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Demarcating Logic

Timothy
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Posted 09/15/09 - 11:40 AM: Subject: Demarcating Logic	#1
A typical characterization of classical logic, as a subject-matter, is that it's a formal study of certain types of relations between sentences (in sentential calculus) and/or n-adic predicates (in FOL, HOL). What this usually means is that the study of those special relations doesn't take into account the content of the sentences/predicates being considered. This is usually paraphrased as saying that logic is "topic-neutral". This is presented as a hallmark of logic over other subject-matters, and as an argument for taking logic as the "foundation" of the other sciences, insofar as the logical forms can be filled with the content of any science. What this view presupposes is that there is a principled difference between the form and the content of a sentence. Let's assume that Davidson was right in rejecting that dichotomy as unfounded. There would seem that there's nothing special about classical logic anymore, and it's not more fundamental than any other science. Do you agree with this prognosis? Or do you feel that this conclusion means that something has gone terribly wrong? Is there different criteria for demarcating logic's subject matter?
"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

Timothy
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Posted 09/20/09 - 05:40 PM:	#2
This should be offensive to the many foundationalist ears out there!
"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

ronlongo
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Posted 10/24/09 - 10:32 AM:	#3
I'm not even entirely sure I understand this post, but I can't help but to bite given what I think I understand about it. First off what I think I'm reading in it is that some have argued that the commonly accepted formal logics (truth-functional, 1st order, etc.) are wholy no more useful than english and so have no value. I would like to attempt to begin by refuting this claim with analogy. Let's take two spoken languages such as english and chinese. It cannot be denied that these two languages are different materially (on grounds of syntax, written system, pronunciation, etc.). However, in terms of function, both languages can be used to express the same ideas. Or can they? Certainly they both can express the same ideas of every day usage. This is supported by the fact that it's possible to translate whole sentences from one language to another. However, when we get into the artistic uses of spoken languages, literature, poetry, etc. It's often desireable to translate on a more detailed level than sentences as a whole. In particular in poetry where some translators attempt to even preserve elements such as meter, rhyme and connotation. That is, even with languages designed to be for general use, different ones are more suitable for expressing different kinds of things. Now if we extend the analogy into specialized languages the differences and, most importantly, strengths become more aparant. My example would be the formal language of mathematics. Translating a formula into an english sentence can be tedious at best. Further, the english sentence obscures the structural elements of the formula that are of interest for math purposes. Imagine attempting now to manipulate that english sentence using algebra to perhaps derive a new formula or solve for x (each step of the derivation being another english sentence). Hence, specialized language can stress, bring out or make aparant structural elements of a proposion which are most important for a particular pupose. I wouldn't argue that they necessarilly do, however anecdotal evidence can demonstrate this oneself and perhaps some sort of social experiment could be conducted to prove this. So I would venture to argue that there is ineed a "principled difference between the form and the content of a sentence." But I would argue this only on basis of practicality. That is, the limits of the human brain. If we can imagine taking human beings out of the picutre (I know, it's about as real as a frictionless pully in a college Physics class), then perhaps there would be no difference between form and contect. But with humans, we've gotta work with what we have. Sometimes that means having different languages for stressing different aspects of ideas. Hence, well designed specialized languages highlight elements need for a purpose while trivializing or even removing the bits we consider irrelevant. I would like to note that the thought had occurred to me to compare logic, math, etc. (languages) to tools. Arguing that a general pupose tool can do many things but only in a mediocre fashion while specialized tools can only do one thing but does it very well. The problem with this argument, I felt, is that tools are physical objects and as such are true elements of the universe. To me logic, math even spoken language exist only in the human mind. This difference was important enough to break the analogy in my mind. But perhaps that's a debate for another thread.

Timothy
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Posted 10/25/09 - 12:12 PM:	#4
The question is not really one about the value of logic, but rather about criteria for defining the "realm of logic" from the other possible realms, i.e. physics, linguistics, maths, etc. The classical criteria is the formalist status of logic over all other subject-matters. Logic, it is commonly said, is not about any particular entity (numbers,masses, taxa...) but rather about abstract relationships that can hold between predications of any entity whatsoever. For this criteria to work, one has to adopt a strong principled differentiation between the form of a predicate and its content, in order to say that logic cares not about content (what you're saying and of what you're saying it about), but rather about the form. Davidson argues against this principled differentiation, by showing that there's no real reason to think one must hold it, while pointing towards some reasons to not hold it. So, assuming Davidson was right, my question is: what other criteria could be proposed in order to differentiate the discipline of logic from all the others? It could be seen as a purely demarcating issue, but I'm sure that different criteria can come from metaphysical considerations, or epistemological, or ontological, or pragmatical, etc...
"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

