Why I Reject Individual Concepts

Consider the sentences 'Caissa is a cat' and 'Every cat is an animal.'  Edward the Nominalist made two  claims in an earlier comment thread that stuck in my Fregean craw:

1. The relation between 'Caissa' and 'cat' is the same as the relation between 'cat' and 'animal'.

2. The relation between *Caissa* and *cat* is the same as the relation between *cat* and *animal.*

Single quotes are being used in the usual way to draw attention to the expression enclosed within them.  Asterisks are being used to draw attention to the concept expressed by the linguistic item enclosed within them.  I take it we agree that concepts are mental in nature in the sense that, were there no minds, there would be no concepts. 

Affirming (2), Edward commits himself to individual or singular concepts.  I deny that there are individual concepts and so I reject (2).  Rejecting (2), I take the side of the Fregeans against the traditional formal logicians who think that singular propositions can be analyzed as general.  Thus 'Caissa is a cat' gets analyzed by the TFL-ers  as 'Every Caissa is a cat.'

To discuss this profitably we need to agree on the following definition of 'individual concept':

D1. C is an individual concept of x =df x is an instance of C, and it is not possible that there be a y distinct from x such that y is an instance of C.

So if there is an individual concept of my cat Caissa, then Caissa instantiates this concept and nothing distinct from Caissa does or could instantiate it. We can therefore say that individual concepts, if there are any, 'capture' or  'grasp' or 'make present to the mind' the very haecceity (thisness) of the individuals of which they are the individual concepts.

We can also speak of individual concepts as singular concepts and contrast them with general concepts.  *Cat* is a general concept.  What makes it general is not that it has many instances, but that it can have many (two or more) instances.  General concepts are thus multiply instantiable. 

The concept C1 expressed by 'the fattest cat that ever lived and ever will live' is also general.  For, supposing that Oscar instantiates this concept, it is possible that some other feline instantiate it.  Thus C1 does not capture the haecceity of Oscar or of any cat.   C1 is general, not singular.  C1 is multiply instantiable in the sense that it can have two or more instances, though not in the same possible world.

And so from the fact that a concept applies to exactly one thing if it applies to anything, one cannot validly infer that it is an individual or singular concept.  Such a concept must capture the very identity or thisness of the thing of which it is a concept.  This is an important point.  To push further I introduce a definition and a lemma.

D2. C is a pure concept =df C involves no specific individual and can be grasped without reference to any specific individual.

Thus 'green,' 'green door,' 'bigger than a barn,' 'self-identical,'  and 'married to someone' all express pure concepts.  'Taller than the Washington Monument,' 'married to Heidegger,' and 'identical to Heidegger' express impure concepts. 

Lemma 1: No individual concept is a pure concept.

Proof.  By (D1), if C is an individual concept of x, then it is not possible that there be a y distinct from x such that y instantiates C.  But every pure concept, no matter how specific, is possibly such as to have two or more instances.  Therefore, no individual concept is a pure concept.

Consider the famous Max Black example of two iron spheres alike in all monadic and relational respects.  A pure concept of either, no matter how specific, would also be a pure concept of the other.  And so the haecceity of neither would be captured by that pure concept.

Lemma 2.  No individual concept is an impure concept.

Proof.  An individual  concept is either pure or impure.  If C is impure, then by (D2) it must involve an individual.  And if C is an individual concept it must involve the very individual of which it is the individual concept. But individuum ineffabile est: no individual can be grasped as an individual.  But that is precisely what one would have to be able to do to have an impure concept of an individual.  Therefore, no individual concept is an impure concept.

Putting the lemmata together, it follows that an individual concept cannot be either pure or impure.  But it must be one or the other.  So there are no individual concepts. Q. E. D.!

 

Do We Love the Person or Only Her Qualities?

We have been discussing the topic of nonqualitative thisness here, here,  and here.  The following post gets at the problem from another angle, the love angle.

