Daily affirmation

All of us must live in constant contradiction. Philosophers wage constant war against it.

Induction and the Axiom of Choice

In this short but strange paper, Alexander George gives a mathematical "proof" justifying induction. The problem of (Humean) induction basically is:

Now as concerns the argument, its conclusion is that in induction (causal inference) experience does not produce the idea of an effect from an impression of its cause by means of the understanding or reason, but by the imagination, by “a certain association and relation of perceptions.” The center of the argument is a dilemma: If inductive conclusions were produced by the understanding, inductive reasoning would be based upon the premise that nature is uniform; “that instances of which we have had no experience, must resemble those of which we have had experience, and that the course of nature continues always uniformly the same.” (Hume THN, 89) And were this premise to be established by reasoning, that reasoning would be either deductive or probabilistic (i.e. causal). The principle can't be proved deductively, for whatever can be proved deductively is a necessary truth, and the principle is not necessary; its antecedent is consistent with the denial of its consequent. Nor can the principle be proved by causal reasoning, for it is presupposed by all such reasoning and any such proof would be a petitio principii.

George's proof uses the axiom of choice and a recent result called the Hardin-Taylor theorem. George's proof requires the axiom of choice. However, it seems to me that this would not make induction any less problematic because the grounds for skepticism on which the problem of induction is formed is analogous, indeed, very similar, to the grounds for doubting the truth of the axiom of choice. Consider the axiom of choice which basically states:

For it amounts to nothing more than the claim that, given any collection of mutually disjoint nonempty sets, it is possible to assemble a new set — a transversal or choice set — containing exactly one element from each member of the given collection.

This axiom presupposes the existence of a choice function for any collection of non empty sets, even infinite collections and even if we cannot specify the details of that function (for example by specifying a selection rule or the distinguishing property of the elements to be picked out). The function is assumed to exist under that axiom. Likewise the reason the problem of induction does not bother scientists, common folks and philosophers alike (who actually doubts the sun will rise tomorrow?) is because we assume that nature has principles of uniformity such as laws, etc even if we cannot directly observe such laws or discover them by deductive reasoning reason as Hume insisted. Hume suggest that we arrive at the principle of uniformity for any series of past events to continue to hold into the future by acts of "imagination" and inference through that imagining. To claim that we can discover the principles through observation is to beg the question, or worse, to get into a vicious circle (what would justify the principle?). To claim that we can discover them through deductive reasoning is to commit a category error.

Similarly, assuming the existence of choice functions is assuming that there is some regularity in any collection of items from a collection of non empty sets even when we cannot specify what that regularity is. We cannot prove it from the axioms (it is an axiom after all). In the case of induction we are not bothered by the "problem" of induction because we assume that our imagination in conjoining repeated contiguous events have some basis in a natural uniformity that is existing independently outside of our imagination (such as some natural law). We assume the existence of some law e.g., which we cannot directly observe but must infer the existence.

So "proving" induction from the axiom of choice seems to do no anti-skeptical work at all. It throws the problem in the lap of mathematics when the foundations of such reasoning can be put under a very similar skeptical lens as the foundations of our everyday inductive reasoning. This is made especially salient when we consider the reasons why mathematicians have accepted the axiom of choice. First, let's consider what George says about his proof:

But might there be some feature of the proof that compromises its ability to offer the kind of justification we are after? One aspect of the proof that suggests itself is its reliance on the Axiom of Choice....

But then he goes on:

Where a condition on conceptual coherence is consistency with ZFC, Zermelo-Fraenkel set theory plus the Axiom of Choice, a theory most mathematicians believe to be true and indispensable for the formal development of mathematics.

If this is the justification then it would render the whole proof implausible because as Penelope Maddy has correctly pointed out, mathematicians have "accepted" the axiom of choice largely because of pragmatic reasons (for ease of proving some theorems like Zorn's lemma). They haven't accepted it because of its philosophically sound obviousness (in fact, many of them and logicians and philosophers have skeptically questioned its truth much as the later have inductive reasoning). Given these pragmatic historical considerations, they seem to mirror the pragmatic considerations of why people accept inductive reasoning as generally true (how will we live without assuming natural regularity and uniformity?).

