TROPE THEORY

 This is a SKETCH!!!

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TROPES, UNIVERSALS, AND MATERIAL OBJECTS

 

 

Of many leaves, we can say that they are green, of many diverse living beings that they are human, and of many actions that they are just, even though they are very different from each other. How can two very different things share one only property? What allows us to apply predicates like ‘…is green’, ‘…is a human being’, and ‘…is just’ to many different things, in order to generalize, to discover unity in the multiplicity – a capacity that seems so fundamental to human understanding?

   There are at least three kinds of answers to this question: realism[1], nominalism, and trope theory. In what follows I will very shortly explain the gist of the first two ontological approaches, saying something more extended in favor of the third approach.

 

Realisms

The realism of universals is the doctrine according to which we can distinguish the same property in many different particulars (individual things) simply because this property is a universal, that is, something able to be in some way instantiated (exemplified) in those many different particulars. This would be, for instance, the abstract property of redness. All particulars that are recognized by us as red are red because they instantiate the universal property of redness. The same with more complex properties, like the property of being human, instantiated by any human being,[2] or relational properties, like the property of being father, instantiated by all fathers and their children. For realist philosophers, it is by the multiple instantiations of these universals that we can say the same of many, in sum: to grasp generality.

   There are two basic kinds of realism: platonic and aristotelian. The difference between them is that in platonic realism universals, properties (ideas or forms) exist before things, or, more precisely, in complete independence of the empirical particulars, while in Aristotelian realism the properties (forms) exist in some way in the things.

    In platonic realism universals are abstract entities understood as non-empirical (transcendent), unchangeable and indestructible, existing outside space and time. The modern concept of instantiation (exemplification) is explanatorily insufficient: how can empirical things like green leaves exemplify something that is hovering outside space and time.[3] It is not pre-defined how many empirical particulars can instantiate one only abstract universal property: maybe none, maybe only one, maybe an indefinite number of them. Important is to note that since platonic universals are abstract, they are independent of the existence of the empirical world: if our world ceases to exist, the world of property-ideas will continue eternally existing; Platonic universals are world-independent. The epistemological consequence of this is that our experience with the world serves only to help us to remember universals innately present in our minds: Plato is a rationalist philosopher. There are many problems with platonic realism. The biggest problem, in my view, is simply that of intelligibility. It seems impossible for our intellect to grasp non-empirical entities outside space and time, like the red-in-itself, the humanity-in-itself, the justice-in-itself, the paternity itself. We simply cannot conceive them. It seems rather that we are fooled by the external clothes of our language in the belief that we are conceiving something more than just the spelling of some meaningful words.

   In its Aristotelian version, universals are not abstract non-spatiotemporal entities. They are empirical entities existing in the material objects as if they a chocolate layer on pieces of cake. This means that, differently from Platonism, the universals only exist because the empirical world exists; they are world-dependent. The epistemological consequence of this is that the universals must be abstracted (separated) from the particulars by means of experience, which means that Aristotle, in opposition to Plato, was a kind of empiricist. There are, however, also serious problem with the Aristotelian solution: that one empirical universal property simultaneously instantiates itself in many different material objects without dividing itself sounds still more incoherent than Plato’s abstract universal idea doing the same. How is it possible that the redness of this red tomato is at the same time present in the redness of a fire extinguisher and in a red dwarf star situated millions light years from the earth that long ago does not exist anymore? How can the humanity be actualized in Gandhi and in Socrates remaining one and the same humanity? So understood the Aristotelian doctrine seems still more hopeless than that of Plato.

   Strangely enough, realism has had a huge influence on the history of philosophy and still today has talented defenders, especially among people with an aptitude for formal sciences and, perhaps, with some mystical disposition.

   The most revealing positive arguments in favor of realism are perhaps those of a linguistic nature. One of them is the so-called nominalization or abstract reference. This is usually achieved when predicates are placed in the position of the subject of a sentence, which seems to make them to actually refer to the universal. Here are some examples of sentences containing nominalized predicates, which I adapted from M. J. Loux[4]:

 

              A

1. Courage is a moral virtue.

2. Wisdom is the object of philosophical life.

3. Suzi prefers red to blue.

 

The nominalizations ‘courage’, ‘wisdom’, ‘the red’, ‘the blue’ seem here to name the respective universal ideas.

   The usual reaction against examples such as the ones mentioned above is that the grammatical form of our sentences hides what should be really considered, namely, their logical structure, which shows what really should be thought in the fully analyzed sentences.[5] From this perspective, here is what the three sentences of Ain fact mean:

 

 

          A*

1.              All that is courageous has at least one moral virtue. Or: “For all x, if x is courageous, then x possesses at least one moral virtue”. Or still: “(x) (Cx) → Ex (Vx)”.

2.              If one studies philosophy, one should seek to be wise. Or: “For any x, if x studies philosophy, x should seek to be wise”. Or still: “(x) (Px → Wx)”

3.              If all other properties of things considered make no difference in choice, Suzi prefers red things to blue things. Or: “For all x and for all y, if for s x and y are indifferent in other respects, if x is red and y is blue, s prefers x to y”. Or still: “(x) (y) (Isxy & (Rx & By → Psxy)”.

 

Logically analyzed the sentences are evidenced as referring as lacking any reference to universals, and the terms that seemed to refer as names of universals – courage, wisdom, red, blue – were all shifted to a predicate position.

   It was much easier for Plato and Aristotle to be realists. Neither of them knew anything of mathematical logic. Because of this it was easy for them to confuse the grammatical clothes of our language with its logical structure. For them, a sentence like “Socrates is wise” would have the same logical structure as “Wisdom is valuable”. Consequently, it was easy for them to believe that the subject ‘Wisdom’ should refer to an object in the same way as the subject ‘Socrates’ refers to a real object. As they could not find any object like wisdom in the visible world, their solution was to invent an entity called universal, which for Plato were an eternal abstract idea outside the visible world and for Aristotle should be a form that would be shared under the many objects belonging to the visible empirical world but remaining (according to some interpretations) in some magical way one and the same.

