Standard Abundant Platonism (SAP) holds that to every predicate there corresponds a property, and items satisfy the predicate if and only if they exemplify the property. Moreover, it holds that exemplifiers are not explanatorily prior to what they exemplify. Normally, we think of SAP as a two-category theory: individuals and properties.
But here is a suspicion I have. Little if any explanatory work is being done by the distinction between individuals and properties. The serious explanatory work is all being done by the relation of exemplification. Here are two examples.
1. Standard Platonists say that x and y are exactly alike in some respect if and only if there is some property P such that x exemplifies P and y exemplifies P. But drop the word "property" from the previous sentence, and we have an account of exact alikeness that is even better: x and y are exactly alike in some respect if and only if there is a z such that x exemplifies z and y exemplifies z. This is extensionally just as good, but simpler. (One can do more complex stuff about determinates and determinables to get resemblance in some specific respect, but again that doesn't need the concept of property, just the relation of being a determinable of.)
2. Standard Platonists say that to each predicate F there corresponds a property Fness, and that x is F if and only if, and if so because, x exemplifies Fness (we should probably have an exception to the "because" clause when Fness is exemplification). But change "there corresponds a property Fness" to "there corresponds an entity Fness", and this works just as well as an account of predication.
Besides, the concepts of "individual" and "property" are foggy. (We might try to say: "x is an individual if and only if x cannot be exemplified." But that doesn't work for abundant Platonism, as abundant Platonism will have properties like being a square circle.)
So, if you're going to be a Platonist, why be a two-category abundant Platonist? Why not be a one-category abundant Platonist instead?
Showing posts with label properties. Show all posts
Showing posts with label properties. Show all posts
Friday, April 15, 2011
Saturday, January 30, 2010
Contest: Can a property be a person?
According to some versions of the doctrine of divine simplicity, God is identical with the property of divinity. I am planning on writing up a (limited) defense of this identity, and to that end I am hereby offering an argument contest with very modest prizes, with the hope of getting really good submissions to argue against in my paper (unless perhaps I am convinced by the submissions!).
Here is the task for the contest. Grant for the sake of the argument that:
- There is at least one necessarily existing person.
- Realism about properties is correct.
The reason why I ask that the arguments grant these assumptions is that I am not interested in variants on the following two arguments: (1) All properties are necessary beings, every person is contingent, and, therefore, no property is a person; (2) There are no properties, and, therefore, no property is a person.
The deadline is the end of February, 2010, Central Time.
I will give a $50 amazon.com gift certificate to the person who, in my subjective judgment, has submitted the most powerful, reasonably brief (there is an approximately 6000 character limit) original argument (of course, an original argument can build on arguments by others, including arguments submitted to this contest). If your argument has already appeared in published work, you may use it for the contest--but don't give a reference in your submission, because then I'll think that it's not original, because I'll be judging blindly. In case I can't decide on the winner, I will do a random draw among those I consider to be finalists.
However, it is not necessary to submit an original argument to enter. All entrants who give a serious argument that was not already posted by the time their entry was submitted, even if that argument is not their own (hopefully it comes with a reference!), will have a chance to win a $30 amazon.com gift certificate by random drawing. While the best-argument prize you can enter several times to improve your chances (with different arguments!), the random drawing you get only one chance at, no matter how many entries you submit.
Submissions must be posted via the form in this link. This ensures that judging will be done blindly--the entries are separated from the entrant names. But to be eligible for a prize, you must include your real name.
From time to time, I'll be posting serious submissions as comments on this blog post, without the entrant's name. (What counts as original will be relative to what was posted at the time.) At the end of the contest, I may post a comment identifying by name those entrants who checked the box releasing their names.
Prior to posting, you might want to see this discussion of the issue, as well as the comments below. This may also keep down the submissions of non-original arguments.
The comments to this post are open to discussion of the arguments posted. I may, for instance, post critical responses. You are free to submit an improved version of your argument--or a supplement to your argument--to be judged together with your original argument (in that case, reference your first version by entry number). But only arguments submitted via the above-linked form count as entries.
I am the final arbiter of how the contest proceeds, and no appeal is possible. I reserve the right to disqualify entries for any reasons I see fit. If computer problems destroy entries or fail to record them correctly, then that's just your tough luck. The winner is responsible for all the tax implications of the prize.
The arguments should not be written as complete papers. A simple, fairly concise numbered or informal argument suffices.
Tuesday, September 29, 2009
Resemblance Nominalism and Tropes
Here’s the outline of a paper I´m starting to work on. If anybody has some spare time and wants to take a look, comments are very welcome (sorry for the length)!
