolf Carnap and Hans Reichenbach.
[7] Ayer’s view wasn’t shared by all positivists. Schlick, closer to Wittgenstein, defended the view that the principle is nothing but a simple statement of the way meaning is actually assigned to propositions, both in everyday life and in science.
[8] This distinction is inspired by Locke’s distinction between intuitive and demonstrative knowledge. I do not use Locke’s original distinction because, as is well known, he questionably applied it to non-analytical knowledge. (See Locke 1975, book IV, ch. II, § 7)
[9]  From J. L. Borges’ magnificent tale ‘El Tintorero Enmascarado Hákim de Merv’.
[10] This difficulty made him propose a more complicated solution that the logician Alonzo Church proved to be equally faulty (See Church 1949).

[11] C. G. Hempel (in Ayer ed. 1959, p. 112) noted that a sentence of the form ‘S v N’, in which S is meaningful, but not N, must be verifiable, in this way making the whole disjunction meaningful. The problem here is similar. The form of this statement is S v @#$. We cannot apply a truth-table to this. Here only the verifiable S has meaning and allows verification, not the whole disjunction, because as such it is incomprehensible, not to say nonsensical.

[12] Later Quine corrected this thesis, advocating a verificational molecularism restricted to sub-systems of language, since language has very different domains. However, our counter-argument will apply to both cases.
[13] I believe that Galileo’s judges unwittingly did a great favor to science by sentencing him to house arrest, leaving him with nothing to do other than concentrate his last intellectual energies on writing his magnificent work: Il Mecanique Celleste.
[14]  Michael Dummett viewed the falsification rule as the ability to recognize under what conditions a proposition is false. But this must be the same as the ability to recognize that the proposition isn’t true, namely, that its verifiability rule isn’t applicable, which presupposes that we know its criteria of applicability. (See Dummett 1996, p. 62 ff.)
[15] My preferred moral view is two-tiered utilitarianism. According to this position, we apply rule-utilitarianism in ordinary situations, but in extreme situations utilitarian rules are derogated and we must turn to act-utilitarianism. (See Hare 1981, ch. 2)
[16] Now we know that Fermat couldn’t have written this seriously, since the mathematics of his time did not provide the means to prove his conjecture.