terça-feira, 31 de janeiro de 2017

### AN EXTRAVAGANT READING OF FREGEAN SEMANTICS (3) (Nature of reference)

Corrected draft for the book Philosophical Semantics to be published by Cambridge Scholars Publishing in 2017 



19. The reference of a sentence as its truth-value
Now we will leave these speculative excurses and come back to the more tangible Fregean semantics, considering what he has to say about the reference of the sentence (Satz). Here I have no compliment. Frege was the author of the unsane idea that the references of sentences are their truth-values, and the thoughts expressed by them are modes of presentation of truth-values. How did he reach this strange conclusion? There are several reasons. First, sentences are independent, saturated, closed; they work as names, and their truth-value is also closed, like the object referred to by a name. Second, he says that the search for truth is what brings us from sense to reference. Third, he notes that sentences without reference lack truth-value: ‘Vulcan is a warm planet’ has no reference and for him no truth-value, as this hypothetical planet has never been discovered. Fourth, he also noted that according to the principle of compositionality the reference must be what remains unchanged after we change the senses of a sentence’s components without changing their references. Now, this is what happens, for instance, if we replace ‘Napoleon lost the Battle of Waterloo’ with ‘Napoleon lost his last battle’; both sentences remain true. The references of the sentence-components do not change, and the reference of the whole sentence should likewise not change. The truth-value remains the same: the truth. Hence, the reference of these two sentences must be their truth-value. The conclusion of all this is that in extensional languages the references of sentences must be their truth-value (1892: 34). For Frege, all true sentences have only one reference, which is the abstract object The True (das Wahre), while all false sentences also have only one reference, which is the abstract object The False (das Falsche).
   Independently of this argument, interpreters have noted that Frege chose truth-value as the reference of sentences, because it is what gives them value for us, because of its Bedeutung in the sense of semantic relevance or meaningfulness (e.g., Tugendhat 1992b: 231).[1] Indeed, truth-value is of decisive importance for logic, because it is what must be preserved in valid arguments. The logician does not need to know more than truth-value regarding the referring function of the sentences he is dealing with in order to evaluate inferential possibilities.
   However, there are a number of well-known embarrassing objections to Frege’s identification of reference with truth-value that in my view completely disqualify the idea. The first one is that, contrary to healthy intuition, Frege’s proposal frontally contradicts the meaning we normally give to the word ‘reference’. It is intuitively obvious that the sentence ‘Napoleon was born on Corsica’ refers to something very different from the sentence ‘2 + 2 = 4’, even if both are true. Another objection is that we expect that the reference of the components of our sentences should belong to the same ontological level of the sentence’s references. But for a Fregean, this would not be the case: the reference of the name ‘Napoleon’ is the Napoleon of flesh and blood, while the reference of the sentence ‘Napoleon was born on Corsica’ must be the abstract object called The True. Moreover, one could also argue that his solution sounds false, because it in fact violates Frege’s own principle of compositionality, whereby the whole depends on its parts, so that a change in a part produces a change in the whole. If the reference of a sentence is its truth-value, it cannot be established by its parts, since the truth-value has no part. And even if it had, then all objects referred to by names in true sentences should be parts of The True. A further objection is that there are serious substitutability problems with Frege’s explanation of the references of sentences. If all true sentences refer to one object called ‘The True’, and the name ‘The True’ also refers to The True, then in the conditional sentence ‘If it rains, then water falls from the sky’, we can replace ‘it rains’ with ‘The True’. The result is the sentence ‘If The True, then water falls from the sky’, which should be true but is in fact unintelligible (Black 1954: 235-6). Finally, to make things still worse, a multitude of obviously false identities between true sentences should be true. For example, ‘Paris is a city = snow is white’ should be a true assertive composite sentence, since both partial sentences of it refer to the same thing: The True.
   The most charitable interpretation is that Frege uses the word ‘reference’ in a completely new, technical sense. The problem is that in spite of any theoretical advantage for the logician, this new way to use the word is gratuitous – What does it add to the plain admission that only truth-value and not how it was achieved is what counts for logical inference? Moreover, in philosophy this view can be – and in my judgment really has been – disastrously misleading from an epistemological standpoint, once we hold that truth has virtually nothing to do with anything that can reasonably be understood as the reference of our statements.

20. Structural status of facts
The Fregean account of the references of sentences as their truth-values turns out to be still less acceptable if we consider that a much more natural alternative is available, which, as Sir Anthony Kenny has noted, was not even mentioned by Frege (Kenny 2000: 133). Since it is more plausible that the references of sentences are facts, it is important to investigate the logical structure and ontological nature of facts.
   Concerning the logical structure of facts, the most plausible hypothesis is that they correspond to the logical structure of the thoughts representing them, assuming these thoughts are expressed in declarative sentences logically analyzable in accordance with appropriate contexts. Singular empirical statements such as ‘Plato has a beard’ and ‘The cat is on the mat’ respectively represent facts that should have the logical structure Fa and bRc. The elements ab and c, as particulars, refer to clusters of appropriate compresent tropes, while F and R would be also analyzed as tropes, usually forming complex configurations dependent upon the clusters. The links b-R-c and F-a, in turn, are only pseudo-relations, since the admission of their existence as relational tropes would generate one inevitable Bradleyan regress. Individuals and their tropes are linked by ‘non-relational ties’ without any ontological addition (Cf. appendix to chapter 3).
   We should also pay attention to the somewhat obvious rule of analysis according to which we should not accept singular terms as components of predicative expressions. Thus, for instance, in a sentence like ‘Stockholm is the capital of Sweden’ we should not take ‘…is the capital of Sweden’ as a predicate, since Sweden is a proper name. The correct analysis is to take relational predicates like ‘…is the same as…’, and since we consider that ‘the capital of Sweden’ is a definite description contextually referring to Stockholm in our world, if not in all possible worlds, this is a case where ‘…is the capital of…’ would be the most appropriate relational predicate. Finally, if necessary we can analyze proper names using Russell’s device of transforming them into quantified predicative expressions, since to a limited degree this device mirrors my own defense of a neo-descriptivist theory of proper names. The structure of facts must correspond with the structure of the so-analyzed sentences that express the structure of thought (the real ‘language of thought’).

