Rationality

The problem of God’s omniscience was incidentally brought up in my metaphysics class and we had a brief discussion about how the arguments might be symbolized in modal logic.  This spurred my interest in spelling out the notion of free will in terms of possible worlds.

My first thought was that if I am free, for example, to go to class or not, then the presence of that choice spawns two possible worlds before me (metaphorically, that is, I’m not a modal realist) – one in which I go to class and one in which I don’t.  However, this seems insufficient since even objects that we agree have no free will can have possible worlds branching in their future in exactly the same way (i.e., a stone may roll down the hill on one side or the other, so there are two such possible worlds in the stone’s future).

It doesn’t help matters to say that I freely choose to go to class in one possible world and freely choose not to in another, since “freely” is just what I am trying to explain.

My second thought was that freedom must have something to do with one’s power to actualize a possibility.  In addition to there being two possible worlds branching ahead of me, if I have free will, it is within my power to actualize one or the other (i.e., to make either one of them the actual world).

In formulating the problem of God’s omniscience we have the following:  God is omniscient.  God’s omniscience entails that he knows everything, including what will happen in my future in the actual world.  So let’s say, for example, God knows that I will go to class today.

On my theory, if I have free will I should be able to actualize the possible world in which I don’t go to class today.  But since this would contradict God’s knowledge, I have no such power and therefore no free will.  We can conclude that I will go to class today in the actual world as a matter of fact.

One might be inclined to say that there is a possible world in which I stay home, in which God foreknows that I stay home – but it seems no such possible world can exist.  The reason is that God’s omniscience requires that there is only one possible world (I’ll expand on this below).  Consequently it is trivially true that I will go to class in all possible worlds and so it is a necessary truth in that sense.

When I say my attending class becomes a matter of fact, what I mean is that “Andrew goes to class on August 31st 2010″ is a true statement in the same way that “Andrew was born in March 1982″ is a true statement.  If God is omniscient and my view is right, then my future is unchangeable, that is to say determined, in the same way that my past is unchangeable.

To complete the picture, as it turns out, we have to say that everything is determined – everything about the way the world is, was, and will be, may be stated as facts and could not have been (be, or turn out to be) any different.  Since God knows every fact about the world, those facts are determined (unchangeable).  For example, if God knows that the stone will roll down the left side of the hill, it cannot possibly happen any other way.  The only possible world is therefore the actual one.

A weak objection that pops into mind is that one might argue God knows all possibilities and that he knows which possibility I will freely choose to actualize.  This response doesn’t get us anywhere since the one he knows I will actualize, in virtue of his knowing it, is the only possible world.  Thus the claim that God knows all possibilities just amounts to the claim that God knows what will actually happen.

Things are complicated by the fact that we think God, being all powerful, should be able to create any possible world.  Keeping this in mind, the problem of God’s omniscience becomes deeper than it initially appears – it exposes a conceptual inconsistency in the properties traditionally attributed to God.  That is, if God knows what he will do, then he cannot do otherwise.  If he knows now (in the absolute sense, viz., perfect knowledge) that he will eat pizza for lunch tomorrow, then if he chooses to eat sardines instead he will have contradicted his omniscience.  So if he knows he’ll eat pizza, he cannot eat sardines instead.  But if he cannot choose to eat the sardines, then he is not all powerful.  Either way he doesn’t fit into our traditional conception of God.

P.S. The king of France is bald.

P.P.S. I think asserting that God exists outside of time doesn’t solve the problem, since if that is the only way out of the predicament, it follows that God cannot exist in time, which contradicts his omnipotence.  Not to worry though, it’s not anyone’s fault, it’s just that omnipotence is an incoherent concept.

I recently stumbled across a version of the problem of evil (given by Peter Singer – though he is not the first to point it out, it is an especially important matter for him) that strikes me as especially problematic for the Judeo-Christian concept of God.  In case you don’t know the basic version, it may be presented as follows:

1. God is omnipotent.
2. God is omni-benevolent.
3. God is omniscient.
4. Evil exists.

The problem is that while each of these propositions are individually acceptable, they appear to be inconsistent – that is, it appears that they cannot all be true at the same time.  Virtually no one will deny (4), that evil exists in the world.  However, if (1)-(3) are also true, then God knows about the evil, he has the power to do away with it, and being all-good he should want to do away with it – yet evil still exists.

Of course, as I said, it may be argued that these propositions merely appear to be inconsistent and that, in fact, they are not.  Some of the typical (and most effective) Christian responses are that evil is the result of (i) free-will, (ii) original sin, or (iii) the fact that evil is necessary in order for us to learn life-lessons but for which evil we are eventually repaid in the afterlife.  I find these answers to be prima facie plausible and consistent with Christian teachings.