   The realist can insist on his solution, giving further examples of sentences that although do not incorporate nominalizations of predicates, seem to affirm something about universal properties or attributes. Some examples[6]:

 

                    B

1.              This tomato and that fire extinguisher have the same red color.

2.              This color has been exemplified many times,

3.              John has the same character traits as Mary.

 

Nonetheless, we can always invent paraphrases that eschew the supposed appeal to universals, for instance:

 

                    B*

1.              This tomato and that fire extinguisher have colors that are identical to each other.

2.              Colors similar to the color of this object here (say, a tomato) were found in many other objects.

3.              All of John’s character traits and all of Mary’s character traits are similar.

 

In all these paraphrases, supposed statements about universals are eliminated, remaining only references to objects of the empirical world: the tomato, the extinguisher, material objects, John, Mary... Moreover, as we will see, the ontology of tropes gives a nice justification to these paraphrases.

 

2. Nominalisms

It seems that Middle-Age philosophers were sufficiently bored with the unsurmountable problems of realism to invent something opposite of it, a doctrine called nominalism. The most fundamental contention of nominalism is that universals do not exist; only individuals exist.[7]

   For nominalism there are no universal properties because there is nothing that can be instantiated in more than one particular. Only the individuals named by the subject term exist. A vivid proposal of nominalism was given by the first known nominalist, the medieval philosopher Roscelin (1050-1125 D.C.). According to him, only individuals exist, and universals are only flatus vocis, that is, emissions of sound. If I say, “This tomato is red”, the subject refers to an object, the tomato, but the predicate ‘…is red’ is only a sound without correspondence with anything in the world!

   Later forms of nominalism were more sophisticated and plausible. I will consider here only three forms of nominalism: predicative, resemblance, and class-nominalism.

   According to predicate nominalism, if I say, “This tomato is red” and “this fire extinguisher is red”, it is a property of the predicative term ‘red’ to apply to both objects. This seems plainly insufficient because it does not explain why a predicate applies to some objects but does not apply to another.

   A less unsatisfactory form of nominalism is the so-called resemblance nominalism. The fire extinguisher is red because it resembles the red tomato, which can be used as a paradigm. All objects that resemble the model or that resemble one another by being red form the class of red particulars. There is, against this proposal, an obvious objection: if a fire extinctor resembles a tomato, it is because there is something by means of which they resemble one another, and this thing cannot be other than the fact that both are red; but in this case, it seems that we are using red again as designating a universal. Moreover, it seems that the only way to explain the similarity is by appealing to the aspect by which different particulars are similar, and this aspect, one can argue, either is a universal or, as we will see later, a trope.

   Still, a form of nominalism is class-nominalism. According to class-nominalism, if I say, “this tomato is red” and “that flag is red”, I can apply the predicate red to both objects because they are both members of the same class of red objects. This is already problematic, since it seems that for the class-nominalist red should be identified with the class of red objects, which is counterintuitive enough.

   Another problem with class-nominalism is that of co-extensive properties. Consider the class of chordates (animals with hearth) and the class of renates (animals with kidneys). Since all animals with heart also have kidneys and vice-versa, we should say that the property of having a heart is the same as the property of having a kidney. But this is absurd.

   David Lewis tried to circumvent this problem embracing modal realism. He suggests that all possible worlds are real, differing our world from the others by being not only real but also actual. Consequently, the class to be considered by the class-nominalist must be not only that belonging to our own world, but of any possible worlds. Since there must be possible worlds where there are animals with hearth but not with kidneys and vice-versa, the two classes do not need to be the same. In any case, class-nominalism does not explain why we decide that one object, for instance, a tomato, should belongs to the class of red particulars. If it is because of it is redness, we fall back into realism; if it is because it has the property of being red, we fall back into trope ontology.

   One could object that I am not considering the arguments in sufficient details. My answer is that the above presented difficulties should be more than sufficient to convince philosophers they are digging in the wrong place. More than thousand years of discussion without any expectative of a concrete result should be sufficient to convince reasonable persons that traditional (and much of the contemporary) ontology is out of track. For this reason, I will pass to the next account, which seems to me to be the only view able to save ontology from death by consumption.

 

3. Trope theory

According to the trope theory, first proposed by Donald Williams[8], our whole world and even any possible world – as a world that we can conceive – is totally constituted by its tropes. But what are tropes? For Williams, a trope is an abstract particular in a very special sense, that is, as a property that remains after we abstract (exclude) all other properties of a singular object.[9]  For instance: I have a tomato: after I abstract its weight, its softness, its size, its shape, its flavor… the only thing that remains is its red color. This particularized red color is a trope![10] It is no universal of redness, but a particularized property of being red, present in space and time. I could do the same with the weight, the softness, the size, etc. They are all tropes. Another way to explain tropes is to say that they are nothing but spatiotemporally localizable properties, which can be identified with our pre-philosophical use of the word ‘property’. Thus, the red of a certain tomato, for example, is a trope; and the red of a certain fire extinguisher is another trope. Both are real entities belonging to the outside world. When we say that two objects, the tomato and the fire extinguisher share the same property, this is just an equivocal way of saying that they have tropes that are precisely similar to one another. When we say that these two objects have the same color, this is also an equivocal way of saying that they have tropes of colors that are precisely similar, that is, they have a qualitative identity (of one thing with another) instead of numerical identity (of one thing with itself).[11]

   The relationship of precise similarity between tropes is internal to them and primitive, since it excludes explanation or analysis: it is a fact of the world, to which we are so used that we find it difficult to perceive. Our cognitive device makes us able to identify such similarities, and because of this we can apply the same predicative term to two or more tropes and say the same of many... The idea of considering property-tropes as spatiotemporally localizable is, if we consider more carefully, perfectly intuitive. They are the immediate objects of our perceptual attention. They are also objects of selective attention: I can focus my attention on the roar of the stormy sea, on the forms of its waves, on its gray color… and when attentive to its gray color I am not thinking about the gray color itself, but in that particular gray, in that tropes I am seeing now.[12] Furthermore, insofar as we see tropes as spatiotemporally localizable properties, then not only sensible qualities can be classified as tropes, but much  more, in  fact, anything with exception of particulars. Consider the forces of nature: electromagnetic forces, as much as weak and strong forces, are spatiotemporally localizable, even if only in a very diffuse way. The curvature of space-time in the proximity of massive bodies characteristic of a gravitational field is also a trope, since it can also be seen as spatiotemporally localizable in a diffuse way. Also, events, like the performance of a concert are tropes, or made up of tropes of sounds, since spatiotemporally localizable. Psychological properties, like personalities, are also spatiotemporally localizable in human brains. The spin of an electron is a trope, since localizable, not less than the rotation of a galaxy.