Nominalists about the ontological constitution of material objects aim to dispense with both universals and bare particulars and yet provide an economic and compelling account of similarity and individuation.
Resemblance nominalism is the view that only concrete particulars exist, and properties are derivative on similarity classes of such particulars. This view has to deal with the traditional Goodmanian objections based on the possibility of coextension, imperfect community and companionship; it must also explain why the very same object couldn’t have any properties whatsoever (since an object’s belonging to a similarity class appears to be a contingent fact). Rodriguez-Pereyra recently defended resemblance nominalism by endorsing counterpart theory (every object possesses its properties - i.e., partakes in specific similarity classes - necessarily) and realism about possible worlds (the coextension problem is solved if similarity classes also comprise merely possible objects); and proposing a complex notion of resemblance, according to which resemblance holds in various degrees and in an iterative way - between pairs of objects, pairs of pairs of objects etc. (this latter move neutralises the problems of imperfect community and companionship). These are, clearly, non-negligible commitments. An alternative would be to give up the assumption that ordinary objects are the ‘unit of discourse’ and assume that the fundamental building blocks of reality are simple (=belonging to one similarity class) concrete particulars. This would immediately solve the Goodmanian difficulties. However, the problem with the contingency of property-possession remains. If one doesn’t like counterpart theory, it would seem, this problem can only be obviated by going trope-theoretic, that is, by identifying each simple concrete object belonging to only one similarity class with its ‘qualitative content’.
Trope theory, however, has the problem that at least some properties appear dependent on objects rather than constitutive of them (think of colour, or shape properties): with respect to their identity (this table’s hardness, not this hardness, which may or may not compose a table) and their number (since I can tear this white sheet in arbitrarily many pieces, it looks as though there is no fixed number of whiteness tropes in it - the so-called boundary problem). The obvious solution is to endorse a sparse and reductionist account according to which only physically basic, simple properties (e.g., the mass or charge of elementary particles) are genuine tropes. However, this seems to go in the direction of resemblance nominalism, as the trope-theorist attempts to defend the view by making tropes concrete, rather than abstract, particulars.
This may seem circular. However, think about the difference between an elementary particle and its qualitative aspects (mass, charge, spin, colour): do they belong to clearly distinct ontological categories? Or would it be plausible to regard mass etc. as material constituents of a more complex, but equally concrete, particular? A third way emerges, in which the nominalist (thanks to the abovementioned sparse-reductionist approach to properties) takes simple, concrete particulars essentially provided with a qualitative content as fundamental entities. Interestingly, this view was proposed by Sellars already in 1963 (‘Particulars’), where he argues in detail that the property/object distinction can and should be overcome, and proposes an ontology of ‘simple particulars’. Perhaps it would be interesting (for nominalists at least) to examine this Sellarsian option in more detail?
Nominalists about the ontological constitution of material objects aim to dispense with both universals and bare particulars and yet provide an economic and compelling account of similarity and individuation.
Resemblance nominalism is the view that only concrete particulars exist, and properties are derivative on similarity classes of such particulars. This view has to deal with the traditional Goodmanian objections based on the possibility of coextension, imperfect community and companionship; it must also explain why the very same object couldn’t have any properties whatsoever (since an object’s belonging to a similarity class appears to be a contingent fact). Rodriguez-Pereyra recently defended resemblance nominalism by endorsing counterpart theory (every object possesses its properties - i.e., partakes in specific similarity classes - necessarily) and realism about possible worlds (the coextension problem is solved if similarity classes also comprise merely possible objects); and proposing a complex notion of resemblance, according to which resemblance holds in various degrees and in an iterative way - between pairs of objects, pairs of pairs of objects etc. (this latter move neutralises the problems of imperfect community and companionship). These are, clearly, non-negligible commitments. An alternative would be to give up the assumption that ordinary objects are the ‘unit of discourse’ and assume that the fundamental building blocks of reality are simple (=belonging to one similarity class) concrete particulars. This would immediately solve the Goodmanian difficulties. However, the problem with the contingency of property-possession remains. If one doesn’t like counterpart theory, it would seem, this problem can only be obviated by going trope-theoretic, that is, by identifying each simple concrete object belonging to only one similarity class with its ‘qualitative content’.
