Author: Bill Vallicella

Hell

Over at The Constructive Curmudgeon I happened upon this quotation which is relevant to recent concerns:

The magnitude of the punishment matches the magnitude of the sin. Now a sin that is against God is infinite; the higher the person against whom it is committed, the graver the sin—it is more criminal to strike a head of state than a private citizen—and God is of infinite greatness. Therefore an infinite punishment is deserved for a sin committed against Him.
–Thomas Aquinas, Summa Theologica, Ia2ae. 87, 4.

 

Deducing John McCain from the Principle of Identity

What, if anything, is wrong with the following argument:

   1. (x)(x = x) (Principle of Identity)
   Therefore
   2. John McCain = John McCain (From 1 by Universal Instantiation)
   Therefore
   3. (Ex)(x = John McCain) (From 2 by Existential Generalization)
   Therefore
   4. John McCain exists. (From 3 by translation into ordinary idiom)

The initial premise states that everything is identical to itself, that nothing is self-diverse. Surely this is a necessary truth, one true no matter what, or in the jargon of possible worlds: true in every (broadly logically) possible world.

(2) follows from (1) by the intuitively clear inference rule of Universal Istantiation.  Surely, if everything is self-identical, then John McCain is  self-identical. The inferential move from (2) to (3) is also quite obvious: if McCain is self-identical, then something is identical to McCain. But (3) is just a complicated way of saying that John McCain exists. So we get the surprising result that the existence of John McCain is validly deducible from an a priori knowable necessary truth  of logic!

You understand, of course, that the argument is not about John McCain: it is about any nameable entity. Supposedly, Wilhelm Traugott Krug (1770-1842) once demanded of Hegel that he deduce Herr Krug's pen. If we name that pen 'Skip,' we can then put that name in the place of 'John McCain' and run the argument as before.

There is one premise and three inferences. Does anyone have the chutzpah to deny the premise? Will anyone make bold to question inference rules U.I. and E.G.? And yet surely something has gone wrong. Intuitively, the existence of a contingent being such as McCain cannot be deduced from an a priori knowable necessary truth of logic.  For that matter, the existence of a necessary being such as God cannot be deduced from an a priori knowable necessary truth of logic.  Surely nothing concrete, not even God, is such that its existence can be derived from the Law of  Identity.

So what we have above is an ontological argument gone wild whereby the  rabbit of real existence is pulled from the empty hat of mere logic!

St. Bonaventura said that if God is God, then God exists. If such  reasoning does not work in the case of God, then a fortiori it does not work  in the case of McCain or Herr Krug's pen.

Note that (1) is necessarily true. (It doesn't just happen to be the case that each thing is self-identical.) If (2) follows immediately  from (1), (2) is also necessarily true. And if (2) is necessarily true, then (3) is necessarily true. And the same holds for (4). But surely it is not the case that, necessarily, John McCain exists. He cannot be shown to exist by the above reasoning, and he certainly cannot be shown to necessarily exist by it.

So what went wrong? By my count there are three essentially equivalent ways of diagnosing the misstep.

A. One idea is that the argument leaves the rails in the transition from (3) to (4). All that (3) says is that something is identical to John McCain. But from (3) it does not follow that John McCain exists.   For the something in question might be a nonexistent something. After all, if something is identical to Vulcan, you won't conclude that  Vulcan exists. To move validly from (3) to (4), one needs the auxiliary premise:

3.5  The domain of quantification is a domain of existents only.

Without (3.5), John McCain might be a Meinongian nonexistent object. If he were, then everything would be logically in order up to (3). But  to get from (3) to (4) one must assume that one is quantifying over existents only.

But then a point I have been hammering away  at all my philosophical life is once again thrown into relief:  The misnamed 'existential' quantifier, pace Quine, does not express existence, it presupposes existence!

B. Or one might argue that the move from (1) to (2) is invalid. Although (1) is necessarily true, (2) is not necessarily true, but  contingently true: it is not true in possible worlds in which McCain does not exist. There are such worlds since he is a contingent being. To move validly from (1) to (2) a supplementary premise is needed:

1.5 'John McCain' refers to something that exists.