21. Ontological status of facts
If we accept that the references of sentence-senses or thoughts are facts, then from an ontological perspective the references of empirical sentences – what they represent – must be empirical facts, most typically located in the external world, though possibly also located in someone’s inner mental world. This assumption speaks for the correspondence theory of truth, according to which empirical facts are truth-makers seen as contingent complex arrangements of elements in the world, which are nothing but arrangements of tropes and things constructed from them.
   However, this assumption runs against Frege’s anti-correspondentialist view of truth. According to him, a fact would be nothing more than a true thought (Frege 1918: 74). Following similar anti-correspondentialist lines, in a very influential article P. F. Straw­son suggested that empirical facts are mere ‘pseudo-material correlates of the statement as a whole’ and not something in the world (1950: 6).[2] According to him, empirical facts, unlike events or things, are not spatio-temporally localizable (‘the world is the totality of things, not of facts’). One reason for this is that the description of a fact usually begins with a that-clause. For instance, I can say ‘the fact that the book is on the table’, but not ‘the fact of a book on the table’. On the other hand, the description of an event typically lacks a that-clause: I can say ‘the event of a tsunami in Japan’, but not very properly ‘the event that there was a Tsunami in Japan’. Facts are for Strawson what statements (when true) state; not what statements are about. They are ‘not, like things or happenings on the surface of the globe, witnessed or heard or seen, broken or overturned, interrupted or prolonged, kicked, destroyed, mended or noisy’ (1950: 6), the same being the case with states of affairs and situations.[3] Finally, to give a striking example, the event of Caesar’s crossing the Rubicon occurred in the year 47 BC, while the fact that he crossed the Rubicon did not occur in the year 47 BC, but it is still a fact today, since facts simply do not occur (Patzig 1980: 19-20).
   An efficacious way to dispose of this argument could be the following. As I understand him, he noted that we need a word to describe the thing in the world that makes our thoughts true. The word ‘fact’ is available. So, why don’t we use it stipulatively in order to designate the truthmaker, whatever condition it is?[4]
   However, it seems clear that even this way to circumvent the problem is avoidable, since it is not difficult to show that the problem exists only in the imagination of philosophers. To begin with, I am of course not saying that everything we may call a ‘fact’ is obviously empirical. The fact that 2 + 2 = 4 is not easily said to be empirical. And we can say it is a fact that the Sun is not green, although this seems only a different way to say that there is no fact that the Sun is green. What I want to defend here is that empirical facts, particularly so-called observational facts, should be considered objectively real: they exist in the external world as possible truthmakers.
   There is a simple and very decisive reason to think that facts can be constituents of the empirical world. It is the fact that of many facts we can easily say that they act causally. Consider the following sentences:

(1)  The fact that the match was scratched caused the flame.
(2)  Thomas died because of the fact that he forgot to turn off the gas.
(3)  Because of the fact that today is a holiday, the class will be canceled.
(4)  The fact that Caesar crossed the Rubicon had important historical consequences.

It does not seem possible that pseudo-material correlates (supposedly abstract contents) can be causally active in the empirical world producing these effects. The admission of the empirical nature of the facts (1) to (4) solves the problem in obvious ways. Scratching the match is a fact-event causing the flame; the situational fact created by Thomas’ forgetfulness of the gas being turned on caused his death; the fact-circumstance that today is a holiday causes the canceling of a class; the fact-event of crossing the Rubicon concretized a state of affairs that causally determined decisive political changes in the Roman Empire.
   Furthermore, I have a key-argument to regenerate the idea that empirical facts are correlates of true thoughts, as the classical correspondence theory of truth has sustained. According to this view, empirical facts are contingent arrangements of elements in the external and/or internal world in general (basically an arrangement of more or less complex predicative or relational tropes contingently tied with clusters of compresent tropes referred to by proper names). This would be the case with facts as simple as those referred to by the sentences ‘Frege had a beard’, ‘The book is on the table’, ‘Lydia suffers from agoraphobia’.
   My argument against Strawson’s opposition between non-spatio-temporal facts and spatio-temporal events begins by showing that there is a serious confusion in his argument. He treats facts (as much as states of affairs and situations) as opposed to events. But this can easily be contested. We begin to be suspicious when we perceive that every event can be called a fact, but not every fact can be called an event. For example: I can replace ‘the event of the sinking of the Titanic’ by ‘the fact of the sinking of the Titanic’, but I cannot replace ‘the fact that Mt. Everest is more than 8,000 m. high’ by ‘the event of Mt. Everest being more than 8,000 m. high’. Hence, it is much more reasonable to consider the event as a kind of fact than to oppose both, as Strawson did. Indeed, my proposal is that the word ‘fact’ is an umbrella term that encompasses events, occurrences, processes, as much as situations, circum­stances, states of affairs… And the reason for this proposal is that we can call all these things facts, but we cannot call all these things states of affairs or events or whatever. So considered, events are sub-types of facts: Linguists should say that the word ‘event’ should is a hyponym of the word ‘fact’. Considering things in this way, it is easy to distinguish two great sub-classes of facts:

