More Square

As I mentioned in my last post we are discussing the traditional vs modern square of opposition in my logic course (which did not go over well btw, most students reacted viscerally to the claim that modern logicians reject the entailment of the I proposition by the A proposition…to the point that one student exclaimed that it was a betrayal of Aristotle!) but at any rate I was reading the entry at the Stanford Encyclopedia on the Traditional Square of Opposition which is written by Terrance Parsons. The article is very interesting and provides a valuable history of the development of the square.

Along the way Parsons develops the very interesting idea that the modern problem with empty terms is not a problem for Aristotle’s original formulation of the square and especially because of the way he formulated the O statement, which is not as the traditional ‘some A is not B’ but rather is ‘Not every A is B’. This, argues Parsons, solves the problem with existential import since ‘not every A is B’ does in fact seem to be true as is required. Parsons blames Boethius for the rewording of the O form,

Aristotle’s work was made available to the Latin west principally via Boethius’s translations and commentaries, written a bit after 500 CE. In his translation of De interpretatione, Boethius preserves Aristotle’s wording of the O form as “Not every man is white.” But when Boethius comments on this text he illustrates Aristotle’s doctrine with the now-famous diagram, and he uses the wording ‘Some man is not just’. So this must have seemed to him to be a natural equivalent in Latin. It looks odd to us in English, but he wasn’t bothered by it.

But isn’t it obvious that ‘not every unicorn is an animal’ is truth-functionally equivalent to the traditional ‘some unicorn is not an animal’? That is to say, it is clearly the case that ~(x) (Hx –> Mx) is equivalent to Ex (Hx & ~ Mx) [by quantifier exchange, the definition of ‘–>’ and DeMorgan’s law]. So…Boethius was right, wasn’t he? And not just because it is a natural translation in Latin, but because the two statements are logically equivalent….right?

Does All Imply Some?

So in the logic course I am currently teaching we are about to start talking about the contrast between the modern and traditional square of opposition. The main difference, of course, is that poor Aristotle thought that if it was true that All A’s are B’s that made it the case that Some particular A was in fact B, and so he would be forced to exclude syllogisms as valid that have fictional terms. Consider the following proposition,

1. Some humans are mammals

Now, I often find that students think that 1 is false. They think that it is false because they think that it implies 2

2. Some humans are not mammals

but in the traditional square of opposition this is not the case. 1 and 2 are subcontraries, which means that they can’t both be false. Now this means that it is a possibility that both of them are true, but there is also the possibility that only one of them is true and the other is false.  Since it is true that all humans are mammals by subalternation we know that 1 is true . Thus, we can say that 1 is true because we know that 3 is true and 2 has to be false because it is the contradiction of 3.

3. All humans are mammals

But what are we to make of this on the modern interpretation? Can we no longer say that 1 is true because of the fact that all humans are mammals? It is still the case that 2 is false, as it is still the contradiction of 1. But what about the so-called existential fallacy?

But if we take this discussion out of the realm of categorical propositions and start talking in terms of truth-functional semantics don’t we get the traditional square back? So, 1 is written as 1* with

1* Ex(Hx & Mx)

Whereas 2 and 3 turns into 2* and  3*

2* Ex(Hx & ~Mx)

3* (x)(Hx–>Mx)

So to get the traditional square back we would need to show that 3* implies 1*.

Consider the following proof,

A. (x) (Hx –>Mx) [assumption]

B.  Ex (Hx) [assumption]

C. Hy [Existential Instantiation of B]

D. Hy –> My [Universal Instantiation of A]

E. My (Modus Ponens D, C)

E. Hy & My [conjunction introduction]

F. Ez (Hz & Mz) [existential generalization]

So, if B is correct and there are humans then 3 does entail 1 just like Aristotle said. Am I missing something?

Plant Rights? Yeah Right!

Over at the Opinionator there is a very nice article examining the issue of whether we should eliminate meat-eating in nature if we could. Personally I think that I agree with McMahan’s conclusion that we have more reason to eliminate meat-eating in nature (if we could without great harm) than we do to preserve the various carnivorous animal species. What is striking are the two themes of the comments, or at least the first page of comments…I did not have the strength of will to go through all 11 pages of them. The first is the ludicrous idea that McMahan is somehow advocating the extinction of the Human Race. He very clearly says that humans should stop eating meat and become voluntarily non-carnivorous. The second theme in the comments is that plants have lives and when we eat them we cause them suffering so even being an herbivore is not good enough. Since this is obviously absurd it is concluded that the original claim was also absurd.

