Author: Richard Brown

Aristotle on Universal Quantification

Richard Brown 5 Comments

I was rereading the Posterior Analytics in preparation for my lecture today and I was struck by the following passage from Book I chapter 4 (72b 28-30)

Now I say that something holds of every case if it does not hold in some cases and not others, nor at some times and not others; e.g. if animal holds of every man, then if it is true to call this a man, it is true to call him an animal too; and if he is now the one, he is the other too;

Here Aristotle seems to be defining ‘all A’s are B’s’ in terms of a universally quantified conditional statement (for any thing (and/)or for any time, if that thing is an A then that thing is a B). This sounds surprisingly modern (indeed, by the end of the chapter he seems to be talking about universal instantiation), since most of us were told in our logic classes that rendering universal statements in terms of a quantified conditional is supposed to correct an error in Aristotle’s logic (i.e. the error of thinking that ‘all’ implies ‘some’). But if we take Aristotle at face value here the way he formally defines ‘all’ will give us perfectly good truth conditions for ‘all A’s are B’s’ even if there aren’t any A’s at all.

So it doesn’t seem that Aristotle’s logic is committed to the existential import of universal affirmative statements (though I know that this isn’t Artistotle’s position since he is clear that No A are B is the contrary of all A are B (i.e. they both can’t be true. He gives as examples ‘all men are just’ and ‘no men are just’)). I wonder if Aristotle had thought explicity about empty categories if he would have rejected the contrary bit from On Interpretation…

UPDATE:

Thinking about this a bit more it occurs to me that what this shows is the implicit truth-conditional definition of the conditional Aristotle is using. ‘If p then q’ From what he says we can see that the sentence will be true when p is true and q is true and it will be false when p is true and q is false (cf his evidence in Post. A. 72b 30). He does not say anything about the case when p is false, but we can infer a bit about this condition by his claim about contraries. Since when All A’s are B’s is true No A’s are B’s must be false we know that the conditional cannot be counted as true when teh antecedant is false (that would render both of these statements true and so not contraries). So, in the F F and F T combinations the conditional must be counted as false. That satisfies the requirement that the two cannot be true together. So we can see a kind of operator being defined here; let’s call it ‘xxx>’. ‘xxx>’ is defined truth functionally as

P         Q     P xxx> Q

t          t        T

t          f         F

f          f         F

f          t          F

Is the ‘XXX>’ connective a connective from relevance logic? No, it is just the ‘&’ of classic first-order logic…this fits very nicely with the metaphor of universal quantification as a giant conjunction…

HOT Imagination

Richard Brown 1 Comment

I was reading this interesing report on some of Frank Tong’s recent work here. Tong’s work is regularly presented at the consciousness conferences I frequent and I have briefly mentioned it before. This recent study asked participants to imagine a certain image. Then these subjects were subjected to a binocular rivarly set up, which is where researchers present a different picture to each eye at the same time. What usually happens is that the person sees the two images switching back and forth. Some of Tong’s other works has focused on showing that we correlate the subject’s report of whcih they are seeing with their neural activity and thus learn to predict from looking at their brain what they are seeig. This is very exciting!

Anyway, in this research Tong shows that imagining one of the two simuli before having them presented influences which of the two you end up consciously seeing. In fact he is able to show that it has the same effect as being presented with a ‘dim’ image of the stimuli. The article points out that this might lead to an empirical way to quantify how strong an individual’s mental imagery is. Super interesting!! But I am interested in this as data for a theory of consciousness.

How do we explain this? Well, from the higher-order perspective it is easy to explain. A conscious mental state is, on this kind of view, consists in my being conscious of myself as bing in some first-order state. Presumably imagining is a conscious mental experience, and so would have to consist in my being conscious of myself as being in the first-order state that I am imagining. Presumably the disparity in first-person reports as to the presence of mental imagery is due to the varrying ability of persons to token this higher-order state in the absence of the firsrt-order sensory state. This also explain why it would be the case that presenting the subject with a dimly lit actual image works just as good as the subjects own imagined experience.

For some people it is easy to token the relevant higher-order state and they have very vivid mental imagery experience. Others have difficulty tokening these higher-order states and manage only to have ‘fleeting’ mental images. There is even a small group that denies to have this ability. I must confess to be one of these people. I have never been able to have vivid mental imagery. When I imagine a situation I usally find myself describing it like you might find in a book. Sometime I can manage vauge mental images, especially when laying down on the verge of sleeping, but when I am alert and awake it is very hard for me to do. Interestingly, I have good auditory ‘imagery’ experieince. I think that this may be due to me being a musician but that is just anecdotal evidence.

The preceeding discussion is all based on the assumption that imagining cannot happen unconsciously. The way I have explained it above has it as only being conscious. Is this a mistake? Rosenthal does not anywhere explicitly talk abou tthe imagination. I wonder if he thinks that we could imagine something unconsciously?