   Our paraphrases of B*1, B*2, and B*3 become clarified if we present them in terms of tropical properties:

 

           B**

1.              That tomato and that fire extinguisher have color-properties that are precisely similar to each other.

2.              Color-properties precisely similar to the color-property of this object here (say, a tomato) were found in many other objects.

3.              All of John’s character trait properties and all of Mary’s character trait-properties are precisely similar.

 

The theorization about tropes can be extended in explaining the nature of individual objects such as stones, chairs, people, planets... A physical object like the book you have in your hands is nothing more than a specially organized bundle of tropes: tropes of shapes, white and black tropes, tropes of solidity, flexibility, etc.

   In this way trope theory also provides an answer to the old metaphysical problem of the substance. For some theories of the substance, such as Locke’s, the substance is a bare substratum, an unknowable “we know not what”, which is a repository of properties.[13] The difficulty is that postulating the existence of something that in principle cannot be known seems to be something profoundly contradictory. How can we say that something exists in the absence of an experience that allows us to infer its existence? Locke believed that there was a reason for such inference in the fact that we need to have subjects for the predication of properties, as we cannot begin by predicating properties of the properties themselves.

   However, trope theory makes this postulate unnecessary. A concrete object, the book you have in your hands, is a more or less organized bundle of tropes, and it is such a combination of properties that serves as the subject of predicates. These properties have the property of being compresent – a technical term that means that they are as much co-spatially located as also co-temporally located. In this way, we could think of a material object – to use a Wittgenstein metaphor – as a kind of artichoke, whose leaves represent its properties. It may seem that after we defoliate the artichoke something will be left: the artichoke-in-itself, its substance. However, nothing, in fact, will be left since the artichoke consists only of its leaves.

   This is a point with which I cannot agree fully. It seems to me that there is a trope common to all material objects, something common to a book, a stone, a galaxy, and an electron, which allows us to unify them as material objects, which is what physicians call rest mass. In physics mass is the resistance to the acceleration, that all bodies have, inclusive sub-atomic particles. But mass can increase with the velocity of the body relative to the observer, reaching the infinite if the object could reach the speed of light. Rest mass, on the other hand, is defined as the inertial mass that an object has when it is at rest within an observational system,[14] and we can see this as a complex trope, namely, as a property common to all material objects, from subatomic particles to galaxies, distinguishing them from energy since energy had no (or almost no) rest mass. If it is so, then rest mass is also a trope, but an essential trope distinguishing material objects. Hence, it seems reasonable to introduce the trope-property of rest mas to unify all material objects, since it is also spatiotemporally located.[15] It seems better than the resource to some shameless naked substances.

   One objection against the idea that material objects are associations of tropes is Cris Daly’s remark that if a material object is made up, say, by the tropes T₁, T₂, T₃… Tn, and we unite them by means of a trope of compresence T_c, we have a new trope, which will form a new bundle that would need a new compresence trope T_c1 able to unite the whole, which would produce a regression ad infinitum.[16]

   The answer to this objection is not difficult. A predicative singular sentence has the form Fa. There cannot be any gap between the predicate F and the singular term a. If there were a gap, we would need a relational property linking F with a so that we could write it as the (strange) form FRa. But then we would have no reason to deny new relational properties linking F and R and R and A, building the (still stranger) form FR₁RR₂a, and so indefinitely. In other words, if there were intermediate links between subject and predicate, we would be forced to stuff our world with an infinite number of intermediary links. It is for a similar reason that Cris Daly’s argument does not work. To show this, suppose that we call an object formed by T₁, T₂, and T₃ with the name m. We could formalize the sentence “The m has compresence” as T_cm. Or, if we wish to be more perspicuous, we can formalize Tcm as “T_c{T₁, T₂, T₃}”. What these examples clearly show is that since the compresence is a property that is predicated from the whole bundle of tropes constituting the singular object, there cannot be any gap between them and, consequently, no intermediary link like Tc₁, Tc₂… should be required.

   An objection against the idea that bundles of tropes can be objects of predication is that in this case, every predication would become tautological: to say that this ball is red becomes redundant, because the subject of the predication, the ball, consists of a combination of tropes that already includes red as a constituent.[17] The answer to this objection is in principle very easy: we must distinguish the tropes that essentially constitute the identity of a physical object from the tropes that adhere to the physical object in a contingent, inessential way. Only a combination of tropes essential to the individuation of an object functions as a subject of predication. That is why when we say, “This ball is round”, we say something that is tautological: admitting that ‘This ball’ is the subject of the predicate, we predict from it a trope that belongs essentially to it; but the same does not happen when we say that the ball is red or that it is a rubber ball.

   This same distinction between the tropes or combinations of tropes that essentially constitute a material object and those tropes that are inessential to its constitution makes it possible to respond to the objection that the trope theory does not allow understanding processes of change in concrete particulars. They change without failing to remain the same insofar as what changes is not the combination of tropes that essentially constitute it, but the tropes that make it up contingently.

   Let us now come back to our main problem, namely, how trope theory could explain our apparent statements about abstract universals. Philosophers such as D. C. Williams have suggested that in the place of abstract universals property terms would represent sets of tropes (precisely) similar to each other.[18] These sets of similar tropes could be called tropical universals because, although they do not have the nature of a realist universal, they preserve its function. For instance, the sentence “This tomato has a red color” could be paraphrased as “This tomato-cluster of compresent tropes has a red-trope that belongs to the class of red-tropes that belongs to the class of color tropes”. 