Here is a remarkable passage from Pascal's remarkable Pensees:

BLAISE%20PASCAL%20PORTA A man goes to the window to see the passers by. If I happen to pass by, can I say that he has gone there to see me? No; for he is not thinking of me in particular. But does he who loves someone for her   beauty, really love her? No; for small-pox, destroying the beauty without destroying the person, will put an end to love. And if I am loved for my judgment, for my memory, am I loved? No; for I can lose these qualities without losing myself. Where then is this 'I,' if it resides neither in the body, nor the soul? And how  love the body or the soul save for these qualities which do not  make the 'me,' since they are doomed to perish? For can one love the soul of a person in the abstract, irrespective of its qualities? Impossible and wrong! So we never love anyone, but only  qualities. (p. 337, tr. H. F. Stewart)

 

This passage raises the following question. When I love a person, is it the person in her particularity and uniqueness that I love, or merely the being-instantiated of certain lovable properties? Do I love  Mary as Mary, or merely as an instance of helpfulness, friendliness, faithfulness, etc.?

These are clearly different. If it is merely the being-instantiated of lovable properties that I love, then it would not matter if the love object were replaced by another with the same ensemble of properties. It would not matter if Mary were replaced by her indiscernible twin Sherry. Mary, Sherry, what's the difference? Either way you get the very same package of delectable attributes.

But if it is the person in her uniqueness that I love, then it would matter if someone else with exactly the same ensemble of properties were substituted for the love object. It would matter to me, and it would matter even more to the one I love. Mary would complain bitterly if Sherry were to replace her in my  affections. "I want to be loved for being ME, not for what I have in common with HER!"

The point is perhaps more clearly made using the example of self-love.  Suppose Phil is my indiscernible twin.  Now it is a fact that I love myself.  But if I love myself in virtue of my instantiation of a set of properties, then I should love Phil equally.  For he instantiates exactly the same properties as I do.  But if one of us has to be annihilated, then I prefer that it be Phil.  Suppose that God decides that one of us is more than enough, and that one of us has to go.  I say, 'Let it be Phil!' and Phil says, 'Let it be Bill!' 

This little thought-experiment suggests that there is more to self-love than love of the being-instantiated of an ensemble of properties.  For Phil and I have the same properties, and yet each is willing to sacrifice the other.  This would make no sense if the being of each of us were exhausted by our being instances of sets of properties.  In other words, I do not love myself solely as an instance of properties but also a unique existent individual that cannot be reduced to a mere instance of properties. I love myself as a unique individual.  And the same goes for Phill: he loves himself as a unique individual.

Now it is a point of phenomenology that love intends to reach the very haecceity and ipseity of the beloved: in loving someone we mean to  make contact with his or her unique thisness and selfhood. It is not a mere instance of lovable properties that love intends, but the very  being of the beloved. And what some of us of a personalist bent want to maintain is that this intending or meaning is in some cases fulfilled: we actually do sometimes make conscious contact with the haecceity and ipseity of the beloved. We arrive at the very being of the beloved, not merely at the co-instantiation of a set of multiply instantiable lovable properties. But how is this possible given Pascal's argument?

The question underlying all of this is quite fundamental: Are there any genuine individuals? X is a genuine individual if and only if X is essentially unique. The Bill and Phil example suggests that selves are genuine individuals and not mere bundles of multiply instantiable properties.  For each of the twins is acutely aware that he is not the other despite complete agreement in respect of  pure properties.  Here are some of my theses to be expounded and clarified as the discussion proceeds:

1. There exist genuine individuals.
2. Genuine individuals cannot be reduced to bundles of properties.
3. The Identity of Indiscernibles is false.
4. Numerical difference is numerical-existential difference: the existence of an individual is implicated in its very haecceity. 
5.  There are no nonexistent individuals. 
6. There are no not-yet existent individuals.

 

Russellian Propositions and the ‘He Himself’ Locution

Commenting on an earlier post of mine, Peter Lupu brought up some themes from David Kaplan which were not quite relevant but interesting nonetheless.   In my response I pointed out that Kaplan is committed to Russellian (R) as opposed to Fregean (F) propositions whereas the problem I had posed presupposes that propositions are Fregean.  In this post I will do three things.  I will first explain the difference between R- and F-propositions and give an argument against R-propositions.  Then I will explain the 'he himself' locution which Hector-Neri Castaneda brought to our attention back in the '60s.  Finally, I will explain how the 'he himself' locution is further evidence that propositions cannot be Russellian.  And since propositions cannot be Russellian, they cannot be introduced in solution of the problem I raised in the earlier post.

