Tag Archives: logic

Quote for the Day – The Fuzzy Line Between Deductive and Inductive Logic

Beyond the level on which we say that the only logical method of anticipating the future is to project the past, there is the level of the everyday practice of logic. Here our confidence in logic arises from our examination into the details of how logic works in practical applications. On this level we recognize that the elements of a logical analysis must have some of the properties of the “things” of experience, in particular, permanence and identifiability. On this level there is no sharp dividing line between the inductive and deductive logic. For both logics demand identifiability and repeatability, which themselves are not sharp concepts and demand a projection of the past. Furthermore, as usually practiced, the premises of our deductions are obtained by inductive methods. When we say that all men are mortal we very seldom have behind us a verification by observation of all men, but the statement implies an inductive generalization of some sort.

~P.W. Bridgman, The Way Things Are, p. 118

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A Brief Response to Moore's Paradox

It is contradictory to simultaneously say “P and not-P”, but could someone coherently say “It is raining, but I don’t believe it is raining”? This odd little sentence is the heart of Moore’s paradox, what Wittgenstein thought was the most significant discovery G.E. Moore ever made as a philosopher. Moore’s sentence doesn’t strike me as obviously contradictory in the same way as “P and not-P”, but it is strange nonetheless. Presumably you would say “it is raining” when you can clearly see it is raining, so how could you not believe it? If you know it is raining such that you say it is raining, the rules of mental logic seem to suggest you should also believe it is raining, otherwise why say “it is raining”?. My solution to the riddle is that the claim about whether it’s raining is ambiguous between different criteria for satisfying the condition “it’s raining”. “It is raining” could mean that water is falling from the sky in a way that looks natural, or it could mean that natural precipitation is actually falling from the clouds. Why would you need the former locution? Suppose you work on a Hollywood set and you know that the artificial rain machines sometimes come on. All of a sudden it starts raining in the sense that water is falling from the sky in a way that looks natural (until you glance up at the giant machines). Now it becomes perfectly sensible to say “It is raining, but I don’t believe it is raining”. This in essence says “Water is falling from the sky but I don’t believe it is natural precipitation”. This is clearly a sensible thing to say in the circumstances.

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An Extended Tractarian Argument for the Simplicity of Objects

I’ve been getting back into Wittgenstein lately. For my proseminar at Wash U we had to read the Tractatus Logico-Philosophicus for a weekly assignment. I had never really studied it in depth before, but I now have a new found appreciation for early Wittgenstein. I’m fascinated by the metaphysical claims in the book. For example, 2.02-2.0212 might be charitably understood as endorsing the following reductio ad absurdum argument for the idea that any meaningful language must presuppose the existence of metaphysically simple objects:

1. Assume that a meaningful language does not necessarily presuppose there being metaphysically simple objects i.e. objects that are not composed of further objects.
2. Assume that in this language you can successfully refer to ordinary middle-sized objects (which are not simple).Accordingly, assume the statement “The cat is orange” is meaningful.
3. If “The cat is orange” is meaningful, it’s because, at the very least, in saying it a speaker presupposes that the cat is an object.
4. If (1) is true, and if the statement “The cat is orange” presupposes a distinct cat exists, then it also presupposes that the cat is a metaphysically nonsimple object (i.e. it is composed of further objects)
5. If statements about a cat presuppose that it is composed of further objects, and (1) is true, then those objects it is presupposed to be composed of are also presupposed to be nonsimple and composed of further objects, ad infinitum.
6. Thus, if (1) is true, the presuppositions built into the statement “The cat is orange” are infinite in complexity.
7. By the same reasoning, the presuppositions about the cat built into the opposing statement “The cat is not orange” are also infinite in complexity.
8. It seems natural to think that if talk about objects like cats has an infinite complexity in its presuppositions about how the cat is composed, then the statement “The cat is orange” can only be logically distinguished from the statement “The cat is not orange” if the most elementary parts of the presupposed infinite complexes of objects are different in some distinctive manner. [2.0201, 2.0211-2, 4.221]
9. By (1), the language is not committed to there being such things as “most elementary parts”; everything is composed of further things ad infinitum, for any posited basic entity would not be basic if it was assumed there were no basic entities. In other words, there would be no “substratum” for the regress to bottom out at; no substance [2.021]
10. Therefore, by (8) and (9), two opposing statements in the language about a complex object with infinite presuppositional complexity cannot be logically distinguished from each other simply on the basis of their elementary presuppositions because it seems strange to say two infinite complexes are different unless their (basic) members are different, but this is ruled out by (1), which assumes there are no basic members.
11. If two opposing statements are logically indistinguishable in the totality of their presuppositions, then they cannot refer to different states of affairs.[2.02331]
12. If two opposing statements cannot refer to different states of affairs, then the statements are not meaningful, for each statement could not be true or false.
13. The statements “The cat is orange” and “The cat is not orange” are obviously meaningful, so we must reject (1), since that is what got us into the infinite regress.
14. Thus, any meaningful language that refers to objects at all must be logically committed to the existence of metaphysically simple objects i.e. objects that are not composed of further objects.