1.     STATIC FACTS: Can be formal or empirical, the latter when clearly located in space and time. As a whole, static facts do not change while they last. Typical of static facts is that the relationships between the elements constitutive of them do not decisively change during the period of their existence. We will see that they are truthmakers of a static kind. And in ordinary language there are names for them: they may be called ‘states’, ‘situations’, ‘circumstances’, ‘states of affairs’, etc.
2.     DYNAMIC FACTS: Are always empirical. They change while they last. The relationships between the elements constitutive of them change decisively during the period of their existence, so that they have a beginning, followed by some kind of development that comes to an end after a certain amount of time. We will see that they work as truthmakers of a dynamic kind. And ordinarily they are called ‘events’, ‘occurrences’, ‘occasions’, ‘pro­cesses’, etc.

Formal facts, like the fact that 7 × 8 = 56, are static in the innocuous sense that they aren’t seen as spatio-temporally located. They are not our major concern here. Many facts are empirical and static, since the relationships between the elements constitutive of them do not change during their existence. Static facts are usually called ‘states’, ‘situations’, ‘conditions’, ‘circumstances’, ‘states of affairs’, with different nuances of meaning. Examples of static facts are my unhealthy state, the situation that I am lying in bed, the circumstance that the airport is closed, the state of affairs that Venice has many canals or that the Earth orbits the sun. The Earth’s movement of revolving around the sun counts as a static fact because it is an internal cyclical relationship that remains the same during the fact’s existence (each orbital period is an event).
   Dynamic facts, on the other hand, are defined by irrevocable changes in the relations among their elements during the period of their existence. The process of World War II, for instance, was marked by events like the Battle of Britain, the defeat of Stalingrad and the Normandy invasion – it had an unforeseeable history. Dynamic facts are usually called events when their duration is comparatively shorter, occurrences when their duration isn’t as short, processes when their duration is longer. Examples of events are a lightning flash under dark clouds or a bomb blast. An example of an occurrence is a volcanic eruption. The process of global warming is a very slow natural process, slower them the economic process of globalization. We can predict the stages of many events and processes, although many are also unpredictable in such a way that (differently from static facts) we cannot entirely grasp them before they end. Important is to see that all these things can not only be called events, occurrences, occasions, happenings, processes… but also facts, since they are nothing but empirical facts and truthmakers of a dynamic kind.
   We are now able to find what may be the real reason why we use a that-clause in the description of facts, but not in the description of events. When we speak of dynamic facts, we do not use a that-clause. Thus, we can speak about the event of Caesar’s crossing the Rubicon, but not about the event that he crossed the Rubicon. We can speak about the process of climate change, but not about the process that the climate changes… But this isn’t the case regarding static facts, which are typically (though not necessarily) described as beginning with that-clauses. So, I can speak about the state of affairs that my book is on the table or that I am lying on the bed, but I can also speak about the state of affairs of my book being on the table and of my lying on the bed. Conclusion: that-clauses have the function to emphasize static facts and exclude dynamic facts. And since the hyperonymic term ‘fact’ can be applied to both – the static facts as much as the dynamic facts – it is plausible to think that the term ‘fact’ inherits the property of being used indifferently, with or without the that-clause. You can say, ‘It is a fact that Mount Vesuvius is located near Naples’ (referring to a state of affairs), as much as ‘It is a fact that Mount Vesuvius has erupted’ (referring to an event). And you can also say: ‘Caesar crossing the Rubicon was an event’ as much as ‘It is a fact that Caesar crossed the Rubicon’, referring less precisely to the event. We can summarize these relationships in a schema:

(a)  Static facts (states of affairs…): can be stated with or without that-clause.
(b) Dynamic facts (events…): cannot be stated with a that-clause.
(c)  Facts in general: admit both cases because they do not differentiate between (a) and (b).

Now, what about the fact that Caesar crossed the Rubicon? Isn’t this fact timeless? This is a good case of a philosophically misleading expression. In most cases it is not understood as the description of an event, but as an illustrative way of referring to a static social fact: the state of affairs established by the movement of Caesar’s army onto Roman territory, violating the law that prohibited this and forcing the Roman state to declare war against him. Only occasionally is the phrase ‘crossing the Rubicon’ understood in the literal sense, as the physical event of crossing the river, which comprises Caesar’s sequential locations in relation to the river from t1 to tn.
   Due to the nature of dynamic facts like events and processes, we say that they not only are, but also occur in time, while of static facts we only say that they are located in time while they last. It seems, therefore, that because philosophers such as Strawson did not realize that events are sub-types of facts, seeing only that we may say of events that they occur in time, they hastily concluded that only events (and things) are located in time, opposing them to timeless facts. But that this isn’t true can be shown even by inter-substitutivity salva veritate: it is not incorrect to say that the event, the occurrence of Caesar’s crossing the Rubicon was a fact and that this fact occurred in 47 BC, as a concrete dynamic fact. On the other hand, the political state of affairs established by Caesar’s crossing the river was far more durable, because it was a static fact, the political situation that led, as is well-known, to the fall of the Republic. However, it seems clear that the state of affairs brought about by the crossing of the Rubicon was spatially limited to the Roman Empire and temporally limited to the time from the crossing of the Rubicon to the crowning of Caesar as dictator and up until his assassination. It was not something that existed in Greenland or that endures until the present, even if we have the custom of using the present tense to speak about historical facts.
   A final point is that by having the broadest scope, the so underrated short word ‘fact’ remains the ideal candidate for the role of truthmaker in a correspondence theory of truth. Under this view, facts are the universal truthmakers.