Russellian Versus Fregean Propositions

1. One issue in the philosophy of language is whether singular terms (including pure indexicals, demonstratives, proper names) refer directly or whether they refer via some descriptive meaning that they encapsulate.  The issue is not whether a word like 'I' — the first-person singular pronoun used indexically, not the Roman numeral or the first-person pronoun used nonindexically — has a meaning apart from its reference.  Of course it does.  The meaning of 'I' — its character in Kaplan's jargon — is given by the rule that uttered tokens of 'I' refer to the speaker.  The issue is whether the reference of a singular term is routed through its descriptive meaning.  For example, when Tom says 'I' he refers to Tom.  But is Tom's self-reference routed through any descriptive meaning of 'I'? It should be obvious that Tom's use of 'I' does not target Tom specifically in virtue of the Kaplanian content of 'I.'  For that is quite general.  So if there is a sense of 'I' that mediates Tom's self-reference, it will have to be a special 'I'-sense, a special mode of presentation (Frege:  Darstellungsweise). 

Now if there are terms that refer directly, without the mediation of a Fregean sense (Sinn), then the sentences in which such terms occur express Russellian propositions.  R-propositions involve individuals directly rather than indirectly by way of an abstract representative as in F-propositions.  So if 'Tom is tall' expresses an R-proposition, then Tom himself, all 200 lbs of him, is a constituent of the proposition, along with the property that the sentence predicates of him.  Such a proposition could be represented as an ordered pair the first member of which is Tom and the second the property of being tall.  But if the sentence  expresses an F-proposition, then Tom himself is not a constituent of it. Instead, the sense of 'Tom' goes proxy for Tom in the F-proposition.

Suppose t is a directly referential term in a sentence S.  T may or may not have a meaning apart from its reference.  If S expresses a Russellian-Kaplanian proposition, then the meaning of t — if there is one — is not a constituent of the propositional content of S:  the constituent of the propositional content of S, corresponding to t, is simply the referent  of t.

2.  That there are propositions I take for granted.  We may introduce them  by saying that they are the bearers of the truth-values.  But this leaves open whether they are Russellian or Fregean.  I think there is a good metaphysical reason for not countenancing R-propositions.

3. The metaphysical reason has to do with false R-propositions.  Given that 'Tom is tall' is true, it doesn't strike me as problematic to say that the world contains, in addition to Tom and the property of being tall, Tom's being tall.  But then  'Tom is short ' is false.  If 'Tom is tall' expresses an R-proposition, then so does 'Tom is short.'  But then the world contains, in addition to Tom and the property of being short, a further entity Tom's being short which has Tom himself as a constituent.  And that does strike me as very problematic.  (And it struck Russell that way too, which is why Russell abandoned Russellian propositions!) For if Tom does not exemplify shortness, then there simply is no such entity as Tom's being short. In other words I have no problem accepting facts such as Tom's being tall assuming that all facts obtain.  But nonobtaining facts such as Tom's being short are a metaphysical monstrosity. 

The 'He Himself' Locution 

4. Castaneda pointed out that one cannot validly move from

1. X judges x to be F
to
2. X judges himself to be F.

(2) entails (1), but (1) does not entail (2).  Unbeknownst to me, a certain document I am inspecting was written by me long ago.  It is possible that I conclude that the author of the document was confused without concluding that I was confused.  (Example adapted from Chisholm.)  In this situation I am an x such that x judges x to be confused, but I am not an x such that x judges himself to be confused.

Given that I am x, there is no distinction between the Russellian proposition which is x's being confused and the one which is my being confused.  For the two R-propositions have the all the same constituents. If propositions are Russellian, then we have to say that 'x judges x to be confused' and 'x judges himself to be confused' express the same proposition.  But obviously they don't.  So propositions aren't Russellian.  Or is that too quick?