Why is this idea so prevalent among people? Our best scientific theories about the world suggest that you at least need some kind of central nervous system in order to have pain or suffering. Carrots have no central nervous system and so cannot suffer. One reason someone might object to this is allegiance to some kind of radical substance dualism. Non-physical minds can be had by anything, even carrots! But just as there is no reason to think that substance dualism is true for humans there is even less reason to think that it is true of carrots. One other line of evidence often cited is that plants react to their environment in ways we didn’t know about 1000 years ago. We have all heard about plants responding to music, “screaming” when in danger, “warning” other trees about fire, etc but isn’t it quite obvious that this is no more evidence that plants feel pain than finding out that a Roomba emits a certain frequency when it is smashed would be evidence for it feeling pain? Plants are alive and react to the environment but unless they have some kind of brain or brain-like system there is no reason to believe that they feel pain or suffer. Reaction to physical damage does not entail that there is pain much less suffering.

Now, I grant that it is conceivable that plants feel pain, and that the issue of whether it is moral to eat them hinges in large part on the answer to this question; if carrots suffered it would be prima facie wrong to eat them. I think I can also grant that we do not know with absolute certainty that plants don’t feel pain, so we cannot rule out that the actual world is in fact a world where carrots feel pain. Even so, if that were the case then McMahan’s argument would have to be put in terms of turning all species into photosynthesizes, or some other non-predatory way of producing energy and the main conclusion would still stand. So it looks like the appeal to plants is doubly off-base. In the first place it is off-base  because though plant sentience is a possibility there is no serious reason to think that it is actual and secondly it is off-base because the conclusion would still follow if we amended the argument in a suitable way.

Can We Think About Non-Existent Objects?

I am scheduled to record a conversation with Pete Mandik for Philosophy TV tomorrow on higher-order approaches to consciousness and in the course of preparing for it I was rereading Pete’s Unicorn paper where, among other things, Pete gives several arguments that we are in fact able to think about non-existent objects. I do not think that we can.

It may seem quite natural to think that the answer to the above question is ‘yes’. For instance, we think of Count Dracula, unicorns, Santa Claus, and many other examples of this kind. If we take ‘thinking about’ to involve having some kind of relationship with the thing that is thought about this can seem crazy. If I am thinking about Santa Claus, for instance, that would mean that there would have to be some object that I was related to and since Santa doesn’t exist the object would seem to be a very strange one indeed! What should we conclude from this? Should we conclude that ‘thinking about’ doesn’t really involve a relationship between the thinker and the thing thought about?

Suppose that one accepted some kind of causal-historical account of the reference of (at least some of) our concepts and that thinking about x means tokening a thought containing a mental representation of x with the approriate causal-historical connection to x. So, to rehearse a familiar picture, Some child is born, his parents say “let’s call him  ‘Saul Kripke'”, other people are told “this is Saul Kripke” and thereby acquire the ability to refer to this child. Over time this name propagates, like a chain, link by link to us. So that when I think about Saul Kripke I employ a thought token that traces a causal-historical route back to the initial “baptism”. If this were the case, and one thought that natural kind terms worked like this as well, one would end up denying that we think about non-existent objects. The concept UNICORN has as its reference whatever it is that actually turns out to have been “baptized”. This may turn out to be a deformed goat, a hallucination, or maybe an imaginative act on the part of a person, whatever it actually turns out to be is what we are thinking about when we think about unicorns and that thing exists. So too for Dracula, Santa Claus, Jackalopes, etc.

But what about when we think thoughts like ‘there are no square circles’? Aren’t we thinking about square circles? I don’t think we are. Rather I think we are having an existentially quantified thought to the effect that nothing is both square and circular at the same time. Aha! Aren’t existentially quantified statements that are actually false examples of thinking about non-existent objects? If I think that the present King of France is bald, and there is no present King of France, are not I thinking about a non-existent object? Of course not! What you are thinking is that there is someone or other who is the present King of France and that is just plain, ordinary, boring false. There is no non-existent object which is correctly described as the one you are thinking about.

But isn’t denying that we can think about non-existent objects self refuting? What have we been talking about this whole time if not whether or not there are any of this kind of thought! So denying that there are any just shows that we have been thinking about non-existent objects all along! The very thoughts about non-existent objects that we have been discussing. But this is too quick. This is again just another example of an existentially quantified statement. ‘There are no thoughts about non-existent objects’ is really just saying that thoughts about non-existent objects don’t exist but that does not thereby mean that I am thinking about some non-existent objects! And this is for just the same reason as above; there are no objects which can be correctly described as the ones that I am thinking about.

So I am inclined to deny that we can think about non-existent objects…I am not saying that everyone should but only that there is a reasonable view, one that we ought to accept for other reasons not gone into here, and which denies that we think about non-existent objects. What this has to do with consciousness and Pete’s unicorn argument I will save for tomorrow’s discussion.

Levine on the Phenomenology of Thought

On Wednesday I attended the inaugural session of the Graduate Center’s philosophy colloquium.  The speaker was Joe Levine and he wanted to examine two of the arguments for the phenomenology of thought as given by people like David Pitt and Charles Siewert and argue that they were not up to the task that supporters thought they were.