22. Church’s slingshot argument
Trying to refute the accusation of implausibility, the Fregean logician Alonzo Church used a slingshot argument, attempting to show that by means of intersubstitutability we can prove that the reference of the most diverse sentences must be only one, namely, their truth-value. Church’s argument is in my view equivocal, but telling. Its basic assumption is that when one constituent expression is replaced by another, so that their partial references are interchangeable, the reference of the whole sentence does not change. I will initially expose his example of a slingshot argument, underlining its supposedly co-referential definite descriptions (Church 1956: 25):[5]

1.      Sir Walter Scott is the author of Waverley.
2.      Sir Walter Scott is the man who wrote altogether the twenty-nine Waverley novels.
3.      Twenty-nine is the number such that Sir Walter Scott is the man who wrote altogether that many Waverley novels.
4.      Twenty-nine is the number of counties in Utah.

According to him, if it is plausible that sentences (2) and (3) are, if not synonymous, at least co-referential sentences, then (1) has the same reference as (4). As (4) seems to concern a fact completely different from (1), it seems that the only thing left as the same reference is the truth of both sentences. Hence, The True is the only referent of all these sentences.
   However, in my view the argument proves to be unsustainable when we pay attention to what should be the real reference of each singular term of these sentences. In the sentence (1) the proper name ‘Sir Walter Scott’ and the definite description ‘the author of Waverley’ are two singular terms expressing different modes of presentation of the same human being, they are partial references to Walter Scott. In sentence (2) again, the nominal expression ‘Sir Walter Scott’ and the definite description ‘the man who wrote altogether the twenty-nine Waverley novels’ both refer to the same Walter Scott. The third sentence is the tricky one. Its reference is unclear: Walter Scott? The number 29? Both in one? An amalgam like Scott29? Is there a way to paraphrase sentence (3) so that it gives back in a transparent way its complete informative content? In my view, the only way to reveal its content in a transparently clear way without any addition or loss of sense is to split the sentence into the following conjunction of two sentences: (5) ‘29 is the number of Waverley novels and Sir Walter Scott is the man who wrote altogether that many Waverley novels.’ Or for the sake of clarity, replacing ‘=’ for ‘is (the same as)’ and ‘&’ for ‘and’, we have:

6.     (29 = the number of Waverley novels) & (Sir Walter Scott = the man who wrote the many Waverley novels altogether).[6]

That is: Sentence (3) confusingly compresses nothing less than a conjunction of two identity sentences, each with its own proper partial references given by the terms flanking their identity signs. They are the number 29 in the first sentence and Walter Scott in the second sentence. Finally, we come to the analysis of the sentence (4): ‘29 is the number of counties in Utah’, which means the same as the identity sentence (7) ‘29 = The number of counties in Utah’. Here, each term that flanks the identity sign has the number 29 as partial reference. So analyzed, the derivation appears as:

1.     Sir Walter Scott = the author of Waverley.
2.     Sir Walter Scott = the man who wrote the altogether 29 novels of Waverley.
3.     (5) (29 = the number of Waverley novels) & (Sir Walter Scott = the man who wrote the many Waverley novels altogether).
4.     (6) 29 = the number of counties in Utah.

Now, although these sentences are all true – assuming a principle of compositionality requiring that the partial references cannot change – this loses its intuitive appeal. Sentences (1) and (2) have as partial references Walter Scott under different guises. However, sentence (3) is a conjunction of two identity sentences, each one with its own very distinct partial reference. The object referred to by the flanking terms of the first identity sentence is the number 29 (as the number of Waverley novels), while the object referred to by the flanking terms of the second identity sentence is Sir Walter Scott (as the man who wrote the Waverley novels). Finally, sentence (4) has as a partial reference of its terms only the number 29 (as the number of counties in Utah), without referring to Walter Scott. This means that in the composed sentence (3), the second sentence of the conjunction is the only one that preserves as its partial reference the references of (1) and (2), while (4) is an identity sentence that has as its partial reference only the partial reference of the first sentence of (3), which has clearly nothing to do with the partial references of (1) and (2) and therefore with their references. That is, the replacements slip equivocally from Walter Scott in (1) and (2) to a Walter Scott together with the number 29 in (3), and to the number 29 in (4), in a surreptitious way. This means, according to the principle of compositionality applied to the complete sentences, that the references of sentences (1) and (4) should be different. Initially the flaw isn’t easy to spot, because sentence (3) contains both these partial references conjoined in a grammatically confusing way; we have the impression that the partial references of (3) are something like an amalgam of Walter Scott and 29, say, a ‘Scott29’, while they are in fact totally distinct. In fact, the replacements would only respect the compositionality principle, warranting the sameness of the sentences’ references, if the argument could prove that the partial references of all the sentences could be replaced without surreptitiously inviting the reader to conjoin in sentence (3) partial references that are of objects completely distinct.