An Argument for Necessary Beings

1. A contingent being is one the nonexistence of which is possible, whereas a necessary being is one the nonexistence of which is impossible. (At play in these definitions is broadly logical possibility which is between narrowly logical and nomological possibility.)

2. Framing a definition is one thing, showing that something answers to it is another. Are there any necessary beings? Since a necessary being could be either abstract or concrete, I can show that there are necessary beings by showing that there is at least one abstract necessary being. To convey the senses of 'concrete' and 'abstract' by example one could say that God and Socrates are concrete while the proposition 7 is prime and Socrates' singleton — {Socrates} — are abstract. All and only concreta are causally active/passive whereas abstracta are not. Please avoid the mistake of thinking that x is concrete iff x is physical.

3. Some truths are necessary, others are contingent. 'I am now blogging' is contingently true: it is true, but it might not have been true. I might have been doing something inconsistent with blogging now, sleeping for instance. By contrast, 'If I am blogging, then I am writing' is necessarily true. To see this, negate the sentence in question. The result is a sentence expressing a broadly logical impossibility: 'I am blogging and it is not the case that I am writing.' Consider also, 'If I am blogging, then it is not the case that I am not blogging.' This too is necessarily true, except that the negation expresses a narrowly logical impossibility: 'I am blogging and I am not blogging.'

I don't see how any reasonable person can deny that there are necessary truths. Another example: '7 is a prime number' expresses a necessary truth. This doesn't just happen to be true in the way that it just happens to be true that there are seven cans of Dr. Pepper left in the reefer. It is necessarily true: true in all (BL)-possible worlds.

4. A truth is a true truth-bearer. Now I don't understand how ink on paper, or chalk on a blackboard, or any physical modification of any physical medium, no matter how complex the modification and how complex the medium, could be true or false. I don't understand how anything physical could, qua physical, be a truth-bearer or truth-vehicle, i.e., an item capable of being either true or false. Marks on paper cannot be either true or false. They just exist. But suppose you think they — or complex modifications of the stuff between your ears — can be either true or false. Still, the marked-up paper exists contingently. Consequently, the sentence-token '7 is prime' scratched onto the paper exists contingently. Similarly for anything inscribed in your brain. Your brain and its 'inscriptions' are contingent.

5. But then how could any truth be necessarily true? How could any truth be necessarily true if no truth-bearer is necessarily existent?  There is no possible world in which 7 is not prime, but there are worlds in which there are no material things.  Material things are contingent.  How could the proposition in question be true in those worlds if there is nothing in those worlds to serve as truth-bearer? Let's spell this out.

If an item has a property, then, pace Meinong, the item exists: existence is a necessary condition of property-possession.   So if an item such as a truth-bearer has the property of being necessarily true, then that truth-bearer necessarily exists. For if the truth-bearer is true in every world, then it exists in every world.  Therefore, if there are necessary truths, then there are necessary beings. Now there are necessary truths. Therefore, there are necessary beings. Given that everything physical is contingent, these necessary beings are nonphysical. So they are either mental (accusatives of mental acts) or abstract. For present purposes, it doesn't matter which of these they are. The present point is that there is good reason to believe in (i.e., believe that there are) necessary beings.

6. But I hear an objection coming: An item can have a property essentially without having it necessarily. Thus Socrates is essentially human, but not necessarily human. He is human in every world in which he exists, but he does not exist in every world. So he is essentially but not necessarily human. Why can't the proposition expressed by '7 is prime' be like that? Why can't it be essentially (as opposed to accidentally) true, true in every world in which it exists, but neither true nor false in the worlds in which it does not exist? If this is the way it is, then your argument from necessary truths to necessary beings collapses.

The objector is suggesting that truth-bearers are contingent beings. But this is problematic as Alvin Plantinga argues (Warrant and Proper Function, Oxford UP, 1993, p. 119.) Suppose that truth-bearers are brain inscriptions, and consider the proposition

1. There are brain inscriptions.

(1) is such that it could not have been false. For in a possible world in which there are no brain inscriptions, there are no truth-bearers, which implies that (1) in those words is neither true nor false, hence not false. And in every world in which there are brain inscriptions, (1) is of course true. So (1) is true in every world in which it exists, and not false in every world in which it does not exist. So (1) could not have been false. But this bizarre. Surely there might have been no brains and no brain-inscriptions. It is not necessarily true that there are brains. If it is not necessarily true that there are brains, then it is possibly true that there are no brains. Now what is this possibility of there being no brains? It is plausibly identified with the possibly being true of the proposition, There are no brains. But then this proposition must exist in those possible worlds in which it is not true.