Trope theory, however, has the problem that at least some properties appear dependent on objects rather than constitutive of them (think of colour, or shape properties): with respect to their identity (this table’s hardness, not this hardness, which may or may not compose a table) and their number (since I can tear this white sheet in arbitrarily many pieces, it looks as though there is no fixed number of whiteness tropes in it - the so-called boundary problem). The obvious solution is to endorse a sparse and reductionist account according to which only physically basic, simple properties (e.g., the mass or charge of elementary particles) are genuine tropes. However, this seems to go in the direction of resemblance nominalism, as the trope-theorist attempts to defend the view by making tropes concrete, rather than abstract, particulars.
This may seem circular. However, think about the difference between an elementary particle and its qualitative aspects (mass, charge, spin, colour): do they belong to clearly distinct ontological categories? Or would it be plausible to regard mass etc. as material constituents of a more complex, but equally concrete, particular? A third way emerges, in which the nominalist (thanks to the abovementioned sparse-reductionist approach to properties) takes simple, concrete particulars essentially provided with a qualitative content as fundamental entities. Interestingly, this view was proposed by Sellars already in 1963 (‘Particulars’), where he argues in detail that the property/object distinction can and should be overcome, and proposes an ontology of ‘simple particulars’. Perhaps it would be interesting (for nominalists at least) to examine this Sellarsian option in more detail?
Thursday, March 26, 2009
The Age of Hyperintensionality
A place in a sentence is extensional if words with the same extension can always be substituted into it without changing the truth-value of the whole sentence. (That definition is a little too crude in about three ways, but bear with me.) A place in a sentence is intensional, in one sense of “intensional”, when words that necessarily share the same extension can always be substituted into it without changing the truth-value of the whole sentence.
It has become increasingly clear since the 1970s that we need to carve meanings more finely than by “intensions” in the sense associated with the specification above. Call the sorts of intensions employed, for example, by Richard Montague possible worlds intensions. Handling belief clauses by insisting that anyone who believes something believes everything necessarily equivalent to it has always caused problems. Once we accept that names are rigid designators, allowing their substitution in all sorts of representational and psychological contexts causes trouble: the Sheriff of Nottingham can be hunting for Robin Hood without hunting for Robin of Locksley, or so it seems.
There seem to be places outside our psychological talk that require hyperintensionality. Talk of entailment in the sense of logical consequence, for example: it does not logically follow from apples being red that all bachelors are unmarried, let alone that water is H2O, even though it does follow that either apples are red or apples are not red. Use of counter-possible conditionals is another example: two conditionals can have necessarily false antecedents but differ in truth-value. Talk about moral obligation and permission seems to be hyperintensional, as anyone struggling with substituting logical equivalents in the scope of deontic operators may have seen. I’m just back from a conference in Colorado where people were insisting that “in virtue of”, “because”, and other explanatory expressions were hyperintensional. (Benjamin Schnieder, Gideon Rosen and Kit Fine were three in particular.) Once you look around you see quite a bit of hyperintensionality.
There’s a piece of rhetoric I associate with Richard Sylvan about this. He was fond of suggesting that there would be a move from using possible-worlds intensions to using hyperintensional resources that would parallel the move made from extensionalism to possible-worlds intensionalism. In the nineteen-sixties, the big goal was to be able to do philosophy of language while treating language extensionally: think of Davidson’s project in particular, though Quine was also a big booster of the extensionalist program. I guess it was typical of that project to assign extensions to categories of expressions, and then have some syncatogramatic expressions that operated on extensions to yield other extensions. (E.g. “all” did not get an extension, but (All x)(Fx) operated on the extension of “F” to yield a sentence-extension, i.e. a truth-value)
There are still people trying to carry out that extensionalist project, but it came under increasingly severe attack since the early 1970s. (And maybe earlier: I think Carnap might be an important precursor here, along with Prior, and perhaps many others). The extensional programme was not very satisfying in its treatment of propositional attitude reports, entailment, normative discourse such as the use of “ought”, and a number of other areas. But the star witness against the extensional programme was modal vocabulary. Treating “necessarily” extensionally does not get you very far, and after Saul Kripke popularised possible-worlds semantics for “necessarily”, the floodgates started to open. Richard Montague and David Lewis were among the vanguard of those arguing for a systematic, intensional treatment of natural language, arguing that it handled all sorts of constructions that extensional treatments faced serious difficulty with.
The intensions that Montague and Lewis relied upon were set-theoretic constructions out of possible worlds and possible individuals. (Not just sets of possibilia or functions from possibilia to possiblia, but also sets of those sets, functions from those functions to other functions, etc. etc.) The Montague project of trying to handle all of language with these possible-worlds intensions is alive and well today: I take Robert Stalnaker to be one of its prominent contemporary philosophical defenders, though I haven’t scrutinised his recent work to see if any weakening has happened.
