Month: August 2010

More on the Ground Zero Mosque

This from a long-time reader:

As a follower of your blog—in all its iterations throughout the years—I have a tremendous amount of respect for your opinions, philosophical and otherwise.  Yet in your recent post on the Cordoba House building plan—apparently now called park51–I found myself disagreeing with you on several points of your discussion.  When I have had this discussion with others—namely my parents and grandparents, all of whom share your opposition to the plan—I found little more than shrill arguing going on. I recognize that intelligent and thoughtful people exist on both sides of this, and I want to understand the rational arguments available to both, not just the blustering rhetoric being bantered [bandied] about.  Hopefully in discussion with you I can find a more rationally driven discussion than I found elsewhere. 

I'll give it my best shot.


Continue reading “More on the Ground Zero Mosque”

Collective Inconsistency and Plural Predication

We often say things like

1. The propositions p, q, r are inconsistent.

Suppose, to keep things simple, that each of the three propositions is self-consistent.  It will then be false that each proposition is self-inconsistent. (1), then, is a plural predication that cannot be given a distributive paraphrase.  What (1) says is that the three propositions are collectively inconsistent.  This suggests to many of us  that there must be some one single entity that is the bearer of the inconsistency.  For if the inconsistency does not attach distributively to each of p, q, and r, then it attaches to something distinct from them of which they are members.  But what could that be?

If you say that it is the set {p, q, r} that is inconsistent, then the response will be that a set is not the sort of entity that can be either consistent or inconsistent.  Note that it is not helpful to say

A set is consistent (inconsistent) iff its members are consistent (inconsistent).

For that leaves us with the problem of the proper parsing of the right-hand side, which is the problem with which we started.

And the same goes for the mereological sum (p + q + r).  A sum or fusion is not the sort of entity that can be either consistent or inconsistent.

What about the conjunction p & q & r?  A conjunction of propositions is itself a proposition.  (A set of propositions is not itself a proposition.) This seems to do the trick. We can parse (1) as

2. The conjunctive proposition p & q & r is (self)-inconsistent.

In this way we avoid construing (1) as an irreducibly plural predication.  For we now have a single entity that can serve as the logical subject of the predicate ' . . . is/are inconsistent.'  We can avoid saying, at least in this case, something that strikes me as only marginally intelligible, namely, that there are irreducible monadic non-distributive predicates.  My problem with irreducibly plural predication is that I don't know what it means to say of some things that they are F if that doesn't mean one of the following: (i) each of the things is F; (ii) there is a single 'collective entity' that is F; or (iii) the predicate 'is F'  is really relational. 

One could conceivably object that in the move from (1) to (2) I have 'changed the subject.'  (1) predicates inconsistency of some propositions, while (2) predicates (self)-inconsistency of a single conjunctive proposition.  Does this amount to a changing of thr subject?  Does (2) say something different about something different?

Against Politically Correct Atheism

If contemporary Christianity and contemporary Islam are judged by their fruits, which is more conducive to human flourishing, or, if you think nothing good comes from religion, which is less conducive to human misery?  I hope you are clearheaded and unprejudiced enough to see that the religion of 'peace'  is far worse than Christianity, at least at present, if you think both are bad.

So why do so many contemporary atheists employ a double-standard?  Why is the full measure of their energy and vitriol reserved for Christianity?  Why the politically correct tip-toe dance around Islam?  Is it fear?  Is it like cops who go after jaywalkers to avoid confronting gangbangers?  Is it because most atheists are leftists and leftists are bred-in-the-bone PC-ers?

Check out this diatribe against politically correct atheism by Pat Condell. 

Sets and the Number of Objects: An Antilogism

Commenter Jan, the Polish physicist, gave me the idea for the following post.

An antilogism is an aporetic triad, an array of exactly three propositions which are individually plausible but collectively inconsistent.  For every antilogism, there are three corresponding syllogisms, where a syllogism is a deductive argument with exactly two premises and one conclusion.  Here is the antilogism I want to discuss:

1. Possibly, the number of objects is finite.
2. Necessarily, if sets exist, then the number of objects is not finite.
3. Sets exist.

The modality at issue is 'broadly logical' and sets are to be understood in the context of standard (ZFC) set theory. 'Object' here just means entity.  An entity is anything that is. (Latin ens, after all, is the present participle of the infinitive esse, to be.)

Corresponding to the above antilogism, there are three syllogisms. The first, call it S1, argues from the conjunction of (1) and (2) to the negation of (3).  The second, call it S2, argues from the conjunction of (2) and (3) to the negation of (1).  The third, call it S3, argues from (1) and (3) to the negation of (2). 