The problem of animal suffering, however, cannot be resolved by any of the typical responses.  We can take the same set of propositions as before, but replace (4) with (4a): Animals suffer needlessly.  Once again, God knows about their suffering, he could stop it, and he should want to stop it – yet they still suffer.  Virtually no one will deny (4a); it seems clear that animals feel pain.  Animals have nervous systems conducive to their feeling pain and they clearly behave as if they feel pain.  Anyone who has had a dog , cat, or other animal as a friend surely believes animals can suffer and that we, as moral beings, have some kind of obligation to prevent their suffering.

However, the typical Christian responses to the problem of evil will no longer apply.  As for (i), Christianity clearly does not teach that animals have free-will, since free-will is a unique gift afforded to human beings.  Regarding (ii), it is equally clear that animals do not suffer due to original sin, since they have no relation to Adam and Eve (and it’s called the fall of man after all, not the fall of animals [although I suppose by this reasoning women would not suffer due to original sin either, so let's call it the fall of humankind {and don't you hate it when I start using nested parentheses!  I blame this on my spending too many hours playing with logic proofs}]).  Last, it cannot be the case that, as in (iii), animals suffer in order to teach human beings life-lessons; this is evinced by the fact that animals have endured much suffering over the many millions of years that they existed on an Earth devoid of human life.  But even today, animals face all kinds of suffering that has nothing to do with human activities (regular things like drought, famine, or being eaten by a tiger); and to top it all off, the animals would get no recompense in an afterlife (since, sadly, all dogs don’t go to heaven).  Without appealing to ‘mysterious ways’, the ‘best possible world’ argument, or pleading ignorance in some other fashion, I’m at a loss as to what a reasonable response would be.

aka: Stop beating the dead straw-man!

Skepticism has to be one of the most widely misunderstood views in all of philosophy.  It is understandable that the folk-concept of skepticism (i.e., the average everyday person’s concept) is somewhat vague and generally wrong.  However, I recently came across a journal article (that was actually published) which summarized arguments (from a book by the same author) that allegedly refute skepticism, but the arguments only serve to knock down the folk-concept-derived straw-man of skepticism.  What bothers me is not that the average person may think about skepticism along these lines, but that someone published a book on it!  Needless to say the author is not a philosopher, but when you go out of your way to get your ideas published you should at least run it by someone who works in the relevant field.  Anyways, I thought I’d present the bad arguments and explain what’s wrong with them because, well, someone should.

Before “refuting” skepticism the author explains his position:

“critical realism”: a world exists independently of human minds (realism), but sifting, judging, and discerning (critical) are often required in the knowledge process.  This sifting enables us to discern between appearances (mirages, optical illusions, dreams) and the way things are, between truth and falsehood.

I take this to be almost everyone’s metaphysical position, I have only heard it referred to as “direct” or “naive” realism.  We all believe that there is a real world and that our perceptions are generally reliable.  This position (as presented by the author) is question-begging; to say that we have knowledge about reality because we can discern between appearances and reality is already to presuppose that there is a difference between the two (i.e., that there is such a thing as ‘objective reality’).  Anyway, the author presumably has an argument for realism and that is a fine position to take.  But problems arise as soon as he attempts to describe skepticism. He writes:

[T]he skeptic often wrongly assumes that if another alternative is even logically possible, then you should question your beliefs, no matter how well-grounded. But this just doesn’t logically follow at all! How is it the case that if it’s possible I’m wrong, therefore I am wrong?

The “logically possible” alternatives to which the author refers are things like Descartes’ evil demon scenario, or the possibility that you are really in the Matrix, etc.  However the skeptic does not use these possibilities in order to make you question your beliefs, nor do they claim that since you could be wrong, you are wrong.  The skeptic has all of the same beliefs that you do regarding regular everyday things.  The possibility that you could be wrong only shows that you may not, in fact, know what you think you know.

[The skeptic argues that] we can’t distinguish between plausible and ridiculous views, but that position is clearly silly. [...] there’s no reason to reject what seems so obvious to us in favor of less-obvious alternatives.

This passage is where the author comes closest to getting skepticism right, and naturally he misses the point entirely.  The skeptic’s claim simply is that all of our evidence is compatible with an infinite number of possible metaphysical explanations about reality.  One possibility is that our perceptions correspond to reality – that when we see a chair, there really is a chair that exists in roughly the way we believe that it does.  Another possibility is that an all-powerful evil demon is toying with our minds and there is no chair at all.  One view seems plausible to us while the other seems ridiculous – but can we distinguish between the two?  Obviously not; there is no way to check for evil-demons and there is no way to check for ‘actual’ chairs.  All we have in the way of evidence is the conscious awareness of our own perceptual states; the whole point of the skeptical scenarios is that they are 100% compatible with the whole of our evidence.  Yes, it would be silly to believe that the demon-possibility is not only possible but actual, but no one believes this (skeptics included).

