Month: October 2010

The Bundle Theory and the Identity of Indiscernibles

I have been defending the bundle-of-universals theory of concrete particulars (BT) against various weak objections over a series of posts, here,  here, here, and here. Now I consider a very powerful objection, one that many will consider decisive.  The objection can be cast in the mold of modus tollendo tollens:  If BT is true, then the Identity of Indiscernibles is a necessary truth.  But the Identity of Indiscernibles is not a necessary truth. Ergo, BT is not true.

1. The Identity of Indiscernibles (IdIn) is the converse of the Indiscernibility of Identicals (InId) and not to be confused with it.  InId is well-nigh self-evident, while IdInis not.  Roughly, the latter is the principle that if x and y share all properties, then x = y.  It is a strictly ontological principle despite the epistemological flavor of 'indiscernible.' As just stated, it is more of a principle-schema than a principle.  We will get different principles depending on what we count as a property.  To arrive at a plausible nontrivial principle we must first rule out haecceity properties.  If, for any x,there is a property of identity-with-x, then no two things could share all properties, and the principle would be trivially true due to the falsehood of the antecedent.  Haecceity properties are creatures of darkness in any case as I argue elsewhere.

A plausible, nontrivial, principle results if we allow as properties all and only relational and  nonrelational pure properties.  A pure property is one that makes no reference to any specific individual.   Being married would then be an example of a pure relational property: to be married is to be married to someone, but not to any specified individual.  Being married to Xanthippe, however, is an impure relational property.  Being obese would be an example of a nonrelational property.  Here then is a plausible version of the Identity of Indiscernibles:

Necessarily, for any x, for any y, and for any relational or nonrelational pure property P, if (x has P iff y has P) then x = y.

2.  It is obvious, I think, that BT entails IdIn in the above form.  Consider a concrete particular, an iron sphere say, at a time.  On BT it is nothing but a bundle of universals. This implies that it is not possible that there be a second iron sphere that shares with the first  all relational and nonrelational pure properties.  This is not possible on BT because on BT a concrete particular is nothing more than a bundle of universals.  Thus there is no ontological ingredient in a concrete particular that could serve to differentiate it from another particular having all the same relational and nonrelational pure properties.  And if it is not possible that there be two things that differ numerically without differing property-wise, then the Identity of Indiscernibles as above formulated is necessarily true.

I am assuming that BT, if true, is necessarily true.  This is a special case of the assumption that the propositions of metaphysics, if true, are necessarily true.  If this assumption is granted, then BT entails IdIn.

3.  But is IdIn true?  Since it is necessarily true if true, all it takes to refute it is a possible counterexample.  Imagine a world consisting of two iron spheres and nothing else.  (The thought experiment was proposed in a 1952 Mind article by Max Black.) They are the same size, shape, volume, chemical composition and so on.  They agree in every nonrelational respect.  But they also agree in every relational respect.  Thus, each has the property of being ten meters from an iron sphere.   What Black's example seems to show is that there can be numerical difference without property-difference.  But then IdIn is false, whence it follows that BT is false.

4.  This is a powerful objection, but is it fatal?  Here are three ways to resist the argument, fit topics for further posts.  He who has the will to blog will never be bereft of topics.

a. Maintain that BT is a contingent truth.  If so, then BT does not entail IdIn as formulated above.

b. Grant that BT entails IdIn, but deny that scenarios such as Black's are really possible.  Admit that they are conceivable, but deny that conceivability entails possibility.

c.  An immanent universal can be wholly present at different places at once.  So why can't a bundle of universals be wholly present in different places at once?  Argue that Black's world can be interpreted, not as two particulars sharing all universals, but as one particular existing in two places at the same time.  From that infer that Black's Gedankenexperiment does show that IdIn is false.

Any other paths of resistance?