The Existence of Infinite Sets

A reader asked whether one can  prove that there are actually infinite sets.  Well, let's see.

It occurs to me that 'actually infinite set' is a pleonastic expresson. If there are infinite sets, then they are actually infinite, such that a potentially infinite set would be no set at all. For if there are mathematical (as opposed to commonsense) sets at all, then they are quite definite objects whose identity conditions are supplied by the Axiom of Extensionality: two sets are the same if and only they have all the same members. A mathematical set is not exhausted by its membership — it is not a mere plurality — since it is a one to their many; nevertheless, sets are rendered determinate by their members. (Let us for the moment not worry about singletons and the null set which give rise to their own difficulties.) 

It is worth noting that in Georg Cantor's oft-quoted definition, a set (Menge) is a collection of "definite and separate objects." (Contributions to the Founding of the Theory of Tranfinite Numbers, sec. 1) If the members of a set are definite and separate, then the same is true of the set itself. We could say that a math. set inherits its determinacy from the determinacy of its members. 

My point is that, if there are mathematical sets at all, then there is nothing potential, indeterminate, incomplete, or unfinished about them. Each such set is a definite single item distinct from each of its members and from  all of them.  It is a one-over-many. So if there are any infinite sets, then they are actually infinite sets, which is to say that talk of 'actually infinite sets' is redundant.

So our question becomes, Can one prove that there are infinite sets?

I don't know if one can prove it, but one can give an argument. (If a proof is a valid deductive argument the premises of which are self-evident, then damn little can be proven. In particular, the axioms of ZFC are far from self-evident, not that set theorists claim self-evidence for them. Is it self-evident that a null set exists?  Hardly.)

Here is an argument, where 'set' is short for mathematical (as opposed to commonsense) set.

1. There are sets.

2. There are infinitely many natural numbers: no finite cardinal is the number of natural numbers. Therefore,

3. If the natural numbers form a set, then they form an infinite set. (1, 2)

4. The natural numbers form a set.   Therefore,

5. The natural numbers form an infinite set. (3, 4) Therefore,

6. There exists an infinite set. (5)

This is a valid argument, and it renders reasonable its conclusion. But it does not prove its conclusion unless there are proofs for its controversial premises (1) and (4). I argued for (1) in Sets, Pluralities, and the Axiom of Pair.  But what is the argument for (4)?  Why must we think of the natural numbers as forming a set?

Why Mix Philosophy and Politics?

I am sometimes asked why I intersperse political entries with narrowly philosophical ones.  But in every case the question was put to me by someone who tilts leftward.  If my politics were leftist, would anyone complain?  Probably not.  Academe and academic philosophy are dominated by leftists, and to these types it seems entirely natural that one will be a bien-pensant latte-sipping lefty.  Well, I'm here to prove otherwise.  Shocking as it will  seem to some, leftist views are entirely optional, and a bad option at that.

I could of course post my political thoughts to a separate weblog.  But given that philosophy attracts more liberals/leftists than conservatives, it is good for them to be exposed to views  that they do not encounter within the enclaves they inhabit.  Or are contemporary liberals precisely illiberal in their closemindedness to opposing views?  One gets that impression.

Posting the political to a separate weblog would also violate my 'theory' of blogging.  My blog is micro to my life's macro.  It must accordingly mirror my life in all its facets  as a sort of coincidentia oppositorum of this situated thinker's existence.

The Millenials: A Chump Generation?

Robert Samuelson, The Real Generation Gap.  Concluding paragraph:

Millennials could become the chump generation. They could suffer for their elders' economic sins, particularly the failure to confront the predictable costs of baby boomers' retirement. This poses a question. In 2008, millennials voted 2-1 for Barack Obama; in surveys, they say they're more disposed than older Americans to big and activist government. Their ardor for Obama is already cooling. Will higher taxes dim their enthusiasm for government?