[S]kepticism tends to eliminate personal or moral responsibility since it systematically ignores or evades truth, which is a crucial component of knowledge.

Here, again, the author nearly makes a good point.  The skeptic never claims that our beliefs about reality are false, only that it is impossible for us to know that they are true.  This is the fundamental problem that the skeptics are trying to point out: truth is indeed a crucial component of knowledge, yet it is the one evading us (not the other way around)!  The skeptic neither ignores nor evades the truth (whatever that would mean), since we do not have access to anything resembling objective truth.  As for the odd claim about skeptics being immoral, I have never known a skeptic to make any claims beyond the realm of epistemology, so I’m not sure where the author is coming from on this point (unless he takes skepticism to entail moral relativism).  I will just say that one does not need to be certain that they know appearances correspond to reality in order to believe in and act according to some concept of moral responsibility.

Think logically. So, I turned in my keys and wasn’t planning on going back to campus anytime soon.  But UH doesn’t want me to leave! Apparently Curtis is getting 120+ logic students in the first summer session and needs a TA. It just so happens that I am qualified and need a summer job (after I finish slacking off for the rest of May). Summer 1 runs June 2nd- July 3rd, so it’s a perfect fit.  Not that any of these teaching gigs pay well, but at least I haven’t had trouble finding a job in philosophy.

The idea of selective confirmation made me realize something about contrastivism. Contrastive knowledge claims are only susceptible to skeptical arguments when the contrast clause includes a contradictory element of the initial proposition P. In other words, claims of the form “S knows that P rather than not-P,” always lead to skeptical results when P is an ordinary proposition about the external world. The equivalent form “S knows that not-P rather than P,” is vulnerable in the same way, though it is less obvious.

First, it’s worth pointing out that contrastivism functions best when the contrastive elements in a knowledge claim are contraries to P. I define contraries as follows: Any two propositions that mutually entail each other’s falsity, but may both be false, are contraries. In symbolic form, A and B are contrary propositions iff the following conditions hold:

(1) A entails ~B
(2) B entails ~A
(3) (A or B) or (~A and ~B)

For example, (4) “the animal is a sheep” and (5) “the animal is a wolf” are contraries by this definition. If either one is true, the other is false – the animal cannot be both a wolf and a sheep at the same time. But (4) and (5) may both be false if, say, the animal is a bunny. In a contrastive knowledge claim, we end up with something like: (C1) “S knows that the animal is a sheep rather than a wolf.” For Schaffer this amounts to something along these lines: Given the choice between (4) and (5), subject S can truthfully answer (4) based on her evidence.

Given a knowledge claim such as (C1) that has a contrary contrast element, one cannot infer a strong skeptical hypothesis under Schaffer’s contrastive account of closure. He gives the rule “contract q,” which says that if S knows that P rather than Q1, and Q2 entails Q1, then we can infer that S knows that P rather than Q2. In the case of C1, in order to reach a skeptical k-claim, there must be some skeptical proposition that entails that “the animal is a wolf.” For example, we cannot use “the animal is a BIV-image of a wolf” as Q2 because it contradicts (and so does not entail) Q1. However, we can give a weak skeptical hypothesis for Q2: “the animal is a wolf in sheep’s clothing.” This statement works under the rule “contract q,” since “the animal is a wolf in sheep’s clothing” entails that “the animal is a wolf.” So from C1, we can make the valid inference that (C2) “S knows that the animal is a sheep rather than a wolf in sheep’s clothing.” If the wolf is sufficiently tricky, then S cannot discriminate between the disguised wolf and a real sheep, so S is clearly not in a position to know C2.

Now, let’s consider the case when the contrastive element is a contradictory to P. We need a statement of the form S knows that P rather than not-P: (C3) “S knows that the animal is a sheep rather than that it is not a sheep.” Under contrastive closure, we can give Q2 as “the animal is a BIV-image of a sheep,” which entails Q1 “that the animal is not a sheep.” From this entailment we can infer that (C4) “S knows that the animal is a sheep rather than a BIV-image of a sheep.” (C4) is obviously false since no one can know that they are not merely perceiving BIV-images (a la classical skeptical arguments).

The conclusion to be drawn is that there are precise conditions under which contrastive closure leads to the skeptical paradox. The conditions are:

P = an ordinary proposition about the external world
Q1 = a contradictory of P (some formulation of not-P)
Q2 = a strong skeptical hypothesis

From these propositions, we start with a seemingly acceptable true knowledge claim, “S knows that P rather than Q1,” and since Q2 entails Q1, we can infer via contrastive closure that, “S knows that P rather than Q2,” which is necessarily false – so we have reproduced the classical skeptical argument from closure.