23. Facts: sub-facts and grounding facts
If we take the whole reference of the sentence as not a truth-value but a fact, things turn out to be much more intuitive. We can seize Church’s derivation not only to introduce facts as referents of sentences, but also to introduce a distinction between sub-facts and grounding facts. As will be seen, this distinction fills a gap in Frege’s explanation.
   We need to distinguish at least two facts referred to by identity sentences. The first is the perspectival fact, the fact as what is immediately exposed through the mode of presentation expressed by the sentence. I will call it a sub-fact and make the different sub-facts responsible for the differences in the modes of presentation constitutive of the different sentence-senses or Fregean thoughts about the same thing, as the planet Venus, Scott, the number 29. This is why Church’s sentences (1) and (2) can be seen as expressing different senses or thoughts by evoking different perspectival sub-facts. They expose different sub-facts, since (i) being Sir Walter Scott is not the same thing as (ii) being the author of Waverley and (iii) being the man who wrote the altogether 29 novels of Waverley … In this way, sentences (1) and (2) show respectively two sub-facts that contain constitutive objects of reference that differ one from the other. Here they are:

(1’) Being Sir Walter Scott ≠ being the author of Waverley novels.
(2’) Being Sir Walter Scott ≠ being the man who wrote the altogether 29 novels of Waverley.

However, it is obvious that (1) and (2) are also identity sentences. Each of these sentences can be understood as referring under different guises to only one object, justifying their ‘is’ of identity. In this sense, sentences (1) and (2) also represent identities, which can be directly expressed by ‘Walter Scott = Walter Scott’ and which express the self-identity of Scott considered in full, as the bearer of all descriptions we attach to it. Under the descriptions attached to the name ‘Walter Scott’ we can find ‘the person with the title of Sir called “Walter Scott”’ (that is, ‘Sir Walter Scott’), ‘the author of Waverley’ and, more definitely, ‘the man who wrote the altogether 29 Waverley novels’, expressions that build (1’) and (2’). This primary fact that unifies all the sub-facts shown by its multiple modes of presentation is what I call the grounding fact. It is what makes sentences with the form a = b identity sentences.
   Considering things in more details: As we saw, the mode of presentation is intentional, also subjective, considering that the reference can be absent. But when the mode of presentation isn’t empty it also exposes something objective, for instance, ‘the author of Waverley’ evokes ‘being the author of the Waverley novels’, which is, we could say, an objective sub-object mediating our reference to the object Scott. Thus, ‘the author of Ivanhoe’ (who was also Walter Scott) is a mode of presentation of the sub-object ‘being the author of Ivanhoe’, though it ultimately refers to Walter Scott. Now, the sentence

The author of the Waverley novels is the author of Ivanhoe.

This sentence evokes two different sub-objects that together form the contrastive sub-fact that being the author of Waverley ≠ (isn’t the same as) being the author of Ivanhoe. But this sub-fact also has two modes by which the same object is given, whose identity is the grounding fact that can be directly represented by the sentence ‘Scott [in full] = Scott [in full]’.
   In other words: when I say ‘The author of Waverley is the author of Ivanhoe’, I am saying two things. First, by the intentional modes of presentation I am evoking an objective difference that can be represented by the sentence ‘Being the author of Waverley ≠ (isn’t) being the author of Ivanhoe.’ Indeed, it is a objective factual difference that a person writing Waverley is not the same as a person writing Ivanhoe, even if they are both the same person (he was writing different stories at different times). However, since when I say ‘The author of Waverley is the author of Ivanhoe’ I use an ‘is’ of identity, I also mean ‘The author of Waverley = the author of Ivanhoe’, so that under different guises I am representing the grounding fact that ‘Walter Scott = Walter Scott’. It is because of the two – the grounding fact along with the sub-fact – that identities of the kind a = b are able to express what I somewhat romantically call the identities in their differences.[7]
   Now, assuming the kind of neo-descriptivism proposed in appendix 1 of this book, we can make explicit the above mentioned duplicity of the represented facts by stating each of the four sentences of Church’s reasoning as follows:

(1) Sub-fact: Being Sir Walter Scott ≠ being the author of Waverley. (1) Grounding fact: Walter Scott = Walter Scott.
(2) Sub-fact: Being Sir Walter Scott ≠ being the man who wrote the altogether 29 Waverley novels. (2) Grounding fact: Walter Scott = Walter Scott.
(3) Sub-fact: (Being 29 ≠ being the number of Waverley novels) & (Being Sir Walter Scott ≠ Being the man who wrote altogether the many Waverley novels). (3) Grounding fact: (29 = 29) & (Walter Scott = Walter Scott).
(4) Sub-fact: Being 29 ≠ being the number of counties in Utah. (4) Grounding fact: 29 = 29.

The sub-facts show why the semantic-cognitive contribution of each referential component may be different. For instance, the sub-fact that Sir Walter Scott wrote 29 Waverley novels discriminates more than the sub-fact that he wrote the Waverley novels, and in true sentences this discrimination isn’t just a mentally considered mode of presentation, but also something objectively, factually given (in Frege’s words, ‘the way the object gives itself to us’). The evocation of these sub-facts all send us to the grounding fact that all the different senses in the end refer to something numerically identical.

24. Taking seriously the sentence’s reference as a fact
I hope I have shown that the most plausible option concerning the nature of reference is to follow Russell and Wittgenstein, assuming that the reference of a statement is always a fact, understood as a contingent arrangement of cognition-independent elements usually given in the external world. Facts would satisfy the Fregean condition that the reference of a sentence is an object: they are independent, complete, closed. They would satisfy his condition that thoughts expressed by sentences are modes of presentation of their references, the last ones being (as sub-facts) as multiple and diverse as their thoughts. Finally, unlike truth-values, facts would clearly satisfy the principle of compositionality: they would always vary in accordance with variations in the references of the component parts of the sentences.
   If we assume this answer, questions arise. The first is the following: how do we establish what fact the thought expressed by a sentence refers to? Consider the following sentences:

1.     The morning star is the morning star.
2.     The morning star is the evening star.
3.     The morning star is Venus.
4.     Venus is the second planet orbiting the sun.
5.     Venus is the most brilliant planet visible in the sky.
6.     Venus is the only planet in our solar system shrouded by an opaque layer of highly reflective sulfuric acid clouds.
7.     The morning star is the only planet in our solar system shrouded by an opaque layer of highly reflective sulfuric acid clouds. …

On the one hand, it is linguistically correct to say that each of these sentences refers to a different fact. Sentence (1) is tautological, proclaiming the self-identity of the morning star, while sentence (2) and the following sentences provide different information on different factual contents regarding the planet Venus. On the other hand, since all singular terms composing these identity sentences have the same ultimate reference, the planet Venus, it also seems that in the end all these sentences must also have the same reference, pointing to the same fact…
   The point already touched in the last section comes back: in such cases there must be a privileged grounding fact able to be described that can be identified as the ultimate truthmaker of all these identity sentences about the planet Venus. This grounding fact must in some way include the facts indicated by the different cognitive values of sentences (1) to (7) above as its perspectival sub-facts. My suggestion is that this task can be accomplished by the references of identity sentences between proper names, insofar as they are their identifying rules considered in full, that is, including all their fundamental and complementary constituents.
   Now, assume our proposed view of proper names’ meanings as abbreviations of bundles of descriptions applicable according to identifying rules as essentially correct. Then the proper name ‘Venus’ in full (i.e., considering all its assumed descriptions and abstracting the limited knowledge of concrete speakers) includes in its most complete content all of those already known modes of presentation. This means that definite descriptions such as ‘the morning star’, ‘the second planet orbiting the Sun’, ‘the most brilliant planet visible in the sky’, etc. can at least be made probable by applying the concept of Venus in full (I say ‘made probable’ because according to the identifying rule any description of the bundle may be empty). If so, then there is indeed a sentence that could describe the grounding fact. This is the ultimate truthmaker or verifier of any identity sentence concerning the planet Venus, including the sentences from (1) to (7) above. Here it is:

8.     Venus [in full] = Venus [in full].

My contention is that rightly understood this sentence is able to express an ideal grounding thought able to refer to the single grounding fact, which – if regarded in its entirety – is able to work as the truthmaker for any identity sentence about the planet Venus.
   It is easy to explain why. If the full meaning of the proper name ‘Venus’ is understood as an abbreviation of a bundle of descriptions that uniquely identifies its object, then this proper name must include descriptions like ‘the morning star’, ‘the second planet orbiting the Sun’, ‘the most brilliant planet visible in the sky’, etc. Consequently, we can inferentially derive from the sentence ‘Venus = Venus’ the sentence (2) ‘The morning star = the evening star’, simply by replacing the first occurrence of the name ‘Venus’ with the definite description ‘the morning star’, which the name ‘Venus’ abbreviates, and the second occurrence with the description ‘the evening star’, which the name ‘Venus’ also abbreviates. In a similar way, we can inductively infer all the other co-referential identities. In this way the sentence ‘Venus [in full] is (the same as) Venus [in full]’ would be ideally able to represent a fact complex enough to contain the sub-facts indicated by each of the thoughts expressed by the above sentences, which may be seen here as contingent a posteriori. (Cf. the meaning of ‘Venus’ as presented in an encyclopedia.)
   In order to reinforce what I am suggesting, I can instead use numerical identities like the following:

1.     2 + 2 = 2 + 2
2.     2 + 2 = 1 + 1 + 1 + 1
3.     2 + 2 = 4
4.     4  = √16
5.     2 + 2 = (14 – 6) / 2

Of course, here the identity sentence expressing the grounding fact would be:

6.     4 [in full] = 4 [in full]

   But could the sub-fact expressed by sentences (1) to (5) be derived from (6)? The answer is obviously in the affirmative, since we are dealing with a deductive system. The obvious reason for this is that I have written the five sentences above simply by conceiving deductive inferences from ‘4 = 4’!
   However, one could still object that a sentence like ‘Venus [in full] = Venus [in full]’ is a tautology: a necessary truth. How could a necessary truth ground contingent truths like ‘Venus is the brightest planet visible in the sky’?
   My tentative answer to this objection is that for a privileged user of the word (the Venus specialist) who is supposed to master all pertinent information about Venus, this proper name expresses the following identifying rule:

IR: In any possible world our proper name ‘Venus’ has a bearer, iff this bearer belongs to the class of celestial bodies that satisfy sufficiently and more than any other the condition of being the second planet orbiting the sun, located between Mercury and the Earth (making probable the application of auxiliary descriptions like ‘a planet somewhat smaller than the earth’, ‘the morning star’, etc.)

This is a one-foot identifying rule. The localizing rule is here the only fundamental description-rule. If Venus loses its atmosphere or an important part of its mass, insofar as it remains the second planet, it will be our Venus. Indeed, so understood the identifying rule for Venus must be applicable in any possible world where the planet Venus exists. The Venus’ case is somewhat like the case of the lines ‘a⁀b-a⁀c’ made to localize the center of a triangle without any further property. No characterizing description is relevant. However, without the localizing condition established by the identifying rule of Venus it would be impossible to identify Venus. The application of many other descriptions does not create criteria, but only symptoms of the existence of the planet, since they make the application of the descriptions only more or less probable. Auxiliary descriptions like ‘the brightest planet in the sky’ are symptoms, like ‘the highly reflective clouds of sulfuric acid’ that cause this brightness. If Venus loses its reflective atmosphere, it may cease to be the brightest planet, but will not cease to be Venus. If the planet loses half of its mass but remains in the same orbit it still does not cease to be Venus. This will occur only if it becomes an asteroid; for an asteroid is not a planet. If in another possible world the second planet had been hurled out of the solar system thousands of years ago (Kripke 1980: 57-58), it would still with right be recognized as our Venus.
   What I said about identity sentences also applies to other singular predicative and relational sentences. Consider the following sentences:

1. Bucephalus was a living being.
2. Bucephalus was an animal.
3. Bucephalus was a horse.
4. Bucephalus was a black horse of the best Thessalonian strain.
5. Bucephalus was a massive black horse of the best Thessalonian strain, owned by Alexander the Great.
6. Bucephalus: (355 BC – 326 BC) was the most famous horse of Antiquity; it was a massive black horse of the best Thessalonian strain, owned by Alexander the Great.