Kerouac October Quotation #13: Buddhist Life Denial

From Some of the Dharma, Viking 1997, p. 175, emphasis added:

No hangup on nature is going to solve anything — nature is bestial — desire for Eternal Life of the individual is bestial, is the final creature-longing — I say, Let us cease bestiality & go into the bright room of the mind realizing emptiness, and sit with the truth. And let no man be guilty, after this, Dec. 9 1954, of causing birth. — Let there be an end to birth, an end to life, and therefore an end to death.  Let there be no more fairy tales and ghost stories around and about this.  I don't advocate that everybody die, I only say everybody finish your lives in purity and solitude and gentleness and realization of the truth and be not the cause of any further birth and turning of the black wheel of death.  Let then the animals take the hint, and then the insects, and all sentient beings in all one hundred directions of the One Hundred Thousand Chilicosms of Universes. Period.

Nature is the cause of all our suffering; joy is the reverse side of suffering.  Instead of seducing women, control yourself and treat them like sisters; instead of seducing men, control yourself and treat them like brothers.  For life is pitiful.

Stop.

The Philosopher as Rhinoceros

George Santayana, Character and Opinion in the United States (New York: Norton, 1967), p. 35:

So long as philosophy is the free pursuit of wisdom, it arises wherever men of character and penetration, each with his special experience or hobby, looks about them in this world. That philosophers should be professors is an accident, and almost an anomaly. Free reflection about everything is a habit to be imitated, but not a subject to expound; and an original system, if the philosopher has one, is something dark, perilous, untested, and not ripe to be taught, nor is there much danger that anyone will learn it. The genuine philosopher — as Royce liked to say, quoting the Upanishads — wanders alone like the rhinoceros.

Is it any wonder that Santayana quit his teaching job at Harvard and spent the rest of his life in retirement in Rome?

The difference between a philosopher and a professor of philosophy is the former lives for what the latter lives from.

Self-Censorship Among the Politically Correct

There is no chicken like a liberal chicken.  Here.  Prager's comment: "Secular + Liberal = Wimp."

UPDATE 10/14.  Reason magazine weighs in.  Just Admit it, Newspapers: You're Scared of Muslims.

Of course.  The self-censorship is motivated by fear.  And it is a rational fear, which is why 'Islamophobia' and cognates are idiotic constructions that ought to be shunned by the intelligent.  Must I point out once again that a phobia is an irrational fear? So why do our leftist pals sling this word?

Some leftists sincerely believe that the concern over radical Islam is alarmist.  But most leftists know that it is not alarmist.  It is just that they hate conservatives more than they hate the threat to their own values.  They hate conservatives so much that they cannot or will not admit that they have more in common with contemporary American conservatives than they do with radical Muslims.  Astonishing, but true.  Apparently, they think they can use the Islamists, as a species of 'useful idiot,' to help destroy capitalism and usher in the socialist worker's paradise, dismissing or converting the Islamists when their services are no longer needed.  It's a bad bet.  It is more likely that they will lose their heads before any dismissal or conversion or mollification or other normalization of Islamists occurs.

Kerouac October Quotation #12: Our Boy Gives the Hinayana the Nod

From Some of the Dharma, pp. 174-175:

Hit the makeless null. Whether or not individuality is destroyed now, it will be complelely destroyed in death.  For all things that are made fade back to the unmade.   What's all the return-vow hassle, but a final metaphysical clinging to eternal ego-life by Mahayana Thinkers.  An intellectualized ego-attachment to taskhood.  Hinayana, nay Ecclesiastes, is best.

Companion posts:  A Philosopher's Notes on Ecclesiastes, Chapters 1-2.  A Philosopher's Notes on Ecclesiastes, Chapter 3. 

Bundling is Symmetrical But not Transitive

Over the phone the other day, Peter L. suggested the following objection to the bundle-of-universals theory of ordinary particulars, 'BT' hereafter.  (I leave out of consideration for the nonce bundle-of-tropes bundle theories.)  I am not sure I understood what Peter was driving at.  But here is the gist of what I thought he was saying. 

1. Suppose x is a proper (spatial) part of y, y being a physical thing.  On BT, both y and x are bundles of universals.  Now it often happens that a whole has a property that is not had by all its parts.  Think of a rubber ball.  The ball is spherical (or spheroid, if you  insist).  But it has proper parts that are not spherical.  For example, its hemispheres are not spherical.  Nor are the cubes of rubber internal to it spherical.  (They too are proper parts of it on classical mereology. These cubes could be 'liberated' by appropriate cutting of the ball.) The ball is red, let us say, but beneath the surface it is black.  And so on.  in sum, wholes often have properties that their parts do not have.