Note that each syllogism is valid, and that the validity of each reflects the logical inconsistency of the the antilogism. Note also that for every antilogism there are three corresponding syllogisms, and for every syllogism there is one corresponding antilogism.  A third thing to note is that S3 is uninteresting inasmuch as it is surely unsound.  It is unsound because (2) is unproblematically true. 

This narrows the field to S1 which argues to the nonexistence of (mathematical) sets and S2 which argues to the impossibility of the number of objects (entities) being finite.  Our question is which of these two syllogisms we should accept.  Obviously, both are valid, but both cannot be sound.  Do we have good reason to prefer one over the other?

Here are our choices.  We can say that there is no good reason to prefer S1 over S2 and vice versa; that there is good reason to prefer S1 over S2; or that there is good reason to prefer S2 over S1.

Being an aporetician, I incline toward the first option.  Peter Lupu, being less of an aporetician and more of dogmatist, favors the third option.  Thus he thinks that the antilogism is best solved by rejecting (1).  Peter writes:

(a) If there are infinitely many numbers, then (1) is false. Are there infinitely many numbers? Very few would deny this. How could they, for then they would have to reject most of mathematics. [. . .]

To keep it simple, let's confine ourselves to the natural numbers and the mathematics of natural numbers. (The naturals are the positive integers including 0.)  If there are infinitely many naturals, then there are infinitely many objects.  If so, then presumably this is necessarily so, whence it follows that (1) is false. 

I fail to see, however, why there MUST be infinitely many naturals.  I am of course not denying the obvious: for any n one can  add 1 to arrive at n + 1.  With a sidelong glance in the direction of Anselm of Canterbury: there is no n that fits the description 'that than which no greater can be computed.'   In plain English:  there is no greatest natural number.  But this triviality does not require that all of the results of possible acts of +1 computation actually be 'out there' in Plato's heaven.  When I drive along a road, I come upon milemarkers that are already out there before I come upon them.  But why must we think of that natural number series like this?  I don't bring the road and its milemarkers into being by driving.  But what is to stop us from viewing the natural number series along Brouwerian (intuitionistic) lines?  One can still maintain that the series is infinite, but the infinity is potential not actual or completed.  Peter's first argument, as it stands, is not compelling.  (Compare:  Everyone will agree that every line segment is infinitely divisible.  But it does not follow that every line segment is infinitely divided.)

(b) If propositions exist, then there are infinitely many propositions. Are there propositions? Kosher-nominalists obviously will have to deny that propositions exist. Sentences do not express propositions. But, then, what do they express?

I am on friendly terms with Fregean (not Russellian) propositions myself. And I grant that it is very plausible to say that if there is one proposition then there is an actual infinity of them.  Consider for example the proposition *p* expressed by 'Peter has a passion for philosophy.'  *P* entails *It is true that p* which entails *It is true that it is true that p,* and so on infinitely.  But again, why can't this be a potential infinity? 

The following three claims are consistent: (i) Declarative sentences express propositions; (ii)Propositions are abstract; (iii) Propositions are man-made. Karl Popper's World 3 is a world of abstracta.  It is a bit like Frege's Third Reich (as I call it), except that the denizens of World 3 are man-made.

I am agreeing with Peter and against the illustrious William that there are (Fregean) propositions, understood as the senses of context-free declarative sentences.  I simply do not understand how a declarative sentence-token could be a vehicle of a truth-value.  But why can't I say that propositions are mental constructs?  (This diverges from Frege, of course.)

(c) Are there sentence types? A nominalist will have to deny the existence of sentence types. But, then, it is difficult to see how any linguistic analysis can be done.

Peter may be conflating two separate questions.  The first is whether there are any abstract objects, sentence types for example. The second is whether there is an actual infinitity of them.  He neeeds the latter claim as a countrerexample of (1).  So again I ask:  why couldn't there be a finite number of abstract objects:  a finite number of sets, propositions, numbers, sentence types, etc.  This would make sense if items of this sort were Popperian World 3 items.

I conclude that, so far, there is no knock-down refutation of (1).  But there is also no knock-down refutation of (3) either, as Peter will be eager to concede.  So I suggest that the rational course is to view my (or my and Jan's) antilogism as a genuine intellectual knot that so far has not been definitively solved.