But I think that project is doomed. There is too much work that needs to be done that requires hyperintensional distinctions, and those trying to hold the line that everything can be done with possible-worlds intensions will look as outdated in thirty years as the extensionalists look to the intensionalists today.
Of course, even if we decided we wanted to do more justice to hyperintensional phenomena than standard possible-worlds semantics, we have several options about how to go on from here. The response that is perhaps closest to the standard possible-worlds tradition is to let the semantic value of a piece of language be a pair of a possible-worlds-intension plus some kind of constituent tree, that serves as a logical form or otherwise conveys information about the internal linguistic structure of the expression. Alternatively, we could let the semantic value of a complex expression be a tree whose nodes are possible-worlds intensions: Lewis discusses this way of going, for example, in OTPW p 49-50.
Another response that is close to the possible-worlds tradition is to use impossible worlds as well as possible ones. Since things that do not vary across possible worlds can vary across impossible worlds, impossible worlds give us finer-grained distinctions. If we allow logically impossible worlds, we can even get the effect of places in sentences where substitution of logical equivalents fail, since for example the worlds where (p or not-p) obtain need not be the ones where (q or not-q) obtain. I take it that semantics using situations instead of worlds is often a close cousin of this.
More radical responses to hyperintensionality include moving to an algebraic semantics, such as the sort advocated by George Bealer. Even these can be seen as successors to the possible-worlds tradition, since the structures of the algebras are often inspired by the structural relationships possible-worlds intensions stand in to each other. No doubt philosophers will come up with other approaches too - some revert to talking about Fregean senses and functions on them, though whether this is much more than a cosmetic difference from algebraic approaches I’m not sure.
Why does this matter for metaphysics? Well, one immediate reason it matters is that the metaphysics of language had better be able to cope with hyperintensionality and hyperintensions. One place that disputes in the philosophy of language often spill over is into the metaphysics of meaning, of truth (or at least truth-conditions), of propositions and so on.
A connected reason is that respect for hyperintensionality might go along with more warmth towards hyperintensional entities. We may be less likely to smile on the demand that properties that necessarily have the same instances are identical, for example. This in turn may motivate rejecting the picture of properties as sets of their actual and possible instances. Indeed, set theory might be of less use in metaphysics in general once we want to individuate things hyperintensionally.
There are other ways the hyperintensional turn could affect metaphysics. It might make us more sympathetic to impossible worlds, for example: I’ve argued elsewhere that counter-possible conditionals give us a good reason to postulate impossible worlds. It might make us think that some relational predicates are not associated with relations, or maybe are associated with finer-grained relata than they appear to be associated with: see Carrie Jenkins’s post about grounding. Modal analyses of hyperintensional pieces of language seem unappealing, since modal analyses are normally only intensional not hyperintensional. I could go on.
So, metaphysicians, join the hyperintensional revolution! You have nothing to lose but your coarse grains!
It has become increasingly clear since the 1970s that we need to carve meanings more finely than by “intensions” in the sense associated with the specification above. Call the sorts of intensions employed, for example, by Richard Montague possible worlds intensions. Handling belief clauses by insisting that anyone who believes something believes everything necessarily equivalent to it has always caused problems. Once we accept that names are rigid designators, allowing their substitution in all sorts of representational and psychological contexts causes trouble: the Sheriff of Nottingham can be hunting for Robin Hood without hunting for Robin of Locksley, or so it seems.
There seem to be places outside our psychological talk that require hyperintensionality. Talk of entailment in the sense of logical consequence, for example: it does not logically follow from apples being red that all bachelors are unmarried, let alone that water is H2O, even though it does follow that either apples are red or apples are not red. Use of counter-possible conditionals is another example: two conditionals can have necessarily false antecedents but differ in truth-value. Talk about moral obligation and permission seems to be hyperintensional, as anyone struggling with substituting logical equivalents in the scope of deontic operators may have seen. I’m just back from a conference in Colorado where people were insisting that “in virtue of”, “because”, and other explanatory expressions were hyperintensional. (Benjamin Schnieder, Gideon Rosen and Kit Fine were three in particular.) Once you look around you see quite a bit of hyperintensionality.