ronlongo
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Posted 10/26/09 - 05:39 PM:	#5
Ah! OK Very interesting. I think I have a better understanding of what you are asking. Philosophy and logic (if you choose to differentiate the two), while being subjects that interest me, are not a true expertise of mine. I claim no exceptional knowledge (and perhaps for that matter not even basic knowledge) on the subject. However, I do have an evolving theory I first started to develop years ago which involves the question of human nature. It was in fact the desire to understand how to properly articulate this theory which drectly led me to study logic. While the theory itself isn't relevant here, there is an element which I believe is. I mention my "story" here only to be open that I'm no expert but at the same time have thought a lot about the fundamental issues of my theory which, again, I believe are relevant. In my theory I start with the individual, the self and in particular the mind of this individual. This "self" perceives the universe, in three fairly distinct parts. While these parts are perhaps not absolutely mutually exclusive, I think they divide the world in much the same way that we all do naively. The names I give to these parts are the external, the internal, and the theoretic (or, dare I create a new word, metaternal). The external is everything outside of the mind of this individual, specifically the physical universe (including the individual's own body and brain). The internal is the mind and thoughts of the person. The metaternal (theoretic) is the thoughts of the thoughts of this person -- the perception of self and observation of one's own thoughts. When I started learning logic, one of the first books I read (I believe the Patrick Hurly book), the author defined logic as the science that studies or evaluates arguments. This was odd to me. It was the first time that I had thought to consider logic (or math or other similar studies) as a science. But as I thought upon it I realized that if I made a small alteration I could categorize the sciences (including logic) into my 3-part universe. The alteration I would make is to consider things not from the point of view of the individual, but from the point of view of humanity as a whole. In this way the "internal" changes from the thoughts of an individual to a broader social context. The breakdown of the sciences into this 3-part universe yields: External: Physics, Chemistry, Biology Internal: History, Sociology, Anthropology, Psychology, Economics, etc... Metaternal: Mathematics, Set Theory, Linguistics, Model Theory, Pattern Theory, Logic, Algorithm Theory, etc. Now I know that many people, in particular math people, like to consider topics such as Set Theory as parts of mathematics. Being a lay person, to me math is about numbers. Sets can contain things other than numbers. For example, I can imagine a set of all the objects in my living room and another set of all the items on the first floor of my home. So to me the metaternal sciences (systems used for communicating theories) are separate, though collectively they support one-another. I reason this because of things like the general failure of Logicism. It would seem currently that none of these theoretical systems is more basic than the others. With this said, however, I admit that I know very little about these systems. As a computer scientist, I have studied algorithms and something of the theory. Next to knowing that Pattern theory exists, I know almost nothing about it though I suspect it to perhaps be a generalization of what we do it formal logic (in that case would logic not be listed separately, but instead come under Pattern Theory?) So, getting to the question. First off, we can differentiate "metaternal sciences" from the other two categories by what they do. The metaternal sciences try to create or define systems by which people can communicate ideas (theories). Some of the properties that these systems share is that they attempt to do this unabiguously, and perhaps (arguably?) objectively (at least in the sense that something such as a math equation can be manipulated/reduced algebraicly, a formal proof can be derived and in both cases these things can be done only by well defined rules) And so, to approach your question, I think, requires something akin or analogous to definition by genus and difference. Most definitely logicians are attempting to uncover correct patterns of reasoning but I suppose that this alone isn't enough. Mathematics and algorithms are also patterns of reasoning. But I think that something that differentiates logic from those two is that logic manipulates ideas themselves. Mathematics manipulates numbers. I didn't think I could come up with an actual set of criteria but I had a thought at the last minute while writing this: Logic is a metaternal science, and as such is a tool for communicating ideas or theories. Most theories draw from more than one metaternal science. For example a theory in Physics will draw at least from Mathematics and logic. From logic it draws a system of reasoning to derive new information from a set of basic princliples (which would be formulated as the axioms of the theory). Hence, as an initial attempt I would dare suggest that the critera for differentiating these various systems (logic, math, etc.) lies in how each contributes to a theory. If we took this as an axiom, an interesting theorem would be this: Given two metaternal systems contributing the same thing to a single theory then those systems are redundant. In such a case the theory could be simplified by tossing out one of those systems and reformulating the theory. (Sounds like a variation on Occam's Razor). Please feel free to be as critical of the above as you want. I make no claims of great knowledge. My ultimate goal is to learn something new.

keda
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Posted 10/26/09 - 06:25 PM:	#6
Timothy wrote: What this view presupposes is that there is a principled difference between the form and the content of a sentence. I'm not sure what this is suppose to mean. Are you talking about sentences that are ambigous or are not propositional? If so, why would any science need them?
All about making money Free Europe Now How to fix your country In thought, men distance themselves from nature in order thus imaginatively to present it to themselves--but only in order to determine how it is to be dominated - Adorno and Horkheimer

Timothy
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Posted 10/26/09 - 08:27 PM:	#7
ronlongo, I'll give you a thorough response tomorrow when I have more time to spare... keda wrote: I'm not sure what this is suppose to mean. Are you talking about sentences that are ambigous or are not propositional? If so, why would any science need them? I'm talking about a dichotomy familiar with the analytic/synthetic dichotomy, e.g. the difference between form and content, scheme and content, etc. Logic is said to be formal because it doesn't really talk about specific propositions. An exmaple: If P, then Q P Therefore Q this holds for whatever propositions P and Q stand for. Say P stands for "The book is blue" and Q for "the cat is black". The above syllogism will still holds, and the content of the propositions (the facts that the book are blue, the cat black, etc) had nothing to do with it. My point is that this clearly presupposes a clear-cut differentiation between the form of a propositions ("if ___ then __") and its content (blue book, black cat, etc). Davidson argued against such a distinction; and my question is, assuming Davidson is right, what criteria could be given that differentiates logic from everything else?
"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

Timothy
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Posted 10/31/09 - 01:14 PM:	#8
ronlongo, I guess what I was looking for was a more restricted, abstract criteria about what makes a certain theory a part of logic. Your account is over-general in the sense that is seeks to relate sciences with a genesis or origin in an individual consciousness. Could there be an account that need not refer to any subjects or cognitive agents whatsoever, and their practices and contingent layout. Also, your conception of logic as a theory about ideas and reasoning is moot. But I don't know if you want to discuss that here, or star a new thread about it...
"Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic." P.F. Strawson

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