Arguably premise (8) is the most problematic and controversial, for it might be begging the question. For this I don’t know how to repair the argument. Either you get it or you don’t. This might be a clash of intuition between people who have a gut feeling that it’s “parts all the way down” or that it bottoms out somewhere. I used to not have a strong opinion on this, but I am now inclined to think it bottoms out somewhere. I take this to be a logical fact, and not a fact of the universe, for only science can tell us what the actual bottom to reality is, be that quarks or whatever physics tells us. The intuition that reality bottoms out is driven by the inner logic of the idea of finite objects being composed of parts. It just seems downright strange, almost mystical, to say that a finite object like a coffee mug is composed of an infinite number of smaller objects. Surely it makes sense to say it is composed of a great many smaller objects, but I see no reason for thinking this amount infinite. Objects must bottom out according to the sheer logic of our ways of talking about composition. If this is right, then we arrive at a different interpretation of Wittgenstein’s argument for metaphysical simples than is commonly given. The concept of simple objects is not arrived at by seeing it in our language and then saying because language mirrors reality there really are metaphysical objects. Rather, the argument is transcendental in the sense that Wittgenstein shows that if we are going to talk about objects at all, we must presuppose metaphysically simple objects. So the Wittgensteinian point is not that language mirrors reality therefore simple objects exist (“One cannot, e.g. say “There are objects” 4.1272). The point is that language use logically commits us to the idea of there being simple objects when discussing objects. As Wittgenstein says, “Logic is transcendental” [6.13].

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Some thoughts on logic, explanation, and the philosophy of mind.

Since I am starting a PhD program in philosophy at Wash U, I will be required to fulfill some logic requirements over the next few years. I have never taken any course on formal logic, except for a class on critical thinking during my undergrad, but I don’t think that actually counts. Although I am starting to get more interested in pure logic for logic’s sake, I have always been skeptical of the direct relevance of formal logic to my research. My primary research interest is to understand the mind. Some logicians might say that insofar as logic is the study of reasoning, and reasoning is a product of the mind, the study of logic will allow one to better understand the mind. But I’m not so sure about how far this takes us. Logic is the study of reasoning at the most general level. When you study pure logic, you are not actually trying to produce a true idea about the world that might turn out to be wrong. In logic, the goal is not to make a substantive claim about reality, except insofar as logic itself as part of reality. Instead, you are trying to study the form of what a true argument looks like. Frankly, this just doesn’t interest me. I am interested in producing true theories about how the mind actually works which involve making substantive claims that might actually turn out to be wrong. The study of logic doesn’t produce true theories about the mind because that just isn’t what logic does. Does this mean that I am uninterested in using logic to produce truth? Hardly. Just like the jazz musician doesn’t need to know about the physics of acoustics in order to play good music, a philosopher doesn’t need to know formal logic in order to produce logical arguments that lead to truth.

When I say I am interested in producing truth about the mind, what does this mean? What does an “explanation” of the mind look like? For some orthodox philosophers, an “explanation” or “account” of the mind might look like this: every mental state supervenes on the physical world; mental states cannot change unless there is a corresponding change in the physical world. For these orthodox philosophers, this is where their job of explaining the mind ends. This type of explanation is supposed to be an argument for a “materialistic theory” of mind. Of course, these philosophers produce crafty arguments in order to reach the conclusion that the mental supervenes on the physical. And these philosophers are probably also involved in the defense of their thesis statement against various counter-examples and thought experiments such as Mary the color-blind neuroscientist, zombies, etc, In order to defend their “materialistic theory” of the mind, these philosophers would spend a significant amount time defending the supervenience theory against these thought experiments. To successfully respond to the “zombie argument” against materialism would count as “progress” in the expansion of the materialistic theory of mind. Likewise, many orthodox philosophers of mind think they are making progress in the field by coming up with counter-examples and purported knockdown arguments against other philosophical “explanations” of the mind, without ever making a substantive claim about the world that may in fact turn out to be wrong.