(1.5) is true in some but not all worlds. With this supplementary premise on board, the argument is sound. It also loses the  'rabbit-out-of-the-hat' quality. The original argument appeared to be  deducing McCain from a logical axiom. But now we see that the argument  made explicit does no such thing. It deduces the existence of McCain  from a logical axiom plus a contingent premise which is indeed   equivalent to the conclusion.

C. Finally, one might locate the error in the move from (2) to (3). No doubt McCain = McCain, and no doubt one can infer therefrom that something is identical to McCain. But this inferential move is not existential generalization, if we are to speak accurately and nontendentiously, but particular generalization. On this diagnosis,  the mistake is to think that the particular quantifier has anything to do with existence. It does not. It does not express existence, pace Quine, it expresses the logical quantity someness.

In sum, one cannot deduce the actual existence of a contingent being from a truth of logic alone. One needs existential 'input.' It follows that there has to be more to existence than someness, more than what  the 'existential' quantifier expresses. The thin conception of existence,  therefore, cannot be right.

Now let me apply these results to what Peter Lupu has lately been arguing.   Here he argues:

(i) (x)(x=x);

(ii) a=a, for any arbitrarily chosen object a; (from (i))

(iii) (Ex)(x=a); (from (ii) by existential generalization);

Now, (i) is necessary, but (iii) is contingent. Yet (i) entails (iii) via (ii), which is also necessary. So I simply do not see how the principle (1*) which you and Jan seem to accept applies in modal logics that include quantification plus identity.

Peter thinks he has a counterexample to the principle that if p entails q, and p is necessary, then q is also necessary.  For he thinks that *(x)( x = x)*, which is necessary, entails *(Ex)(x = a)*, which is contingent.

But surely if *a = a* is necessary, i.e. true in all worlds, then *(Ex)(x = a)* is necessary as well.

The mistake in Peter's reasoning comes in with the move from *Necessarily, (x) (x = x)* to *Necessarily, a = a*.   For surely it is false that in every possible world, a = a.  After all, there are worlds in which a does not exist, and an individual cannot have a property in a world in which it doesn't exist.  One must distinguish between essential and necessary self-identity.  Every individual is essentially (as opposed to accidentally) self-identical: no individual can exist without being self-identical.  But only some individuals are necessarily self-identical, i.e, self-identical in every world.  Socrates, for example, is essentially but not necessarily self-identical: he is self-identical in every world in which he exists (but, being contingent, he doesn't exist in every world).  By contrast, God is both essentially and necessarily self-identical: he is self-identical in every world, period (because he is a necessary being).   

Does Any Noncontingent Proposition Entail a Contingent Proposition?

This post continues the discussion in the comment thread of an earlier post.  

Propositions divide into the contingent and the noncontingent.  The noncontingent divide into the necessary and the impossible.  A proposition is contingent iff it is true in some, but not all, broadly logical possible worlds, 'worlds' for short.   A proposition is necessary iff it is true in all worlds, and impossible iff it true in none.  A proposition p entails a proposition q iff there is no world in which p is true and q false.

The title question divides into two:  Does any impossible proposition entail a contingent proposition?  Does any necessary proposition entail a contingent proposition?

As regards the first question, yes.  A proposition A of the form p & ~p is impossible.  If B is a contingent proposition, then there is no possible world in which  A is true and B false.  So every impossible proposition entails every contingent proposition.  This may strike the reader as paradoxical, but only if he fails to realize that 'entails' has all and only the meaning imputed to it in the above definition.

As for the second question, I say 'No' while Peter Lupu says 'Yes.'  His argument is this:
1. *Bill = Bill* is necessary.
2. *Bill = Bill* entails *(Ex)(x = Bill)*
3. *(Ex)(x = Bill)* is contingent.
Ergo
4. There are necessary propositions that entail contingent propositions.

Note first that for (2) to be true, 'Bill' must have a referent and indeed an existing referent.  'Bill' cannot be a vacuous (empty) name, nor can it have a nonexisting 'Meinongian' referent.  Now (3) is surely true given that 'Bill' is being used to name a particular human being, and given the obvious fact that human beings are contingent beings.  So the soundness of the argument rides on whether (1) is true.