There’s a piece of rhetoric I associate with Richard Sylvan about this. He was fond of suggesting that there would be a move from using possible-worlds intensions to using hyperintensional resources that would parallel the move made from extensionalism to possible-worlds intensionalism. In the nineteen-sixties, the big goal was to be able to do philosophy of language while treating language extensionally: think of Davidson’s project in particular, though Quine was also a big booster of the extensionalist program. I guess it was typical of that project to assign extensions to categories of expressions, and then have some syncatogramatic expressions that operated on extensions to yield other extensions. (E.g. “all” did not get an extension, but (All x)(Fx) operated on the extension of “F” to yield a sentence-extension, i.e. a truth-value)
There are still people trying to carry out that extensionalist project, but it came under increasingly severe attack since the early 1970s. (And maybe earlier: I think Carnap might be an important precursor here, along with Prior, and perhaps many others). The extensional programme was not very satisfying in its treatment of propositional attitude reports, entailment, normative discourse such as the use of “ought”, and a number of other areas. But the star witness against the extensional programme was modal vocabulary. Treating “necessarily” extensionally does not get you very far, and after Saul Kripke popularised possible-worlds semantics for “necessarily”, the floodgates started to open. Richard Montague and David Lewis were among the vanguard of those arguing for a systematic, intensional treatment of natural language, arguing that it handled all sorts of constructions that extensional treatments faced serious difficulty with.
The intensions that Montague and Lewis relied upon were set-theoretic constructions out of possible worlds and possible individuals. (Not just sets of possibilia or functions from possibilia to possiblia, but also sets of those sets, functions from those functions to other functions, etc. etc.) The Montague project of trying to handle all of language with these possible-worlds intensions is alive and well today: I take Robert Stalnaker to be one of its prominent contemporary philosophical defenders, though I haven’t scrutinised his recent work to see if any weakening has happened.
But I think that project is doomed. There is too much work that needs to be done that requires hyperintensional distinctions, and those trying to hold the line that everything can be done with possible-worlds intensions will look as outdated in thirty years as the extensionalists look to the intensionalists today.
Of course, even if we decided we wanted to do more justice to hyperintensional phenomena than standard possible-worlds semantics, we have several options about how to go on from here. The response that is perhaps closest to the standard possible-worlds tradition is to let the semantic value of a piece of language be a pair of a possible-worlds-intension plus some kind of constituent tree, that serves as a logical form or otherwise conveys information about the internal linguistic structure of the expression. Alternatively, we could let the semantic value of a complex expression be a tree whose nodes are possible-worlds intensions: Lewis discusses this way of going, for example, in OTPW p 49-50.
Another response that is close to the possible-worlds tradition is to use impossible worlds as well as possible ones. Since things that do not vary across possible worlds can vary across impossible worlds, impossible worlds give us finer-grained distinctions. If we allow logically impossible worlds, we can even get the effect of places in sentences where substitution of logical equivalents fail, since for example the worlds where (p or not-p) obtain need not be the ones where (q or not-q) obtain. I take it that semantics using situations instead of worlds is often a close cousin of this.
More radical responses to hyperintensionality include moving to an algebraic semantics, such as the sort advocated by George Bealer. Even these can be seen as successors to the possible-worlds tradition, since the structures of the algebras are often inspired by the structural relationships possible-worlds intensions stand in to each other. No doubt philosophers will come up with other approaches too - some revert to talking about Fregean senses and functions on them, though whether this is much more than a cosmetic difference from algebraic approaches I’m not sure.
Why does this matter for metaphysics? Well, one immediate reason it matters is that the metaphysics of language had better be able to cope with hyperintensionality and hyperintensions. One place that disputes in the philosophy of language often spill over is into the metaphysics of meaning, of truth (or at least truth-conditions), of propositions and so on.
A connected reason is that respect for hyperintensionality might go along with more warmth towards hyperintensional entities. We may be less likely to smile on the demand that properties that necessarily have the same instances are identical, for example. This in turn may motivate rejecting the picture of properties as sets of their actual and possible instances. Indeed, set theory might be of less use in metaphysics in general once we want to individuate things hyperintensionally.
There are other ways the hyperintensional turn could affect metaphysics. It might make us more sympathetic to impossible worlds, for example: I’ve argued elsewhere that counter-possible conditionals give us a good reason to postulate impossible worlds. It might make us think that some relational predicates are not associated with relations, or maybe are associated with finer-grained relata than they appear to be associated with: see Carrie Jenkins’s post about grounding. Modal analyses of hyperintensional pieces of language seem unappealing, since modal analyses are normally only intensional not hyperintensional. I could go on.
So, metaphysicians, join the hyperintensional revolution! You have nothing to lose but your coarse grains!
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