2.  On BT, property-possession is understood, not in terms of the asymmetrical relation of exemplification, but in terms of the symmetrical relation of bundling.  Accordingly, for a property to be possessed by something is not for it to be exemplified by this thing, but for it to be bundled with other logically and nomologically compossible properties.  Exemplification, the asymmetrical relation that connects a substratum to a first-level property is replaced by bundling  which is a symmetrical relation that connects sufficiently many properties (which we are assuming to be universals) so as to form a particular.  When the universals are bundled, the result is a whole of which the universals are ontological constituents, with the bundling relation taking over the unifying job of the substratum.  While bundling is symmetrical — if U1 is bundled with U2, then U2 is bundled with U1– ontological constituency is asymmetrical:  if U is an ontological constituent of B, then B is not an ontological constituent of U.

3.  Given that the  ball is a bundle of universals, and that the ball is spherical, it follows that the ball has as one of its ontological 'parts' the universal, sphericality.  Now sphericality and cubicality are not broadly-logically compossible.  Hence they cannot be bundled together to form an individual.  But our ball has a proper part internal to it which is a cube.  That proper part has cubicality as a constituent universal.  So it seems a broadly-logical contradiction ensues:  the ball has as constituents both sphericality and cubicality, universals that are not compossible.

4. An interesting objection!  But note that it assumes Transitivity of Bundling:  it assumes that if sphericality is bundled  with sufficiently many other Us to form a complete individual, and cubicality is bundled with one of these Us — say being made of rubber — then sphericality is bundled with cubicality. But it is well-known that bundling is not transitive.  Suppose roundness and redness are bundled in our ball, and redness and stickiness are bundled in a numerically distinct disk, but there is nothing that is both round and sticky. That's a possible scenario which shows that Transitivity of Bundling fails. From the fact that U1 is bundled with U2, and U2 with U3, one cannot infer that U1 is bundled with U3.  So from the fact that sphericality is bundled with rubberness, and rubberness with cubicality, it does not follow that sphericality is bundled with cubicality.

The  bundle theory can accommodate the fact that a property of a whole needn't be a property of all its proper parts.  Or am I missing something?

 

Krauthammer on Obama’s Policies

Read it.  Excerpt:

For the first time since modern budgeting was introduced with the Budget Act of 1974, the House failed to even write a budget. This in a year of extraordinary deficits, rising uncertainty and jittery financial markets. Gold is going through the roof. Confidence in the dollar and the American economy is falling – largely because of massive overhanging debt. Yet no budget emerged from Congress to give guidance, let alone reassurance, about future U.S. revenues and spending.

The day of reckoning approacheth. 

Can a Bundle Theory Accommodate Change?

0.  Peter L. has been peppering me with objections to bundle theories.  This post considers the objection from change.

1. Distinguish existential change (coming into being and passing out of being) from alterational change, or alteration.  Let us think about ordinary meso-particulars such as avocados and coffee cups.  If an avocado is unripe on Monday but ripe on Friday, it has undergone alterational change: it has changed in respect of the property of being ripe.  One and the same thing has become different in respect of one or more properties. (An avocado cannot ripen without becoming softer, tastier, etc.)  Can a bundle theory make sense of an obvious instance of change such as this?  It depends on what the bundle theory (BT) amounts to.

2. At a first approximation, a bundle theorist maintains that a thing is nothing more than a complex of properties contingently related by  a bundling relation, Russellian compresence say.    'Nothing more' signals that on BT there is nothing in the thing that exemplifies the properties: there is no substratum (bare particular, thin particular) that supports and unifies them. This is not to say that on BT a thing is just its properties: it is obviously more, namely, these properties contingently bundled.  A bundle is not a mathematical set, a mereological sum, or a conjunction of its properties.  These entities exist 'automatically' given the existence of the properties.  A bundle does not. 