   There are well-known difficulties with this solution. One of them is that similarities must be similar to one another. If precise similarities are tropes, by being similar two similarity tropes generate a higher-order trope of similarity in a process that can be repeated indefinitely producing an infinite regress of new similarity tropes. Another problem is that as a class of tropes as the functional Ersatz for the realist kind of universal must be able to increase and decrease in the number of members, and it does not seem that universals are variable in size. Moreover, sets themselves are considered by many abstract objects.

   To circumvent these problems, I propose translating the classic solution that empiricists like Berkeley and Hume gave to the problem of universals in terms of tropes. As Berkeley noted, if I use a blackboard to prove that the sum of the sides of a triangle is 180⁰, I do not need resort to an abstract triangle to convince that this proof is correct and can be generalized to any triangle.[19] Accordingly, the grasp of a what may be called the tropical universal would demand an operation of the mind based on one only trope, say, a red trope that I have in my mind. Now, to grasp the tropical universal redness, all that I need to be able is to consider the trope of red that I have in my mind or any other trope precisely similar to the first trope. More formally, considering a trope T, in order to reach the tropical universal of T, all that we need is to consider any trope T arbitrary chosen, which I take as a model and call T*, and consider T* or any other trope that is precisely similar to T*. Thus, we can define a tropical universal of T as follows:

 

A tropical universal of T (Df.) = an arbitrarily chosen T* or any other trope precisely similar to T*.

 

That is, to conceive the universal of a trope, we must first be able to represent this trope and then, be able to conceive of the possibility of any trope precisely similar to that trope. In doing so we are already conceiving the tropical universality through that trope.

   We can figure out this simple procedure in a clearer way setting it outside the mind. Imagine a student of painting who is caring a model of an unusual color, say, amaranth red, with him. He intends to verify if there are patches of amaranth red in the pictures present in the room. He compares his piece of amaranth red with the others. After some time, he has found a set of amaranth reds in the studio. Now, to understand or grasp the universal in the sense I am proposing is nothing but to be able to realize such a procedure, not behaviorally, like the student, but mentally, appealing to memory. Nothing more is required. It is true that such conceivable procedures (behavioral or mental) imply the existence of some class of similar amaranth red tropes, a possibly with an immense number of members. Moreover, it is also possible to generate classes of higher-order tropes of precise similarity, and we really appeal to a higher-order precisely similarity when we consider the concept of precise similarity. However, nothing of the kind concerns neither the student nor we, when we identify the color of a picture and say, “this color is amaranth red” in the sense in which we mean “This color is (a property-instance of) amaranth red”, which assumes that we have the capacity to compare qualitatively identical patches of amaranth red.

   If we think in this way, we do not need to be worried in having in our minds perhaps an infinite multitude of patches of amaranth red as the referent class of the conceptual word in our heads, a class to be called the universal amaranth red. In fact, this is an error perpetuated by the logicians who have too hastily identified the reference of a concept word with a class of objects or properties or tropes, and it is the long tradition of identifying the referent of a conceptual word with a class that made many philosophers go astray, including Williams, in his attempt to identify the universal with a sum or class of precisely similar tropes.

   Another point concerns our ordinary concept of property. The word ‘property’ has in my view two senses. In the first sense, it means a trope, a spatiotemporally localizable property like the red of the walls of the Kremlin. In this sense it means a trope, a so-called property-instance. For example, if I am for the first time in the Red Square, point to the wall and say: (i) “This wall is painted red”. Here I simply mean the property-trope of being red that I am looking. In the second sense, however, I mean the tropical universal. When I say to others, (ii) “The Kremlin is painted red”. I typically mean something more general. I mean: (iii) “The Kremlin has a trope of red T that is precisely similar with any trope T of red like the trope of the red model T* that we have in our minds”. In this sense, I also speak about the redness of the walls of the Kremlin. It is true that I could have in mind: (iv) “The Kremlin has a trope of red T that belongs to the class of tropes precisely similar to T”, since this can be deduced from (iii). But since I do not even know this class, this information is of secondary importance.

   We can ask how to interpret more abstract concepts in terms of tropes. Consider the concept of existence. We cannot see the existence of a book, but we see that the book exists. One needs at least one (warranted) applicability of a conceptual rule to assert existence. Consider: “The Moon exists”. Calling Moon ‘M’ and the functor of existence E, the logical analysis will be Ex (Mx) & (y) (My → y = x), which means that the concept of Moon of the earth has the higher-order tropical property of applicability to precisely one object.

   Still, a problem would be that of formal entities like numbers. For the trope theory, they should not be abstract entities, but something constructed out of tropes. For applied arithmetic, this is easy: the two horns of a caw are in some way there since I can see the caw and count her horns. But what about abstract arithmetic? For instance, the abstract number 2? Well, in this case we will need to handle numbers as constructed tropical universals. We can define the number 2 as a set[20] of tropes of double (warranted) applicability (symbolized as ‘a’). The definition of the constructed tropical universal of the number 2 can be stated as follows:

 

The number 2 (Df) = a selected model of a higher-order set-trope of located countable applicability {a, {a, a}}* or any further higher-order set-trope of located countable applicability that is strictly similar (equinumerous) to {a, {a, a}}*.

 

The great advantage of this approach – in the case it shows to be feasible – is that it with a simple stroke solves the old problem of the applicability of arithmetic to our physical world, since it also belongs to it.[21]

   Only the carpet tip of the trope theory has been raised here and, if my amendments are correct, it would be necessary to defend it in a much more careful and detailed way than it has been done so far. The construction of an adequate theory of tropes is an open undertaking that allows us to refrain from the appeal of concepts with questionable intelligibility, particularly because it more correctly analyses the concept of property as it is really used in our common language. As a result, it would finally provide the true descriptive ontology instead of the wishful-thinking ontologies provided by all previous ones.