Philosophers’ Carnival & Some Announcements

Richard Brown 6 Comments

Carnival here

There has been a lot happening out here in the real world lately (see my website for details). Here is a synopsis

1. I have a committee and a date to defend my dissertation! This is simultaneously exhilerating and terrifying…

2. My paper “The Metaphysical and Epistemic Impossibility of Moogles” has been accepted to appear in the forthcoming Final Fantasy and Philosophy volume…does this make me a super nerd?

3. I put some new tunes up at the Logical Form site…check them out! (Rumor has it that there may be a NC/DC reunion soon…

 

OK, I got to go, but I’ll be back…

Fodor on Natural Selection

Richard Brown 16 Comments

I am back from Philly. I had a veggie-cheese steak and saw the Liberty Bell.

As for the SPP, it seemed to be doing quite well. I missed the first day of the conference, which I was bummed about. I wanted to see Devitt’s talk on ‘The “Linguistic Conception” of Grammars’. From what I know of Devitt’s recent work I would guess that the talk was an attack on the assumption that the rules of grammar are explicitly or implicitly represented in the mind of a typical language user. I am sure that would have been interesting to see.

I did catch Jerry Fodor’skeynote speech on Friday. He was there giving a version of a talk that I have heard a couple of other times at various conferences around the New York area. The basic theme of his latest work has been an attack on standard formulations of adaptationism of the Darwinian variety. This theory aims to explain how it comes to be the case that animals come to be adapted to their environment. This is a question that has puzzled biologist for some time. The Darwinian answer is in terms of natural selection. The basic idea is as follows. The traits that are useful for the species (cashed out in terms of reproductive success) are selected for and the traits that are detrimental to reproductive success are selected against.

Fodor’s argument againts this well established view proceeds in a couple of steps. The first step is to look at intentional actions and point out a certain kind of problem. Take the frog. It snaps at flies in order to survive. Now consider the intentional state of the frog itself. Is it intending to snap at flies? Or is it intending to snap at ‘ambient black dots’? These are twp different properties. It happens to be the case that whichever one the frog is doing will help it in the environment it finds itself in, so in a sense natural selection cannot distinguish between these two very different properties. Since it can’t distinguish between them it cannot select between them.

This problem generalizes, according to Fodor. Consider the Polar bear. The standard story that is supposed to explain why the polar bear is white involves selection for white polar bears. But ‘selection for’ as an intensional context. What this means is that we do not get truth preservation with substitution of co-referring terms. So, in the case of belief attribution which are the exemplars of what happens in an intensional context. So, I can believe that 50 cent is a great rapper without believeing that Curtis JAckson is an excellent rapper even though 50 cent and Curtis Jackson are the same person. Now consider ‘selection for’. Say that white is my favorite color. Being white and being my favorite color are different properties and selection for one is not selection for the other. The problem then becomes of explaining how we can say that white polar bears were selected for, as opposed to polar bears that are my favorite color. There are an indefinate number of properties which are distinct from yet coextensive with being white. If you don’t like that of being my favorite color Fodor’s example is ‘being the same color as the environment’. Which of these properties were selected for? To answer that question you would need a selector, but the Darwinist is not allowed to this claim. So then, the traditional adaptionist theory fails to do what it promises to do.

As usual, the scientist in teh room were very upset with Fodor, and it was quite entertaining. Lot’s of people have been upset with Fodor recently. Dennett says that Fodor’s argument is good for two things. Providing a reductio of the Fodor-inspired Representational theory of Mind in cognitive science. And demonstrating how NOT to do philosophy. I worry that this is half right. It seems to me that if one does approach the problem in the way that Fodor does, which whether or not correct is one of the most widely held views about the mind in current cog sci, then you do have this problem.

How much of a problem it turns out to be remains to be seen. Fodor thinks that it is no big deal. He certainly doesn’t think that this should provide comfort to the intelligent design folks.  

The Empirical Justification of Mathematics

Richard Brown 22 Comments

Things have been quite around here lately, mostly because I have been lost in GTA IV and finishing my dissertation. Well I am making some progress (on both 🙂 ) and so will try to get to some of the comments around here.

In answering the comments on the Refutatioin of Rationalism I started thinking about Quine’s indispensibility argument for the empirical justification of mathematics. The argument starts from Quine’s claim that we are ontologically committed to the things which we quantify over in our best theories. The indispensibility of mathematics to physics means that we are committed to the existence of numbers (but not, obviously, to their non-physical existence). So Quine went on to argue that, since our theories all get confirmed or disconfirmed together as a group, the empirical confirmation of physics is empirical confirmation for mathematics. In this way mathematics is empirically justified.