3.  Properties are either universals or property-instance (tropes).  For present purposes, BT is a bundle-of-universals theory.  Accordingly, my avocado is a bundle of universals.  Although a bundle is not a whole in the strict sense of classical mereology, it is a whole in an analogous sense, a sense sufficiently robust to be governed by a principle of extensionality: two bundles are the same iff they have all the same property-constituents.  It follows that the unripe avocado on Monday cannot be numerically the same as the ripe avocado on Friday.  And therein lies the rub.  For they must be the same if it is the case that an alteration in the avocado has occurred. 

So far, then, it appears that the bundle theory cannot accommodate alterational change.  Such change, however, is a plain fact of experience.  Ergo, the bundle theory in its first approximation is untenable.

4.  This, objection, however, can be easily met by sophisticating the bundle theory and adopting a bundle-bundle theory.  Call this BBT.  Accordingly, a thing that persists over time such as an avocado is a diachronic bundle of synchronic or momentary bundles.  The theory then has two stages.  First, there is the construction of momentary bundles from universals.  Then there is the construction of a diachronic bundle from these bundles. The momentary bundles have properties as constituents while the diachronic bundles do not have properties as constituents, but individuals.  At both stages the bundling is contingent: the properties are contingently bundled to form momentary bundles and these resulting bundles are contingently bundled to form the persisting thing.

Accordingly, the unripe avocado is numerically the same as the ripe avocado in virtue of the fact that the earlier momentary bundles which have unripeness as a constituent  are ontological parts of the same diachronic whole as the later momentary bundles which have ripeness as a constituent.

5. A sophisticated bundle theory does not, therefore, claim that a persisting thing is a bundle of properties; the claim is that a persisting thing is a bundle of individuals which are themselves bundles of properties.  This disposes of the objection from change at least as formulated in #3 above.

6. BBT also allows us to accommodate the intuition  that things have accidental properties.  On the proto-theory BT according to which a persisting thing is a bundle of properties, it would seem that all properties must be essential, where an essential property is one a thing has in every possible world in which it exists.    For if wholes have their parts essentially, and if bundles are wholes in this sense, and things are bundles of properties, then things have their properties essentially.  But surely our avocado is not essentially ripe or unripe but accidentally one or the other.  On BBT, however, it is a contingent fact that a momentary bundle MB1 having ripeness as a constituent is bundled with other momentary bundles.  This implies that the diachronic bundle of bundles could have existed without MB1 and without other momentary bundles having ripeness as a constituent.  It therefore seems to follow that BBT can accommodate accidental properties.

7. That is, BBT can accommodate the modal intuition that our avocado might never have been ripe.  But what about the modal intuition that, given that the avocado is ripe at t, it might not have been ripe at t?  This is a thornier question and the basis of a different objection that is is not defused by what I have said above.  And so we reserve this objection for a separate post.

The History of Philosophy as Akin to an Intellectual Arms Race

Nicholas Rescher, The Strife of Systems: An Essay on the Grounds and Implications of Philosophical Diversity (University of Pittsburg Press, 1985), pp. 205-206:

The history of philosophy is akin to an intellectual arms race where all sides escalate the technical bases for their positions.  As realists sophisticate their side of the argument, idealists sophisticate their counterarguments; as materialists become more subtle, so do phenomenalists, and so on.  At the level of basics, the same old positions continue to contest the field — albeit that ever more powerful weapons are used to defend increasingly sophisticated positions.

The context is an argument for the thesis that philosophy is susceptible of technical but not doctrinal progress.  The nature of philosophy precludes consensus.  Resolution of "the substantive issues in such as way as to secure general approbation and assent" (206) is out of the question. Such consensus is impossible and therefore not even an ideal.

Strife of Systems is essential reading for anyone interested in metaphilosophy.

Too Many Laws

You've heard me say it before.  Laws should be few in number, rational in content, enforceable, and enforced.  As it is, we have too many laws, indeed, too many 'Ls':  too many laws, lawyers, legislators (most of whom are lawyers), and liberals.  How can a government claim to be representative of the people when it is top-heavy with lawyers?  That is a question that ought to be asked.  While you're at it, ask whether it might not be a good idea to have some de-legislators in among the legislators.

America is Drowning in Law.