 

 

 

 

 

 

 

 

 

 

 

 

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[1] The present distinction realism/nominalism is sometimes confused with the distinction realism/idealism about the external world. The first is an ontological distinction (i.e., relative to what is, to what exist) about the most fundamental entities that constitute reality; the second is an epistemological-metaphysical distinction about the nature of what experience gives to us, realism stating that we know an external world independent of the mind and distinct from it, while idealism states that the outside world is in some way mental in nature.

[2] Predicates (predicate expressions, general terms) can be of two types. Adjectival predicates, which have an application rule characterizing the entity to which they apply, and substantive or sortal predicates, whose rule of application involves a rule of particularization, allowing us to distinguish the entity to which they apply from other similar entities. If, for example, someone asks us how many greens there are in the square, we will not be able to answer, because ‘... is green’ is an adjectival predicate; but if someone asks us how many trees there are in the square, we can count them and answer by distinguishing one tree from another, for ‘... is (a) tree’ is a sortal predicate.

[3] Plato’s terms ‘participation’ (methéxis) and ‘copy’ (mímesis) were equally insufficient: participation undoes the unit of the idea, copy, being a symmetric concept, makes the idea identical to its copy. (See Parmenides, part I).

[4] These examples are adapted from the introduction of Loux, Metaphysics (London: Routledge 1998), pp. 25, 31, 32. 

[5] See Gilbert Ryle’s article “Systematic Misleading Expressions”, Meeting of the Aristotelian Society, London 21/3/1936.

 

[6] I adapt these examples from Loux, p. 32.

[7] See D. M. Armstrong. Nominalism and Realism: Universals and Scientific Realism (Cambridge: Cambridge University Press, 1978), vol. 1, p. 12.

[8] In its radical form of one category ontology the theory of tropes was born with D. C. Williams’ article, “The Elements of Being I”, Review of Metaphysics 7, 1953, pp. 3-18 and 171-92. A good selection of papers from Williams, including his locus classicus article, can be found in The Elements and Patterns of Being: Essays in Metaphysics, ed. A. R. J. Fisher (Oxford: Oxford University Press 2018). Later attempts to develop William’s ideas make them in my view unnecessarily weak, Keith Campbell’s Abstract Particulars (Oxford: Oxford University Press 1990) inclusive. My intent here is to preserve Williams radically empiricism and his genially simple insight.

[9] Williams 2018, pp. 32-33. Here abstraction is used in a sense like that of John Locke’s identifying, separating, and excluding. See Locke, An Essay Concerning Human Understanding (Oxford University Press 1979 (1690)), p. 159.

[10] This is also why I do not prefer to classify trope-theory as a form of nominalism. It is true that it denies the existence of universals. But it affirms the existence of references of predicates. The word ‘red’ in the sentence ‘This tomato is red’ refers to the property of being red of this tomato as a property-in-rebus, at least. But it’s the lack of due reference of predicates that is the kernel of nominalism, that concedes existence only to names of individuals.

[11] The concept of similarity alone would not do because it is not transitive.  It is possible that T1 is similar with T2, which is similar with T3… until we reach Tn which though similar with Tn-1 has nothing to do with T1. If we understand precise similarity as the same as qualitative identity, we preserve transitivity, since the degrees of differences between similar tropes are from the beginning established.

[12] See Loux, p. 81.

[13] Locke, p. 95

[14] Physlink.com, # 161. Note that although rest mass isn’t directly accessible to our senses, this fact obviously does not disavow its indirect tropical nature: it is calculated by means that in the end can be grasped by our senses.

[15] Could rest mass unify all particulars? An army, a city, a country, are particulars, but do not have rest mass. But are you sure? A country full of mountains like Tibet must have a lot of rest mass. The fact that the rest mass may be spread does not hinders the definition.

[16] Daly: "Tropes", in D. H. Mellor and A. Oliver (eds.): Properties (Oxford: Oxford University Press) 1997, p. 157.

[17] See M. J. Loux: Metaphysics: a Contemporary Introduction, London 1998, p. 103.

[18] Williams 2018, p. 30.

[19] Berkeley, Of the Principles of Human Knowledge (1710), Introduction, section 12.

[20] The concept of set should also be treated in terms of tropes, though this is not a point to be considered here.

[21] A more extended explanation can be found in Costa, “Natural Numbers as Tropes”, WAB Archives, v. 41, pp. 65-68, 2019. 

WHAT IS PHILOSOPHY?

  

 DRAFT

I

          

NATURE AND DIVISIONS

                                 OF PHILOSOPHY

 

 

 

The philosophy considered in this book arose in ancient Greece. The very word ‘philosophy’ is of Greek origin, literally meaning love (philos) of wisdom (sophia). On the origin of the name, legend has it that, asked what he was, the Greek philosopher Pythagoras would humbly answer that he was not a sage, but only a person in search of wisdom, namely, a philosopher. As we shall see, this answer is illustrative of the difference between the philosopher and the scientist: the philosopher is someone looking for knowledge; the scientist is a person who has sufficient reasons to believe he has found it, to the extent that it makes sense to speak of “finding” knowledge.

 

1. Philosophy and science

One way to try to understand the nature of philosophy is to consider the origin of Western philosophy in ancient Greece around the sixth century B.C. It is well-known that philosophy was conceived as an alternative to mythological and religious explanations of natural phenomena. Rather than continue accepting the explanation of the foundation and origin of our world exclusively by appealing to gods, early Greek philosophers speculatively suggested natural explanatory principles such as water (Thales), fire (Heraclitus), air (Anaximenes), atoms (Democritus), or even abstract principles such as the undefined (Anaximander) and Being (Parmenides). What was the reason for such an extraordinary change in ways of thinking about the world?