I grant that Bill is essentially self-identical: self-identical in every world in which he exists.  But this is not to say that Bill is necessarily self-identical: self-identical in every world.  And this for the simple reason that Bill does not exist in every world.  So I deny (1).  It is not the case that Bill = Bill in every world.  He has properties, including the 'property' of self-identity, only in those worlds in which he exists.

My next post will go into these matters in more detail.

Addendum 28 May 2011.  Seldom Seen Slim weighs in on Peter's argument as follows:

I believe your reply to Peter is correct. It follows from how we should define constants in 1st order predicate logic. A domain or possible world is constituted by the objects it contains. Constants name those objects. If a domain has three objects, D = {a,b,c}, then the familiar expansion for identity holds in that domain, i.e., (x) (x = x) is equivalent to a = a and b = b and c = c. But notice that this is conditional and the antecedent asserts the existence in D of (the objects named by) a, b, and c. Thus premise 2 of Peter's argument is actually a conditional: IF a exists in some domain D, then a = a in D. The conclusion (3) must also be a conditional: if a exists in D , then something  in D is self-indentical. That of course does not assert the existential Peter wants from (x)(x = x). Put simply, a = a presumes [presupposes] rather than entails that a exists.

Socialist, Shmocialist

It is a tactical mistake for libertarians and conservatives to label Obama a socialist.  For what will happen, has happened: liberals will revert to a strict definition and point out that Obama is not a socialist by this definition.  Robert Heilbroner defines socialism in terms of "a centrally planned economy in which the government controls all means of production."  To my knowledge, Obama has never advocated such a thing.  So when the libertarian or conservative accuses Obama of socialism he lets himself in for a fruitless and wholly unnecessary verbal dispute from which he will emerge the loser.

It is enough to point out that the policies of Obama and the Democrat Party lead us toward bigger government and away from self-reliance, individual responsibility, and individual liberty.

It is even worse to label him a 'communist.'  Every communist is a socialist, but not every socialist is a communist.  If our president is not a socialist, then a fortiori he is not a communist.  It is intellectually irresponsible to take a word that has a definite meaning and turn it into a semantic bludgeon.  That's the sort of thing we expect from leftists, as witness their favorite 'F' word, 'fascist,' a word they apply as indiscriminately as 'racist.' 

"But haven't you yourself said, more than once, that politics is war conducted by other means?"  Yes, I have said it, and more than once.  In the end that's what politics is.  I call it the Converse Clausewitz Principle.  But we are not quite at the end.  Before we get there we should exhaust the possibilities of civil and reasonable debate.

"But what if the tactic of labeling Obama a socialist or even a communist would keep him from a second term.  Wouldn't that inaccurate labeling then be justified?"  That's a very tough question.  An affirmative answer would seem to commit one to the principle that the end justifies the means — in which case we are no better than liberals/leftists.  On the other hand, how can one play fair with those who will do anything to win?

Idolatry and Iconoclasm: A Weilian Meditation

In one of its senses, superstition involves attributing to an object powers it cannot possess. But the same thing is involved in idolatry. Someone who makes an idol of money, for example, attributes to it a power it cannot possess such as the power to confer happiness on those who have it. So we need to work out the relation between superstition and idolatry.

What is idolatry? I suggest that its essence consists in absolutizing the relative and finite. To make an idol is to take something of limited value and relative being and treat it as if it were of unlimited value and absolute being. Practically anything can be idolized including pleasure, money, property, name and fame, another human being, family, friends, country, the Party, the Revolution.  There are theologians who idolize their idea of God.  

Money, for example, is instrumentally good, and undeniably so. I think it is a plain mistake to consider money evil or the root of evil, as I  argue in Radix Omnium Malorum. But its value cannot be absolute since money is relational in its very nature as a means to an end.

To idolize money, to pursue it as if it were a thing of absolute value, is to commit a philosophical mistake — even if there is no  God. For only something absolute is worthy of worship, and money is   not absolute. If there is no absolute reality, then nothing is worthy of worship and everything should be treated as relative and finite  including one's own life. If there is an absolute reality, God for example, then everything other than this absolute reality should be treated as relative and finite.