Another Look at Anderson’s Trinitarian Mysterianism (Peter Lupu)

(Hauled up from the vasty deeps of the ComBox into the light of day by BV who supplies minor edits and comments in blue.)

I strongly recommend to everyone interested in the subject to read Anderson’s “In defense of mystery: a reply to Dale Tuggy” (2005), Religious Studies, 41, 145-163 in which he replies to Dale Tuggy’s paper “The unfinished business of Trinitarian theorizing”, Religious Studies, 39(2003), 165-183.  I was unable to obtain Dale Tuggy’s original paper.

Continue reading “Another Look at Anderson’s Trinitarian Mysterianism (Peter Lupu)”

Cottingham on the Origin of the Religious Impulse

John Cottingham, On the Meaning of Life (Routledge 2003), p. 52:

. . . the whole of the religious impulse arises from the profound sense we have of a gap between how we are and how we would wish to be . . . .

This is not quite right, as it seems to me. The sense of the gap between 'is' and 'ought' is undoubtedly part of the religious impulse, but there is more to it than this. It must be accompanied by the sense that the gaping chasm between the miserable wretches we are and what we know we ought to be cannot be bridged by human effort, whether individual or collective. Otherwise, the religious sensibility would collapse into the ethical sensibility. There is more to religion than ethics. The irreligious can be aware of the discrepancy between what we are and what we should be. The religious are convinced of the need for moral improvement together with a realization of their impotence in bringing it about by their own efforts.

But now, if I may be permitted to argue against myself:  "Haven't you maintained more than once that Buddhism is a religion?  And isn't Buddhism a religion of self-help?  And haven't you quoted the 'Be ye lamps unto yourselves' verse?  So something has to give.  If Buddhism counts as a religion, then it cannot be essential to a religion that it invoke 'other-power' for moral improvement.  And if the latter invocation is essential to religion, then Buddhism is not a religion."

Well, my man, it looks like we are going to have to think about this some more. 

"And another thing.  You say that there is more to religion than ethics. This implies that ethics is an essential component of religion.  But doesn't Kierkegaard speak of the teleological suspension of the ethical?  Might it not be that one can have religion without ethics?"

A religion worth having cannot be decoupled from ethics.  See Abraham, Isaac, and an Aspect of the Problem of  Revelation and  Kant on Abraham and Isaac.

Simone Weil and the Illusoriness of Worldly Goods

A correspondent, responding to Weil's Wager, has this to say:

[. . .] What worries me when I turn to Weil’s argument is that she seems to be trying to replace Pascal’s serviceable scale of goods with a dichotomy of illusory and absolute goods. I have no idea what it means to say ”health and fitness are illusory goods” or “only God is absolutely good.” The former seems to me just some metaphysically tricked-out term of abuse. I have no idea at all how to unpack “God is the absolute good” (despite your remarks in Part IV ). Pascal at least talks about salvation and an eternal afterlife. Is that what is supposed to be absolutely good for me? And so God as the provider is somehow also valuable or “absolutely good” for me? All of this dark and murky to me in Weil’s argument, while I think I understand what Pascal is proposing.

I agree that the whether-or-not version of (7) is incompatible with (1), but otherwise I remain lost at sea in her attempt to argue that I must pursue the only thing that is “absolutely good” whether or not it really exists. [. . .]

Central to Weil's thought is the notion that the goods of this life are unreal: "Things of the senses are real if they are considered as perceptible things, but unreal if considered as goods." (Gravity and Grace, p. 45) To understand this one must see it in the light of Plato, Weil's beloved master. It has been said with some justice that every philosopher is either a Platonist or an Aristotelian, and there is no doubt that Weil is a Platonist and was hostile to Aristotle. My correspondent, however, is an Aristotelian (to force him into our little schema) and so it comes as no surprise to me that he is at a loss to understand what it could mean to say that such things as health and fitness, food and drink, property and progeny, are illusory goods.

Continue reading “Simone Weil and the Illusoriness of Worldly Goods”