One could say that each of the first five sentences refers to different sub-facts by means of increasingly detailed modes of presentation expressed by their respective predicative expressions. However, relative to them there is a grounding fact that is more completely referred to by sentence (6), since the truth of all the others can be implied by the truth of this sentence. Indeed (6) is nothing but a shortened expression of the identifying rule for Bucephalus, with a localizing and a characterizing description. The sub-facts represented by sentences (1) to (5) are all included in the grounding fact represented by sentence (6). These facts are the immediate satisfiers of the diverse modes of presentation of Bucephalus indicated by each sentence.

25. The problem of identity in difference
There is a final point concerning the relationship between the sub-fact and the grounding fact. It concerns the deficient way by which Frege solved the puzzle of identity. As he writes, differently from a sentence of the form a = a, a sentence of the form a = b is informative because it refers to the same object by means of different modes of presentation, different senses (1892: 26). However, we can still ask how this identity is possible, since the modes of presentation are different and since we are not intending to speak about the mere self-identity of the reference, as Frege also acknowledged. I call this the riddle of identity in difference.
   To see the problem more clearly, consider again the sentence (1) ‘The morning star = (is the same as) the evening star’. A more fully unpacked cognitive sense of (1) can be presented as:

The brightest star in the morning sky, understood as representing the second planet orbiting the Sun (Venus) = the brightest star in the evening sky, understood as representing the second planet orbiting the Sun (Venus).

Here we have the hidden reason for the riddle of identity in difference: the senses of the expressions flanking the identity sign in (1) are obviously different, but they both evoke a sense that is identical, which is that of being the second planet orbiting the sun, namely Venus. It is important to note that this last sense is not yet the reference, but still a cognitive identifying rule (expressed by the underlined definite descriptions) constituting the core sense of the name ‘Venus’. It is only because both expressions flanking the identity sign indirectly evoke the identifying rule for the planet Venus that we are allowed to put the identity sign between them! In order to make the point clearer we can use the following schema:

Sentence:    The morning star          = (is)           the evening star.

immediate   IR: the brightest            ≠                 IR: the brightest
sense:          star in the morning                           star in the evening
                                 ↓                  sub-fact:                  ↓
                   Being the morning star isn’t being the evening star

mediated     IR: the second planet…     =              IR: the second planet…
sense:          (Venus)                                               (Venus)
                                    ↓              grounding fact:           ↓
                                     Venus [in full] is Venus [in full]

In sum: the singular terms ‘morning star’ and ‘evening star’ are responsible for a difference in what I call immediate senses, evoking a relational sub-fact showing the difference between them. Indeed, the sub-fact is that being the brightest star seen in the morning sky differs in place and time from being the brightest star seen in the evening sky. Furthermore, the word ‘is’ (the same as) indicates the identity of the implicitly mediated senses pointing to a relational grounding fact that is constituted by the fact of Venus’ self-identity, here expressed by the statement ‘Venus [in full] = Venus [in full]’.
   A somewhat different example is the sentence ‘The morning star is Venus’. Here the schema is:

Sentence:        The morning star            =         (is)      Venus.

Immediate:      IR: the brightest             ≠          IR: the second
sense                star in the down                               planet
                                        ↓                 sub-fact:           ↓
                         Being the morning star isn’t being Venus

Mediated         IR: the second planet      =          IR: the second planet
Sense:             (Venus)                                               (Venus)
                                         ↓           grounding fact:      ↓
                                       Venus [in full] is Venus [in full]

In this way, the identity expressed by sentences of the kind a = b is an identity in difference. This means that in fact we have two levels of sense. The first exposing the phenomenal sub-fact expressing a difference (Being the morning star isn’t the same as being the second planet). The second, intermediated by the first one and indicated by the ‘is’ of identity (is the same as), represents the ultimate grounding fact that Venus is the same as Venus.
   Now, how should we deal with cases in which the mediated sense responsible for the identity, like the planet Venus, lacks a proper name? Consider the identities (i) ‘Everest = Chomolungma’, (ii) ‘a⁀b = a⁀c’ (concerning Frege’s example of the different ways to name the center of a triangle), (iii) ‘Afla = Ateb’ (the two names of the same imaginary mountain conceived by Frege). I would answer this by creating a conjoint sense, a conjoint identifying rule, respectively the ‘Everest-Chomolungma’, the ‘a⁀b-a⁀c’, and the ‘Afla-Ateb’, which in fact produce three new nominative expressions. By the law of identity it is now obvious that ‘Everest-Chomolungma = Everest-Chomolungma’, ‘a⁀b-a⁀c = ‘a⁀b-a⁀c’, and ‘Afla-Ateb = Afla=Ateb’ represent the three different grounding facts. This is what maintains the identity of sentences (i), (ii) and (iii).
   We can apply a similar analysis to identities between concept-words: (x) (Fx = Gx). Consider the identity ‘Water is H2O’. The schema will be:

Sentence:       Water                        = (is)     amount of H2O.
                          ↓                                                    ↓
Immediate     aqueous                      ≠           amount of
sense:            liquid…                                   hydroxide of oxygen
                          ↓                        sub-fact:              ↓
                      Being water isn’t being an amount of H2O

Mediated       amount of                   =            amount of
sense             hydroxide of oxygen                 hydroxide of oxygen
                              ↓               grounding fact:        ↓
                              Water [in full] is water [in full]

As already noted (appendix to chapter 2), the concept-word ‘water’ has two nuclei of meaning: a superficial one, of the aqueous liquid (transparent, insipid, odorless, etc.), and a deep one, of a chemical substance often called hydroxide of oxygen. Regarding the immediate sense, it exposes the sub-fact of the difference: the sub-fact that being an aqueous liquid isn’t the same thing as being a quantity of H2O molecules. Regarding the mediated sense, the grounding fact indicated is the self-identity of the chemical substance, which remains the same independently of its mode of representation. It is because of this deep identity that we can say that the two different modes of representation of an aqueous liquid and of H2O are those of the same substance.
   This duplicity of sense levels explains much of Saul Kripke’s, in my view illusory, discover of the necessary a posteriori. In different contexts we can enhance or magnify or emphasize the immediate Fregean perspectival sense or thought of a sentence (representing a sub-fact) or the mediated sense or thought of the sentence (representing the grounding fact).[8] Here I need to speak again of the contexts of interest of the linguistic agents, meaning by this their pragmatic aims. Two contexts of interest are important regarding several examples above: the popular context of interest and the scientific one. Thus, considering the sentence ‘The morning star is the evening star’, we can contextually emphasize the immediate senses (modes of presentation, identifying rules) for the phenomenal objects the morning star and the evening star, considering the difference between being the brightest star in the morning and the brightest star in the evening, leaving the identity in the background. This can be the case, for instance, when we contemplate the beauty of the starry sky in the night and, after localizing the evening star, we say to a child that it is also the same thing as the morning star. In this case, we read the thought as contingent a posteriori, since we are well aware that we are emphasizing the difference between the two modes of representation, which is an empirical phenomenal sub-fact. We are emphasizing our representation of the phenomenally given sub-fact. However, in a scientific context of interest, e.g., in which we use a telescope to study the surface of Venus, in considering the sentence ‘The morning star is also the evening star’, what we emphasize is the identity between both stars, the mediated sense representing the grounding fact of the self-identity of Venus. In this case we read the statement as meaning that ‘[in full] Venus = Venus [in full]’, what is a necessary a priori statement, leaving the different guises of sense in the background as secondary effects of an astronomical theory that is already assumed to be true.
   Now, consider the statement ‘Water is H2O’[9]. In a popular context of interest of fishermen interested in digging a well to find water to drink and to wash, this sentence is read as emphasizing the sub-fact that the word ‘water’ means a precious aqueous liquid, a transparent, tasteless, odorless, drinkable fluid, and this is not exactly the same as saying it is constituted by H2O. Since what is emphasized here is the difference between senses, the statement is seen as contingent a posteriori treating the deep identity as an irrelevant empirical discovery. On the other hand, when the context of interest is scientific, e.g. chemists measuring the acidity of a quantity of water, the word ‘water’ in the sentence ‘Water is H2O’ can be read as meaning the same thing as hydroxide of oxygen. In this case, the whole sentence is seen as representing the grounding fact expressed by the identity ‘Hydroxide of oxygen = H2O’, which is the same as ‘H2O = H2O’, that is, a necessary a priori tautology. A similar emphasization can be found in other examples.
    Now, I think Kripke is misleadingly conjoining the a posteriority of emphasizing the immediate sense or thought with the necessity of the mediated sense or thought, concluding that the identity of names and concepts has a necessary a posteriori nature only metaphysically explicable. If these names or concept-words have a work as rigid designators, applying to the same entities in all possible world, this is explained by their mediated senses, which are of the king a = a, and not b. A Wittgensteinian therapist would say that Kripke is victim of a linguistic hypostasis. Finally, as far as the singular terms in such identity sentences are seen as rigid designators, applying to the same ultimate object in all possible worlds in which it exists, this also justify the self-identity of the grounding fact.




[1] See Frege, Letter to Russell of 28.12.1912.
[2] For him ‘a situation or state of affairs is, roughly, a set of facts, not a set of things’ (1950: 8).
[3] For a relevant reply see J. L. Austin, ‘Unfair to Facts’ (1961: Ch. 5). It seems to me at least curious that the posthumously published arguments of J. L. Austin against Strawson’s view have had so little impact.
[4] John Searle once proposed something similar to this: ‘…we neither have nor need a thick metaphysical notion of “fact”. Anything sufficient to make a statement true is a fact. Thus the fact that there are no three-headed cats is as much a fact as the fact that the cat is on the mat’ (1998: 392).
[5] I take the following better ordered formulation from Marco Ruffino, 2004: 25.
[6] This also gives back the whole sense of the original still more convoluted sentence of Church: ‘The number such that Sir Walter Scott is the man who wrote that many Waverley Novels altogether is twenty-nine’.
[7] It seems that the mode of presentation of the sub-fact can be approximated with what defenders of two-dimensionalism call primary intention, while the mode of presentation of the grounding fact can be approximated with what they call secondary intention. (see Chalmers 2002).
[8] The concept of emphasization was fruitfully applied in Jürgen Habermas’ excellent work on universal pragmatics (Habermas 1976).
[9] An example is already discussed in the addendum of the appendix to chapter 2 in this book.

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