 

Thinking About Nothing

Suppose I try to think the counterfactual state of affairs of there being nothing, nothing at all.  Can I succeed in thinking pure nothingness?  Is this thought thinkable?  And if it is, does it show that it is possible that there be nothing at all?  If yes, then (i) it is contingent that anything exists, and (ii) everything that exists exists contingently, which implies that both of the following are false:

1. Necessarily, something exists.  Nec(Ex)(x exists)

2. Something necessarily exists.   (Ex)Nec(x exists). 

(1) and (2) are not the same proposition: (2) entails (1) but not conversely.

Phylogenetically, this topic goes back to Parmenides of Elea.  Ontogenetically, it goes back to what was probably my first philosophical thought when I was about eight or so years old.  (Ontogeny recapitulates phylogeny!)  I had been taught that God created everything distinct from himself.  One day, lying in bed and staring at the ceiling,  I thought: "Well, suppose God never created anything.  Then only God would exist.  And if God didn't exist, then there would be nothing at all."  At this my head began to swim and I felt a strange wonder that I cannot quite recapture, although the memory remains strong 50 years later.  The unutterably strange thought that there might never have been anything at all — is this thought truly thinkable or does it cancel itself in the very attempt to think it?

My earlier meditation was to the effect that the thought cancels itself by issuing in contradiction.  (And so I concluded that necessarily there is something, an interesting metaphysical result arrived at by pure thought.) To put it as simply as possible, and avoiding the patois of 'possible worlds': If there were nothing, then it would be a fact that there is nothing.  And so there would be something, namely, that very fact.  After all, that fact has a definite content and can't be nothing.  But this is not quite convincing because, on the other hand, if there were truly nothing, then there wouldn't be this fact either. 

On the one hand, nothingness is the determinate 'state' of there being nothing at all.  Determinate, because it excludes there being something.  (Spinoza: Omnis determinatio est negatio.) On the other hand, nothingness is the nonbeing of absolutely everything, including this putative 'state.'  That is about as pithy a formulation of the puzzle as I can come up with.

Here is a puzzle of a similar structure.  If there were no truths, then it would be true that there are no truths, which implies that there is at least one truth.  The thought that there are no truths refutes itself.  Hence, necessarily, there is at least one truth.  On the other hand, if there 'truly' were no truths, then there would be no truth that there are no truths.  We cannot deny that there are truths without presupposing that there are truths; but this does not prove the necessity of truths apart from us.  Or so the objection goes.

How can we decide between these two plausible lines of argumentation? 

But let me put it a third way so we get the full flavor of the problem.  This is the way things are: Things exist. If nothing else, these very thoughts about being and nonbeing exist.  If nothing existed, would that then be the way things are?  If yes, then there is something, namely, the way things are.  Or should we say that, if nothing existed, then there would be no way things are, no truth, no maximal state of affairs?  In that case, no determinate 'possibility' would be actual were nothing to exist.

The last sentence may provide a clue to solving the problem.  If no determinate possibility would be actual were nothing to exist, then the thought of there being nothing at all lacks determinate content.  It follows that the thought that there is nothing at all is unthinkable.  We may say, 'There might have been nothing at all,' but we can attach no definite thought to those words.  So talking, we literally don't know what we are talking about.  We are merely mouthing words.  Because it is unthinkable that there be nothing at all, it is impossible, and so it is necessary that there be something.

Parmenides vindicatus est.

My conclusion is equivalent to the thesis that there is no such 'thing' as indeterminate nonbeing.  Nonbeing is determinate:  it is always and necessarily the nonbeing of something.  For example, the nonbeing of Pierre, the nonbeing of the cafe, the nonbeing of Paris  . . . the nonbeing of the Earth . . . the nonbeing of the physical universe . . . the nonbeing of everything that exists.  Nonbeing, accordingly, is defined by its exclusion of what exists. 

The nonbeing of everything that exists is not on an ontological par with everything that exists.  The former is parasitic on the latter, as precisely the nonbeing of the latter. Being and Nothing are not equal but opposite:  Nothing is derivative from Being as the negation of Being.  Hegel got off on the wrong foot at the beginning of his Wissenschaft der Logik.  And Heidegger, who also maintained that Being and Nothing are the same — though in a different sense than that intended by Hegel — was also out to lunch, if you'll pardon the mixed metaphor.

If this is right, then nonbeing is not a source out of which what is comes or came.  Accordingly, a sentence like 'The cosmos emerged from the womb of nonbeing,' whatever poetic value it might have, is literally meaningless:  there is no nonbeing from which anything can emerge.

Being is. Nonbeing is not.