Many mathematicians are equally adept and comfortable working with axioms that are inconsistent with choice (such as the axiom of determinacy). Maddy's experience with mathematicians on the philosophical aspects of their discipline is similar to my own experience in asking them about foundational issues. They are, almost unanimously in my experience, far more pragmatic and anti-platonist than philosophers would believe and are in general less likely to have platonist intuitions than philosophers of math in my experience. When asked if they think the axiom of choice (or the Continuum Hypothesis) is true they will usually say something like "well, it's true under some models but not others." This is not them being flippant but stems from their general pragmatic outlook. So George's appeal to the authority of the mathematician in his reliance on that axiom for his proof of induction seems odd and rather unconvincing.

Animalism

Eric Olson argues that a person is just an animal. This implies that anyone is identical to some biological being with certain properties such as being multicellular, having cellular differentiation, capacity for sexual reproduction, motility and so forth. So an individual begins to exist at about the 2nd week after conception when cells begin to take on different characteristics (bone cells, nerve cells, muscle etc) and work together in unison to maintain homeostasis of the whole organism.

He argues against the view I think plausible that persons are just their brain (or actually some temporal stage of their brain). His argument is that views like mine must explain how it is that we can have properties that are not instantiated in the animal or physical brain that is co located with our selves when both things share the same constitution (made of the same stuff). There must be both an animal and a person sharing the same body, he argues, that we must explain how it is that there is much similarity between us without being the same thing and why we posit different properties despite the similarities. When I think a thought, does the animal that occupies the same spacetime region as me (or incorporates me if I am my brain) think the same thought or a different but qualitatively identical thought or no thought at all? If the animal no longer exists and was replaced by me, the person, we must explain where that animal went.

This is just a version of the grounding problem. Here, I can only respond that Karen Bennett has argued that the grounding problem is not really a serious problem because those who believe in coincident objects can simply posit the existence of (de se) modal properties as brute facts about things' having properties not grounded in their physical constitution. I find Bennett's argument very persuasive.

But I think I can also offer a tu quoque against Olson's view (i.e., that the same weakness he claims is a feature of the view I favor is a feature of his view as well). Oslon's view is the animalistic view. An animal comes into existence at the 2 week or so of gestation. However, there was an organism there before the animal; namely, that organism was a single celled organism (zygote) then became a multicellular embryo (without all the other criteria officially qualifying it as an animal). Is the animal which Olson think we all are the same being as the organism that came before it? If so then we would come into existence at the same time as it (not two weeks into gestation but about 48 hours after conception). If the organism came into being 48 hours after conception and the animal is identical with that organism then the animal must have also came into existence at that same time (by Leibniz's law of identity). If not, what happened to that organism? Was it replaced or does it exist coincidentally with the animal? So similar problems plague Oslon's view I believe. But it doesn't stop there. What of the oocytic view? This view is just that we are the original egg in which was fertilized by some sperm. Since the egg is about 1000 times larger than the sperm, the joining of both cells may be seen as the egg simply incorporating the sperm and changing a bit in terms of mass etc instead of going out of existence along with the sperm and both being replaced by a new being (the zygote). But the oocytic view is clearly preposterous.

The modal argument for dualism

Here's what I understand about this argument. Versions of it has been used by Kripke and Chalmers and here by Plantinga to argue that we are not our bodies or brains. The argument goes like this: Imagine yourself without a body. That seems easy enough. Can you imagine your body without its body? It seems not. That would be patently contradictory. Thus, your mind must have at least one property that your body doesn't: namely the modal property of possibly existing without a body. By Leibniz's law, they cannot be identical. That law simply says that everything has the property it has. If A has a property B does not have, they are not identical by that law. Your mind would have the modal property of possibly existing without a body while your body cannot exist without itself.

There are at least two ways to attack this. One may wish to deny Leibniz's law for modal properties; that is, one may wish to assert that it is possible for some things to have some modal properties they don't have. But I don't see this as a plausible avenue. It seems to me that Leibniz's law is true unrestricted, true for all properties, genuine, relational and modal.

So I will concentrate on the other possible objection which I will term the epistemic constraint to modality (ECM). It may seem plausible at first that anything one can imagine being true may be true in some possible world. Your car may be green when it is actually red. We know that your car has the modal property of possibly being green. How do we know that? We just imagine it so and if we can imagine it so, it is possible it is so. That's how we seem to know what is and isn't possible in the broadest sense. I can imagine your car being green when it's red and thus it must have the modal property of possibly green. I cannot imagine your car being green all over and red all over at the same time and thus your car must not have the modal property of being possibly green and red all over at the same time.