If there is no God, then idolatry is a philosophical mistake. If there is a God, then idolatry is both a philosophical and a religious mistake, and as the latter, a sin.  Man is both an idol-erector and an idol-smasher. Our setting up of idols is rooted in a deep spiritual need to worship, honor, respect, and glorify. We need to look up to something.  But we are limited sense-bound creatures who tend to  latch onto foreground objects in the mistaken hope that they can satisfy us. We think a job, a house, a man, a woman, will satisfy us.   What we want they can't provide, but failing to realize this we succumb to the illusion of attributing to them powers to satisfy us that they cannot have. What is romantic love if not the illusion that possession of man or a woman could make one completely happy?

Idolatry gives rise to iconoclasm. Idol-positing leads to idol-smashing. What is revealed as hollow and unsatisfactory is destroyed in the name of the truly valuable. Both our tendency to erect idols and to smash them derives from our being oriented to the Absolute, our being unsatisfiable by the merely finite. Idolatry is the mistake of absolutizing the relative, infinitizing the finite. Iconoclasm tries to undo the mistake by destroying the would-be absolutes in the name of the true Absolute. It runs the risk, however, of falling into nihilism.  In the twilight of the idols there arises the specter of nihilism, a specter which, despite all his heroic efforts, Nietzsche could not lay.

In Gravity and Grace (Routledge 1995, p. 53), Simone Weil writes:

     Idolatry comes from the fact that, while thirsting for absolute
     good, we do not possess the power of supernatural attention and we
     have not the patience to allow it to develop.

What Weil is saying is that the absolute good is accessible only to inner listenting, inner passivity, an attentive stillness of the mind and heart. But cultivating such attention demands a patience we do not possess. So we create idols to do duty for the transcendent and inaccessible Absolute.

True religion is actually the enemy of idolatry and superstition. One who worships the true God sees the finite as finite and is secure against the illusion that the finite is ultimate. The true religionist is a bit of an iconoclast and indeed an atheist since he denies the God made in man's image. As Weil puts it, "Of two men who have no experience of God, he who denies him is perhaps nearer to him than the
other." (p. 103)

Hyphenation and Other Punctilios of Grammar

Dear Bill,

Being someone who uses gerunds not only correctly but elegantly and bothers to hyphenate compound modifiers, you'll appreciate, I hope, my noting that '20 year old' should be '20 year-old' because it is a hyphenated noun. Were ;">we to make his age adjectival by the addition of an extra noun, though, an extra hypen would be required, as in 'the 20-year-old man'.

Best wishes,
Will. 

I accept the correction, Will.  But there is a residual puzzle. How can '20' modify the noun 'year-old'?  There is also the question whether I should have written 'twenty' instead of '20.'   This is clearly bad writing: 'He gave me 5 books.'  Correct is: 'He gave me five books.'  But few will write, 'He gave me five thousand four hundred and seventy seven books' instead of 'He gave me 5,477 books.'

There is no end to punctiliousness once you start down that road.  For example, I just used 'you' in a slightly nonstandard way.  And as for hyphens, should we follow the Teutonic tendency of letting them fall into desuetude? 'Nonstandard' or 'non-standard'?  'Truth maker' or 'truth-maker' or 'truthmaker'?

 Do you say, 'The engine whose plugs are fouled?' or 'The engine the plugs of which are fouled'?  I prefer the latter despite its stiltedness.  An engine is not a person.  And if you don't agree with me on this point, will you say it is acceptable to write, 'The man that was shot' rather than 'The man who was shot'?

'She hanged herself' is correct.  But few nowadays are observant of the 'hanged'/'hung' distinction.

But should a writer like me, who aspires to a certain muscular elegance in his style, be using a slightly quaint and archaic, and perhaps even obsolete word such as 'nowadays'?

I distinguish 'each other' from 'one another' and call down my anathema upon those who write like this:  'Due to  their almost exclusive association with each other, liberals reinforce their political correctness.'

And so it goes.  

How Could an Impassible God be Offended or Know Any Contingent Fact?

Earlier (here and here) I asked how an all-good God could sentence a human agent to sempiternal punishment, punishment that has a beginning but no end.  If the punishment must fit the crime, and the crimes of finite agents are themselves finite, then it would seem that no one, no matter what his crimes, would deserve sempiternal punishment.  To make this a bit more precise we ought to substitute 'sin' for 'crime.'  They are different concepts.  Sin, but not crime, implies an offense to God.  If there is no God then there cannot, strictly speaking, be any sin.  But there could still be crime relative to an accepted body of positive law.  And if there is no positive law, but there is a God, then there could be sin but no crime.  (Positive law is the law posited by human legislators.) 