The two arguments were what he called the self-knowledge argument and the phenomenological argument. The self-knowledge argument claims that the only way we could have genuine acquaintance-like knowledge of our cognitive states was if they had a phenomenology. Levine rejects this argument as question begging. The second argument he takes more seriously. The phenomenological argument points to several distinct kind of phenomena. So, take an ambiguous sentence like ‘visiting relatives can be boring’. When one understands it to mean that the relatives who are visiting are boring and when one understands it to mean going to visit relatives is boring there seems to be a difference and this difference intuitively seems to be phenomenal. Or take listening to someone speaking a language you don’t understand versus one that do. When people are speaking a language you do not understand it often sounds as though they are speaking really fast and that there are no spaces or pauses in their speaking but this is very different from listening to a language you do understand. The idea is supposed to be that there is a distinctive cognitive phenomenology that goes beyond any associated internal monologue or mental imagery. Levine admitted that he felt there was something to theses kinds of cases and argued that intuitively it is just as string an intuition as that there is something that it is like to see red or feel pain. I agree. The question, then, is what does this force us to conclude about the phenomenology of thought?

As a contrast Levine introduced a null hypothesis, what he called the Non-Phenomenal Functional Representation thesis. NPFR, as he calls it, is basically a standard higher-order view about self-knowledge. When one knows what one is thinking one tokens a higher-order state the content of which is that one is in the first-order state. This is why the self-knowledge argument doesn’t really pull any weight. Both camps have an explanation of how we have self-knowledge. What about the phenomenological argument?

In order to respond to this Levine distinguishes two versions of the claim that there is a phenomenology that is distinctive to thought that he calls a pure and and an impure view. On the pure view there is a phenomenal character of an occurrent thought that is not tied to any sensory state while on the impure view “attributes phenomenal character only to sensory states, but allows that cognitive states can create phenomenal distinctions among otherwise identical sensory states,” (from the handout). The pure view is the just the usual idea that there is a distinctive phenomenology for thought. The impure view is a bit harder to get ahold of but the basic idea seems to be based on an analogy with the way sensory states work. So, take the higher-order view about consciously seeing red. On the HOT view there is a first-order sensory state that has phenomenal character and then there is a higher-order state that represents oneself as being in a red sensory state. One can a higher-order thought to the effect that one is in a generic red state or that one is in a specific red state and this will determine what it is like for you to have the experience but the HOT itself has no phenomenal character. So by analogy then Levine’s impure view seems to be that we have a first-order state, say a hearing or seeing  of ‘visiting relatives can be boring’ and one’s higher-order state can then represent it as either being about the relatives coming or your going to them and this will result in a distinctive phenomenology. That is to say that on the impure view what it is like to hear the sentence will be different when one is aware of it one way or the other but there is no cognitive phenomenology. All there is is two different kinds of auditory phenomenology.

I think my own view about cognitive phenomenology is similar except that I think that this can happen in the case of a propositional attitude and not just through some sensory state. For instance when one has a conscious belief that p I claim that it will be like believing that p for you and this is because one is aware of oneself as believing that p. This makes it a version of the pure theory. So, is there any reason to prefer the impure theory to the pure one? Levine argued that the phenomenological argument supported only the impure account and so it was no reason to think that the pure view was correct. His idea seemed to be that since the data was hearing a sentence one way versus hearing it another we only had evidence that there were two different ways of hearing the argument.

At the end of his talk he introduced another distinction between transparent and opaque cognitive phenomenology. On the transparent view “what the cognitive state is about, what it is representing, constitutes the “look” of the cognitive state while on the opaque view there is only a contingent relationship between what is represented and the cognitive state. The issue here seemed to be diagnosed buy whether one thought that there was any possibility that one could find out that one was radically mistaken about what one thought. His example seemed to be the standard brain in the vat scenario. If one came to be convinced that one was a brain in the vat, or that Quinian indeterminacy of referce, were correct one might come to find out that one was radically wrong about what one thought. On some theories of mental content one wouldn’t be mistaken, but let that slide. The point he was trying to make was that we could “wrap our heads” around the idea that our cognitive states are not transparent. He compared the opaque view to Block’s view about mental paint.

During discussion Levine discussed a comparison with people like David Pitt and Sussanna Seigel. Seigel argues that the content of our perceptions is richer than we thought (e.g. it is part of our perception of a tree that it is a tree)  and in so doing end up making perception more like cognitive states while people like Pitt argue that thoughts have a phenomenal feel and thereby make thoughts more like perceptions. This led some to wonder how we might distinguish between the two states. On my own view this is wrong headed. What we should take this as is a trajectory towards a unified account of the mark of the mental.