But does this kind of epistemic access always cut modality at its joints? Cut it precisely such that the space of epistemic possibility covers the same space as the modal space? Let's imagine we live 500 years ago. We would know what water was. It's that clear, potable, odorless liquid. Can we imagine it not being H2O? Yep, I believe we can. We could imagine it being XYZ for example. But we now know that water = H2O. It could not have been possible that water did not turn out to be H2O because water = H2O is a necessary identity statement. This is a case where our epistemic space over steps the boundaries of possibility. Thus zombies may not be possible though we can (now) imagine them.

Defenders of the claim that epistemic space and modal space are perfectly overlapping can deny that people 500 years ago really can imagine that water = H2O because they are not thinking about water when they imagine it not being H2O. But this doesn't seem like a way to defend that claim because then how would we know we are talking about or believing anything about some putative object when we imagine it being so (having some property) when science may tell us one day that it does not have that property? It doesn't seem that my ability to refer and to think about things are so dependent on contingencies in future scientific discovery.

Porn

Michael Rea's paper got me thinking about porn (not the content but the subject). As the old joke goes, porn is undefinable but you know it when you see it. If so then Rea tries to define the impossible. His attempt at a definition of porn is on the 3rd page. It basically defines an instance of porn as a token of some communicative material (pictorial, print, audio, etc) which will be reasonably expected to be used to sexually arouse or gratify members of some population to which it is targeted. Some provisos are that the intended audience can not expect it to be private communication (such as when a wife sends nude pics of herself to her husband) and that the material be used to that end for its communicative content.

I think there is a very damning counter example to this definition. Consider if some large population of porn subscribers were to read up on their sex negative feminist literature and as a result have a change of mind about porn. Now they see it as oppressive of women and denounce it and refuse to tend to their porn. Now it intended audience no longer seek to arouse and gratify themselves but that doesn't mean that the materials stop being porn. In fact, they may burn such material because it is porn. Rea may reply that once the audience changes their state of mind, they are no longer the intended audience of the porn producers. But that seems false. It seems that it is far more natural to say that their intended audience has had a change of mind about their products. The intended audience is still around, just not interested in the way they had been. It doesn't make sense to say that the intended audience dropped out of existence just because they had a change of mind. In fact, the porn producers may try to "win back" that audience through suasion and so forth. That would still make them a targeted audience.

Intention

The post on copy and original got me thinking about intention. What is intention and does it involve mental states and if so does it involve specific kinds of mental states? Can zombies and machines have intention? Let's say that you think intentions must involve a kind of "what it feels like to intend to do A" or any kind of phenomenal mental state. What if mind-body reductionism or eliminativism is true? That would either mean that the what it feels like or phenomenal quality is just some physical process in the brain or whatever or in case of eliminativism, there is nothing that it is like, just an illusion of what it's like perhaps.

Let's look at mind-body reductionism. If it is true, then there must be some specific physical process necessary if those who think that the "what it feels" is necessary for intention. But that seems implausible. What makes that process any different and special (deserving of being called intention) from a functionally similar process and externally identical one that does the same thing? Indeed, philosophers have definitions of intention that do not include a mental state criterion.

If our brains are just computational devices and our thoughts, emotions, and other mental states are just computations or the results thereof and the Church-Turing thesis is correct then it would seem that "intention" can be captured by a fully functional analysis. Indeed, think of even computers now. An example is a chess playing program. We may term a particular move made by the program as an intention to do something (capture a queen, set a trap, checkmate, etc). It has some of the features of intention such as a goal and decision(s) made among possible options towards that goal, etc, though presumably, no phenomenal mental features

Vague objects

Few philosophers believe in vague objects. Vagueness, many say, stem from our language, our conceptual scheme, or our epistemic limitations. Attribution of vagueness to objects, they maintain, is committing the fallacy of verbalism or the fallacy of mistaking that the property of things have the property of the words that describe them. There are exceptions (David Lewis, Gareth Evans, and Roy Sorensen I believe) who believe in vague objects. But if quantum mechanics says particles can be vague why not all else that are often thought vague like mountains (or just about everything, both particulars and categories and natural kinds)?