So let us say that the punishment must fit the sin.  My claim, then, is that no sin or sins committed by a human agent is such as to merit sempiternal punishment.  To put the point more sharply, a God who would condemn a finite human agent to unending misery is a moral monster, and not God.  (I am assuming that the agent in question has come to admit the error of his ways and is truly sorry for them. I have no problem with the unending misery of a recalcitrant rebel.) 

In response, Leo Mollica said that the offense to God, as an offense to a being of infinite dignity, is itself infinite and so deserves sempiternal punishment.  This prompted me to ask how an impassible God could be offended, which is the topic of this post.

Impassibility.  To say that God is impassible is to say that nothing external to God can affect God.  As Brian Leftow points out in his SEP article, impassibility is not the same as immutability.  He gives two reasons, but all we need is one: a God who induces a change in himself is not immutable but still could be impassible.  Now if God is impassible, then he cannot be offended by the antics of the Israelites as when they fell to worshipping a golden calf, etc.  He cannot be offended by sin.  And if he cannot be offended by sin, then he cannot be 'infinitely' offended by it.  Or so I maintained.

In response Mollica made a clever move.  He pointed out, rightly, that a person could be offended (wronged, slandered, calumniated, etc.) without knowing that he is.  Such a person would be offended without being affected.  I took the suggestion to be that God too could be offended without being affected.  Thus impassibility does not rule out God's being offended.

To this my reply was that God is omniscient.  He knows everything there is to know. So although it is true that a finite person could be offended without knowing it, and so not affected by the injury that was done to him, God could not be offended without knowing it. Good Thomist that he is, Mollica came back at me with the notion that God is not affected by what he knows.  So when the creature sins, God is offended; but his being offended in no way affects him:  he is not affected 'cognitively' by his knowledge that he is being offended, nor is he affected or injured  'morally' by his being offended.

Very interesting, but very problematic, as problematic as the Thomist line on divine knowledge.  If God is God, then he must be a metaphysical absolute and the pressure is on to say that he is both impassible and immutable.  (An immutable being is one that cannot undergo 'real' as opposed to 'mere Cambridge' change.)  After all, a decent absolute is not the sort of thing that could change or be affected by other things. If it underwent change or affection it would be relativized. But how could such an unchanging  God know anything contingent?  If God is unchanging, then his knowledge is unchanging: it cannot vary over time, or from possible world to possible world.  Here is an argument adapted from  Hartshorne.

1.  If p entails q, and q is contingent, then p is contingent.
2. *Tom sins at time t* is contingent.
3. *God knows that Tom sins at t* entails *Tom sins at t*.
Therefore
4. *God knows that Tom sins at t* is contingent.
Therefore
5. The property of knowing that Tom sins at t is an accidental (not essential) property of God.
6. God has no accidental properties: it is no part of his unchangeable essence that he know any contingent fact, any fact that could have been otherwise.
7. (5) and (6) are contradictories.  So one of the premises must be rejected.  (6) is the premise most plausibly rejected; but then impassibility and immutability go by the boards.

The challenge for our resident Thomist is to explain how an impassible and immutable God can know any contingent fact.

Bad to Die Young but Not Bad to Die? An Aporetic Dyad

Herewith, a rumination on death with Epicurus as presiding shade. The following two propositions are both logically inconsistent and yet very plausible:

1. Being dead is not an evil for anyone at any time. 

2. Being dead at a young age is an evil for some.

Obviously, the limbs of the dyad cannot both be true.  Each entails the negation of the other.  And yet each limb lays serious claim to our acceptance. 

(1) is rendered credible by Epicurean reasoning along the following lines. It is reasonably maintained that bodily death is annihilation of the self or person.  Now in the absence of a person, there is nothing to possess properties, experiential or not, such as  being conscious, being dead, being nonexistent, etc. We are assuming that a person's corpse cannot be the subject of the putative state of being dead.  When I am dead and thus nonexistent my corpse will continue to exist for a time.  (Assuming my end doesn't come in the form of 'vaporization.') But I am not my corpse.   My being dead is not my corpse's being dead, for it is not dead: only what was once alive can properly be said to be dead, and my corpse is never alive.  I am dead, if I am, not my corpse.  So my corpse cannot be the subject of the putative state of my being dead.  And anyway my being dead will obtain at future times when my corpse will not exist.  So for this reason too my corpse cannot be the subject of the putative state of my being dead.