One problem with this argument is that it depends on confirmation holism. That is, it depends on the claim that all of our theories are confirmed or discomfirmed together. None ‘face the tribunal of experience alone’. I then started thinking about how Rosenthal’s version of this argument avoids this commitment and so is a better argument. Sadly Rosenthal has never published this argument (I heard it in a seminar on Quiene and Sellers he gave) so I will try to recreate it as best as I remember.

The basic idea is: if we ever had empirical evidence that some truth of arithmatic was false we would have to admit that it was false. But if so then mathematics is empirically justified. To make the case he asks us to entertain the following scenerio. Suppose that you had two pens of sheep; one with 6 and one with 7 sheep. Now suppose that you counted the sheep individually in each pen (and got 6 and 7) and then you counted all of the sheep and got 14. Suppose you did it again. 1. 2. 3. 4. 5. 6. Yep six sheep in that pen. 1. 2. 3. 4. 5. 6. 7. Yep seven sheep in that pen. Then all the sheep. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. Suppose that this was repeated by all of your friends with the same results. Suppose that it was on the news and tested scientifically and confirmed. Suppose that this phenomenon was wide spread, observable, and repeatable.

If this were the case we would be forced to admit that 7+6=14 is true therefore mathematics is empirically justified.  

The Refutation of Rationalism

Richard Brown 19 Comments

I am back from my vacation in Liberty City 🙂

Seriously though, gta 4 is a lot of fun and very addictive!

I have recently been very interested in showing that rationalism is hopeless. To be open, I confess that I used to be a rationalist when I was younger. When I first started studying philosophy I was very influenced by Descartes and found his talk of clear and distinct ideas and ‘the light of nature’ very compelling. There is no suprise here, as rationalism has been the dominant view in the Western tradition since its inception. But, as rationalists like Bonjour admit, rationalism has suffered several notorious and embarrassing setbacks. Perhaps the first of which goes back to Gallileo showing empirically that Aristotle’s physics was wrong in assuming that heaverier bodies fall faster than lighter bodies. More dramtically, perhaps, is the discovery of non-Euclidean geometry which showed that various of the fundamental postulates of geometry were not necessary (like the parralel postulate). We should perhaps add to this the discovery of Russell’s paradox and the various self-referential semantic/syntactic problems (i.e. Godel, the liar, etc) which have led to the development of alternative logics.

What this shows is that intellectual seemings are fallible. It cannot therefore be argued that something seeming to need no empirical support and seeming to be justified purely by reason is enough to establish that the fact in question is really justified independently of experience or not. So, take 1+1=2. It certainly seems that this is true, in fact it is hard for me to imagine how it could be otherwise. There is a strong subjective sense of certainty that I experience when I think about it. All of this is no doubt true. But we have as of yet no reason to think that it is REALLY necessary, or that its justification is independant of experience. This is because we can not tell a priori whether the intelectual seeming is indeed correct. This shows that rationalism is in serious trouble. There is no other reason to take rationalism seriously other than the strong pull these rational insights have on us.

One might want to reply by saying that is overly skeptical. We shouldn’t abandon a priori knowledge just because we have mistakenly identified somethings as necessary which weren’t. So too, the objector goes on, just because we hallucinate doesn’t mean that we don’t normally see objects. Fair enough. But then what we need is an actual account to back this up. What is the difference between the cases? We can give that in the empirical case. We can describe ways in which we could find out whether the person was hallucinating or not based on our ability to monitor the brain of the animal in question and our visual impressions of the experimental set up. We can give a sketch, if not every detail, of a story which desribes how the brain interacts with the enviornment it finds itself in and generates representations of that environment. But can you do the same for rationalism? To date no one has. What is an eternal, necessary, non-physical/non-natural object like a number or modus ponens really like? How do we interact with it? No one knows. How could they?

Now this would be a pressing concern if it were impossible for us to fully understand the world we live in except for the truth of rationalism. But this certainly isn’t the case. We have good candidates for materialistic accounts of every disputed area. For instance, in the area I know most about, we have the mind-brain identity theory and the higher-order theory of consciousness. I do not mean to say that we know that they are true, but only that they are viable candidates. For all we know right know they could be true. They have not been absolutely refuted by any a priori arguments, nor have they shown themselves to be inconsistent with the findings of science, quite the converse actually. As for math and logic we have either constructivism or Mill’s view that they are empirical generalizations (I interpret this to mean that they are an attempt to model the way that the physical world works and to grow into Quine’s indispensibility argument that the justification for mathematic is empirical), or a more modern version of deflationism or fictionalism about this stuff. The same is true for ethics.

Again, none of these has been demonstrated to be correct. The point, rather, is that we should prefer natuaristic/materialistic accounts ove their non-natural/non-physical competitors. They automatically become more plausible because of their reliance on the more plausible empiricist/scientific account of knowing.