But honestly, I am not very impressed by such “materialistic theories”. I even think it might be problematic to call such ideas “theories of mind”. So what does a real materialistic explanation of the mind look like? For one, it’s going to be incredibly complicated and not easily compressed into a neat claim like “the mind supervenes on the physical” given that the brain, the seat of the mind, is the most complicated three pounds of matter in the known universe. To be sure, the mind sciences are in their infancy. This is why I have a love/hate relationship with philosophers. An orthodox philosopher might be content with “explaining” the mind without once referencing the brain. To me this is totally unacceptable. An explanation of the human mind MUST involve some reference to the science of mind, not just the philosophy. Thus, I think philosophy of mind is simply the theoretical branch of psychology, much like theoretical physics and its relationship to experimental physics. Philosophy jumps ahead of the data and produces theories that unify data into a more explanatory framework, which leads to better experimentation, which leads to better theory, and so on.

Now, the orthodox philosophers will probably respond by saying that such a brain-based explanation of the mind is surely limited to the local domain of earth-bound creatures, but that’s not what they are interested in. Surely, they will say, if we met an alien entity who appeared to be intelligent but did not have a brain like ours, we would not say that it lacked a mind. Hence, these orthodox philosophers claim to be interested in explaining the mind at such a level of generality that it applies to ALL minds, including exotic aliens with strange nervous systems. So any explanation of the mind that references the human brain must not be a real explanation of the mind, because it cannot handle different kinds of exotic minds. So when philosophers come up with “theories” of mind like “everything mental supervenes on the physical”, this explanation is supposed to apply to all minds in the universe, and not just humans. Thus, these philosophers think that they have some deeper insight into the mind because their account is so general.

But I think this generality and lack of concreteness is precisely the weakness of such theories. Let’s grant that an alien species would have a radically different way of thinking. Now, if we wanted to theoretically study an alien mind, would what be the best way to do so? By coming up with a priori necessary truths like supervenience? Hardly. I think the best way to learn about possible alien minds would be to study something like xenobiology. Evolutionary theory would still apply to the aliens. So would other scientific theories. I thus think that the best way to learn about “minds in general” is to study science, not a priori philosophizing. If you understand a great deal about how biological organisms evolved on this planet, I think you would have a better chance of understanding what an alien mind might be like than if you were to simply sit in your armchair and try to come up with a priori necessary truths such as “the mental supervenes on the physical”. Now, don’t get me wrong. I actually do think that the mental supervenes on the physical. How could I not being the materialist that I am? It’s just that I don’t think philosophy of mind should stop there and consider its job of explanation finished. And no, responding to endless counter-examples is not “progress”. Progress involves better understanding the biology and social conditioning of the mind, in all its glorious complexity. It involves at least making specific hypotheses locating mental functions to anatomy, and looking closely at the effects of development and the social milieu on mental function .

But isn’t this just going back to phrenology? I don’t think so. Phrenology was an unprincipled investigation into the location of brain function. It is based on a false belief, namely, that brain function can be understood by looking at bumps on the head. But “locating” mental processes to specific neural circuits (or distributions of circuitry, as is more likely) is vastly superior as an explanation of the mind than any kind of orthodox philosophical explanation. For example, my colleague Micah Allen and I have made concrete hypotheses about the default mode network’s involvement in reflective consciousness, and proposed a provisional model of how the DMN interacts with lower processes in the course of everyday human cognition. Our model is based on both phenomenological principles (i.e. that humans have both a prereflective and reflective consciousness) and neurofunctional principles based on recent discoveries in cognitive neuroscience. Is our model the end of the story? No. The explanation of the mind is just getting started. The proper way to progress from here would be to continue the interdisciplinary style of explanation wherein philosophy and science work in harmony to produce true statements about the mind that may or may not turn out to be false.

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