   The most plausible explanation is that after earlier Greek thinkers imported scientific knowledge (geometrical, arithmetical, physical, astronomical…) from other cultures, mainly from Egypt, they were the first to consider the nature of such knowledge in itself, as generalizations, in complete abstraction from any conceivable practical applications.[1] The best example is the axiomatization of geometry by Euclid. Although the Egyptians already used geometry in their engineering projects, notably their pyramids, temples and monuments, only the Greeks had the idea of constructing a deductive system of geometry apart from any application. Another example was the development of physical and astronomical laws and explanations. Although Archimedes’ principle of the lever was practically useful, Aristarchus’ genial heliocentric hypothesis, according to which the earth rotates about its axis once a day and revolves around the Sun in a year, the fixed stars being celestial bodies similar to the Sun, although much more distant… was surely useless in his time. And possibly the most striking example of an empirical scientific achievement without any practical application at the time was Eratosthenes’ measurement of the diameter of the earth by by means of triangulation.

   This curiosity going far beyond practical aims can very well explain the birth of speculative philosophy in the thinking of pre-Socratic philosophers. They were also scientists. Thales of Miletus, identified by tradition as the first Greek philosopher, was also an astronomer who once predicted a solar eclipse. This means that these philosophers had already achieved an understanding of the procedures of the sciences, both formal and empirical, that is, they already had a well-formed conception of science. This makes it plausible that Greek philosophy was born from the application of this already incorporated conception of science to speculative issues which were previously addressed exclusively by religion and mythology, such as the question of the ultimate nature of all things or of the origins and fate of the universe. Even if these issues were far from being concretely addressed and explained by the science of their time, they could still be speculatively addressed using the resources of vague ideas like “natural powers”, “abstract entities”, and “personified abstractions”, to borrow some terms of Auguste Comte. Proposing first principles such as water, air, the undefined and Being, was an early attempt to unify the understanding of reality within the framework of highly speculative generalizations.

     If this explanation is correct, if Western philosophy was born from an application of the conception of science to domains in which scientific procedures were objectively impossible, how then can we distinguish the philosopher’s procedures from the scientist’s procedures? It seems that the answer to that question leads us to important considerations about the nature of philosophy itself, or at least parts of it. Even though the rational procedures of philosophers are similar to those of natural scientists (philosophy usually seeks to establish true generalizations from data of some kind, trying to offer explanations based on these generalizations, as much as the natural sciences...), there is a fundamental difference in that for philosophy, unlike science, such rational procedures are merely conjectural or speculative. That was the way it was from the start. What the first Greek philosophers did was to speculate, to proceed by conjectures, and the fact that during more than two millennia these conjectures have come to be argued in more and more refined, complex, and diversified ways, receiving a treatment that tends to become increasingly rigorous and sophisticated, does not transform them into something else.

   On the other hand, philosophy is said to be the cradle of the sciences.[2]  As J. L. Austin explained in an insightful, well-known passage:

 

In the history of human inquiry, philosophy has the place of the initial sun, seminal and tumultuous: from time to time it throws off some portion of itself to take a station as a science, a planet, cool and well regulated, progressing steadily towards a distant final state. This happened long ago at the birth of mathematics, and again at the birth of physics; only in the last century have we witnessed the same process once again, slow and at the time almost imperceptible, in the birth of the science of mathematical logic, through the joint labour of philosophers and mathematicians.[3]

 

Austin’s own speech act theory, explaining the rules of linguistic interaction, is an example of this. He needed many years to develop what is today taught more in linguistics than in philosophy courses. The fact that philosophy is the cradle of the sciences gives rise to another question: how much of philosophy can be considered as a kind of anticipation of science – a protoscience? Its entirety, or only its non-essential domains?

   Another question is: what does it mean to say that an investigation is speculative or conjectural? The answer is: an investigative procedure is purely conjectural (or speculative) whenever the possibility of consensus about its results is totally out of reach. This is, as we shall see, the fundamental difference between philosophy and science: while in science it is relatively easy (or at least not impossible) to obtain a consensus – an interpersonal agreement about results – this consensus remains unattainable for philosophy. The explanation of the effects of levers using the law of the lever offered by the Greek scientist Archimedes can be tested and publicly verified Everyone can agree on this explanation after making a few empirical measurements. In contrast, to explain the generation and destruction of things through the action of the forces of love (philía) and hatred (neîkos) on the four elements (water, air, earth and fire), as the pre-Socratic philosopher Empedocles did, is to embark on an inevitably vague and obscure speculative investigation. This encompasses areas of questioning in which the possibility of achieving free consensual agreement based on empirical methods seems practically impossible.

     The conjectural character of philosophy explains why it is typically an argumentative and aporetic undertaking: where consensus cannot be reached on results, what remains possible is to formulate hypotheses and discuss their possible consequences. The conjectural character of philosophy also explains the lack of linear progress in its domains. The fact that philosophy cannot reach consensus on its results means that in philosophical practice, philosophers find it almost impossible to make decisive inter-theoretical comparisons. While it is generally agreed that relativistic mechanics is superior to Newtonian mechanics, given its greater explanatory power, many do not agree that Berkeley’s proposed nominalism provides more plausible explanations than Platonic or Aristotelian realism, since these are philosophical doctrines.

     Why is it that philosophy cannot reach consensus on results? The answer is that there can only be consensus about results when there is a previous consensus about what is being assumed in research – a kind of agreement that is lacking in philosophy. In philosophy there is no agreement on the adequacy of the questions (many of the philosophical questions, it is suspected, are nothing more than pseudo problems resulting from verbal confusions). Nor is there agreement on the adequacy of the evaluation procedures leading to answers for questions (an argument may seem conclusive to one philosopher and irrelevant to another). Indeed, all these conditions are only really satisfied by science, because only science has consensually accepted assumptions and evaluation procedures. Without satisfying any of these presuppositions, we cannot hope to achieve true consensus concerning results, and are limited to the aporetic discussions typical of philosophy.