There is, then, no subject of being dead if death is annihilation.  Since there is no subject, there is, strictly speaking, no state of my being dead.  A state is a state of something in the state, and in this case nothing is in the state.  It follows that the 'state' of my being dead cannot be an evil state.  There is no such state, so it can't be evil — or good, or anything.  It furthermore follows that being dead cannot rationally be feared — or looked forward to either. 'I'll be glad when I'm dead 'makes  as little  sense given the cogency of the Epicurean reasoning as 'I'll be sad when I'm dead' or Warren Zevon's 'I'll sleep when I'm dead.' 

Support for (2) has its source in a widely-accepted intuition.  Suppose a happy, healthy, well-situated 20 year old full of life and promise dies suddenly and painlessly in a freak accident.  Almost all will agree that in cases like this being dead (which we distinguish from both the process and the event of dying) is an evil, and therefore neither good nor axiologically neutral.  It is an evil for the person who is dead whether or not it is an evil for anyone else.  It is an evil because it deprives him of all the intrinsic goods he would have enjoyed had he not met an untimely end.

It is not quite the same for the 90 year old.  One cannot be deprived of the impossible (as a matter of conceptual necessity), and the older one gets the closer the approach to the nomologically impossible.  (I assume that there is some age — 150?  — at which it become nomologically impossible for what could reasonably count as a human being to continue to live.) So one cannot employ the same reasoning in the two cases.  If we say that the being dead of the 20 year old is bad because it deprives him of future goods, we cannot give the same reason for the badness ( if it is badness) of the being dead of the 90 year old.  Someone who lives a life that is on balance happy and healthy and productive and then dies of natural causes at 90 or 100 is arguably not deprived of anything by his being dead. 

The problem, then, is that (1) and (2) cannot both be true, yet each is plausible.

Just Say ‘No’ to Panhandlers

What do you do when a beggar approaches you on the street? Do you give him money? I've given away food, but as a general rule it is foolish and wrong to give money to bums. Once, in downtown Phoenix, I came out of a rib joint with a box of luscious leftovers. A beggar approached asking for money for food. I opened the box, showed him the ribs, and said, "If you are  hungry, you can have these." He thankfully accepted the gift and we both went away satisfied.

But if a bum asks for money, I refuse, sometimes adding, 'Get a job.' This isn't the Great Depression. There are jobs galore. That's why there is a Mexican invasion.

Beggars are for the most part scammers and liars. A bum in Hawaii once asked me for a quarter to make a phone call. I foolishly gave him the quarter.  Later in the day, he passed me again and again asked for a quarter to make a phone call. (No, I am not hasty generalizing, I am illustrating a general proposition to the effect that bums are for the most part liars and scammers.) If you give beggars money, they will buy alcohol or drugs with it. Do you want to contribute to their further degradation? Do you want more inebriated people on the streets?  Do you give any thought to what the bums do to others when drunk?  But even if they use the money for a good purpose, by giving them a handout, you undermine what little work ethic they have.

It is not easy to be genuinely helpful to others.  It takes thought, lest you make them worse. 

Of course, I don't expect the typical  liberal to understand this. For a guilt-ridden, feel-good liberal, one who substitutes emoting for thinking, one shows 'compassion' by contributing to people's dependence and degradation.  It is not that liberals intend to degrade and make dependent, but that is the unintended consequence of their unthinking  'compassion.'

The conservative who refuses to aid and abet unproductive behavior is the man of true compassion. For he gives the bum a reason to cease his bumming. This is why the expression 'compassionate conservative' is ill-advised. True conservatism is compassionate by its very nature. The expression 'compassionate conservative' is a foolish concession to the Left, suggesting as it does that conservatives are not as a rule compassionate. It is an expression like 'articulate black,' which   suggests that blacks are not as a rule articulate.

Further reading: Have a Heart, Give Smart.