   The considerations presented so far vindicate the attempt to clarify the nature of philosophy by developing its similarity and contrast with science. This kind of comparison is impossible if we define science from the reductionist conceptions imposed on us by traditional philosophers of science, especially those of the positivist trend, who improperly extrapolate criteria to all domains of current science that are drawn from the research of a particular fundamental science like physics (Karl Popper, for example, thought that the theory of evolution should not be considered scientific, because it is unable to be the object of repeated observations, as is the case with the theory of relativity). We feel that our idea of philosophical research is one of something too comprehensive and abstract to let itself be possibly captured by any such down-to-earth experimentalist conceptions of science. In contrast to this, it should be noted that this is in no way what we usually mean when most of us – even scientists themselves – talk of science. In what follows I present a conception of science that is liberal enough to encompass any would-be science that could be derived from philosophical speculation.

   We can find this liberal conception of the nature of science in the kind of social conception of science proposed by the physicist J. M. Ziman.  According to him, science in all its forms should be understood as “consensualizable” public knowledge.[4] Under his perspective, the most striking characteristic, common to all sciences, both empirical and formal, is that they contain generalizations able to be consensually accepted as true by members of a scientific community of ideas. This conception of science, in addition to being perfectly in line with what we usually and naturally tend to call science, seems ideal as a means to contrast science with philosophy. Indeed, not only physics, but also chemistry, biology, geology, linguistics, philology, anthropology, and much of psychology and economics, for instance, can be called scientific from this broad perspective.

     Against the conception of science as consensual public knowledge we can make the following objection. There are political, religious, mystical communities in which consensus is imposed from the top down, excluding the possibility of critical evaluation of the issues in question. Notable examples of this were the intrusions of political ideologies into what could or should count as science in Nazi Germany and the former Soviet Union. However, it seems that according to Ziman’s characterization, the results of these ideological intrusions should be admitted as belonging to science, since they were consensually accepted as true by a scientific community. But that cannot be! Therefore, the consensualist-oriented conception of science suggested above seems unable to separate science from ideology.

    The answer to this difficulty is to apply here a distinction between true and false consensus, based on a better characterization of what can be understood as a community of ideas able to produce science. We can call this institution a critical community of ideas, understanding it as one that satisfies conditions like those specified by Jürgen Habermas for what he called the ideal speech situation (ideale Sprachsituation).[5] This means that a critical community of ideas must satisfy some conditions of freedom and rationality for the evaluation of the results of investigations, such as:

 

1.              the condition of making it possible for the members of a community of ideas to hold critical discussions oriented to the truth and free of any coercion, to exclude pressures other than those of the rationality of arguments themselves,

2.              the condition that members of the community of ideas have free access to information and the same chances of offering new ideas, improvements, objections, and critique,

3.              the condition of competence and equivalence in the training of members of the community of ideas.

 

These are conditions for authentic consensus. It is true that conditions like these are never completely met. However, a reasonable satisfaction of such conditions is simply indispensable to establish a consensus suitable for scientific rationality. In fact, scientists can only do science because they idealize a critical community of ideas in their minds when doing their research. And when we hear of a new scientific discovery, we always believe scientific claims for it only if we can reasonably assume that in developing its new findings, the scientific community has satisfied to a sufficient extent conditions such as those mentioned above.[6]

   Beyond this, there are, certainly, the criteria of objectivity, that the members of a scientific community accept necessary assumptions in order to achieve agreement (for instance, the replicability of an experiment in biology). It is this previous agreement on assumptions (methods, data, theories, etc.) which only science has and that is a pre-condition for the possibility of agreement and scientific progress.

   With all this in hand, we are now prepared to present a straightforward comparison between philosophy as anticipation of science (proto-science) and science as consensualizable public knowledge. The contrast is possible insofar as we characterize science as follows:

 

1) Science:  An investigation aimed at obtaining a set of non-trivial generalizations, which will be accepted as consensually true by the members of a critical community of ideas (the so-called scientific community).

 

On the other hand, we characterize philosophy by its similarity and contrast with scientific research, as follows:

 

Philosophy: An investigation aimed at obtaining a set of (non-trivial) generalizations, which is carried out by members of a supposed critical community of ideas (philosophers), but only to the extent that this community is unable to reach any agreement regarding the truth of these generalizations.[7]

 

What this contrast suggests is that everything that belongs to philosophy can in principle, at least, become part of science, insofar as agreement can be established on assumptions that are sufficient to enable authentic consensus about results. In other words: philosophy is what can be done in the impenetrable domains where science – understood as critically consensual knowledge – has not yet been proved possible and perhaps never will be. “Science,” as Russell noted, “is what we know; philosophy is what we don’t know”... “Science is what we can prove to be true; philosophy is what we cannot prove to be false”.[8] With this, the observation made at the beginning of this chapter, that philosophy is the search for truth, and not finding and having it, is better clarified: when philosophy finally finds the truth, it has already lost it to science.

   Surveying the history of science, the idea of philosophy as an anticipation of science has been confirmed again and again. Let’s look at some examples. Mathematics began to separate itself from philosophy already in the ancient world, as Euclidean Geometry shows, though in the ideas of Pythagoras it was still entangled with philosophy and mysticism. Classical logic, though only systematized as a syllogistic by Aristotle, had its law of non-contradiction already anticipated by Parmenides, though still dressed in the garb of metaphysics. Turning to the empirical sciences, according to Karl Popper, the Greek philosopher Anaximander (century VI B.C.)  vaguely anticipated the ideas of inertia and gravitation by suggesting that the earth could be a cylinder floating in empty space, without falling down or to either one side or another, because of its distance from the other stars.[9] The atomist philosophers Leucippus and Democritus, more than two thousand years ago, had already launched the idea of the existence of an infinite number of invisible and physically indivisible particles, which could be aggregated, constituting visible matter, thus explaining its properties. They thus anticipated the scientific discovery of subatomic particles by contemporary physics. The periodic table of current chemistry has taken the place of the long-superseded doctrine of the four elements (water, earth, air and fire) of ancient philosophy. Galileo’s experimental physics replaced Aristotle’s rocking-chair speculative physics of natural places and motions, making possible the scientific development of this fundamental science. Contemporary biology has replaced the vague vitalist theories of philosophers, who flourished from Aristotle to Bergson. The platonic theory of the tripartition of the soul finds a more developed equivalent in the structural theory of mind in Freudian psychoanalysis, which divides it into Ego (Ich), Id (es) and Super-ego (Über-Ich) (although psychoanalysis still falls short of having scientific standards which would make it possible to achieve consensus among its practitioners). And today we believe that when we finally obtain confirmed scientific knowledge of how the human mind actually works – the most puzzling enigma of our time – many problems of our current philosophy of mind and psychology will give way to critical consensus and, therefore, to scientific solutions.

     We cannot for sure say the same about the central fields of philosophy considered in the present book, including metaphysics, epistemology, mind-body relationships, ethics… But it is not impossible. One can argue that it only seems impossible when we consider these fields from a reductionist viewpoint that denies possible scientificity to the presently unmeasurable non-experimental domains of science, as positivist philosophers have done. But when we consider the mutual support that a growing number of different fields of science can give one another, when we consider the idea of science free from prejudices (as in Ziman’s case), this idea ceases to be fanciful.

 

DIVISIONS OF PHILOSOPHY

Starting with Aristotle, philosophy has usually been subdivided into theoretical and practical domains.  We can understand practical philosophy as one which deals with human activity and its products; theoretical philosophy, for want of a better definition, can be negatively defined as the philosophy that does not serve such purposes.

   Under these assumptions, traditionally we find two main subdivisions of theoretical philosophy: epistemology and metaphysics. Epistemology, or theory of knowledge, is concerned with the investigation of the nature, origin, and limits of knowledge. Questions such as “What is knowledge?”, “What is truth?”, “How is knowledge justified?”, “What are the sources of knowledge?”, “How can we answer skeptics?”, can be considered as belonging to epistemology. Metaphysics, on the other hand, is above all[10] an investigation of “being qua being”, better said, the investigation of those things that constitute the broadest domain of knowledge and their relations to one another.[11]  Such things can be universal properties, material substances, states of affairs, space and time, causality, number, etc. The extreme breadth of the domain where we deal with such things marks a difference between metaphysics and particular sciences, since most objects of metaphysics pass through the sciences by being absorbed into their terminology. Thus, the category of property applies simply to all scientific domains, empirical and formal. The category of material substance, as well as of causality, is presupposed by physics, chemistry, biology, and many other empirical sciences. Space and time are assumed by all empirical sciences. The same with the category of number: after all, what science does not presuppose numbers? (because of this, metaphysical categories are also called “framework questions”, though this can be deceptive, suggesting that they are subjective constructs). Furthermore, since Descartes, modern philosophy has considered epistemology and metaphysics as in some way complementary disciplines: as Locke noted[12], only by knowing the limits of what we can know will we be aware of which objects legitimately belong to the domains of our knowledge and what are beyond its possibilities (possibly entities like God, and questions like “Why does the world exist?”). The reciprocal, however, seems equally true: it is only by identifying and examining the objects belonging to the most general domains of knowledge that we acquire methods to evaluate the most general characteristics of our cognitive faculties.

    Traditionally related to metaphysics is today’s much discussed philosophy of mind. It deals with issues such as the nature of consciousness, the relationship between the mental and the physical, mental causality, which allows our identification of persons as remaining the same across time (the so-called problem of personal identity) …

    Regarding practical philosophy, which comprises human activity and purposes, as well as its products, we could include much, much more than this book can cover. Philosophy of action, the complex domain of ethics (which investigates moral action), the philosophy of history (which broadly investigates the changes effected by social action), political philosophy, aesthetics (which investigates artifacts resulting from human action), the philosophy of culture (which investigates human culture and its products like art and even philosophy), the philosophy of life...

   In fact, philosophical questions intertwine in such a way that it can often be difficult to tell which division a problem belongs to. Due to this intertwining of philosophical questions, I chose to divide this book not into general sections, but into chapters, each of them introducing and discussing some central problem of philosophy.

 

 

 

 

---

[1] W. K. C. Guthrie: A History of Greek Philosophy (Cambridge: Cambridge University Press, 1962), vol. 1, p. 36 ss.

[2] Anthony Kenny, Aquinas on Mind (London: Routledge 1993), Introduction.

[3] J. L. Austin, Philosophical Papers (Oxford: Oxford University Press, 1979), p. 232.

[4] This is the thesis on the nature of science advocated by J. M. Ziman in Public Knowledge: An Essay Concerning the Social Dimension of Science (Cambridge: Cambridge University Press 1968), cap. 2. As ne noted: “science, as a corpus of knowledge, as what scientists do, and as an institution, can’t be treated separately, more than a solid can be reconstructed from its projection upon separated Cartesian planes.” p. 42.

[5] See Jürgen Habermas, Wahrheitstheorien, em H. Fahrenbach (ed.), Wirklichkeit und Reflexion (Neske Vlg. Pfullingen 1973).

[6] One point to be emphasized about this characterization is that the exercise of philosophy presupposes a critical community of ideas able to discuss philosophical ideas, even if in some cases, such as those of wrecked philosophers like Vico, Peirce and Nietzsche, in a counterfactual way.

[7] This is not, of course, an all-inclusive definition, since philosophers have also suggested views of what they do that oppose this characterization (e.g. Wittgenstein’s descriptivist view of philosophy). Nevertheless, it agrees fairly well with what we really find in practice.

[8] Apud. afterword by Allan Wood to Bertrand Russell’s book, My Philosophical Development (London: Routledge, 1995).

[9] See K. R. Popper in "Back to the Pre-Socratics", in Conjectures and Refutations, New York 1962, p. 138.

[10] The term ‘metaphysics’ (Aristotle’s first philosophy) has several meanings, this is maybe the most proper.

[11] See G. E. Moore: “What is Philosophy?”, in Some Main Problems of Philosophy, (London: Routledge 2003).

[12] See “Epistle to the Reader”, in J. Locke: An Essay Concerning Human Understanding, (Oxford: Oxfor