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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/29/2008 4:13:24 PM | | no, great thinkers still exist, they come to life in all ages but they always end up being crucified or being given a very hard time in one way or the other, just for speaking the truth. Go figure. So, the lesson is: say whatever, but not the truth: too revolutionary, too controversial. This is why I now keep silence when personally asked about some issues. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 5:08:30 AM |
kirk763 wrote:
The language of "proof" in the strict sense is typically logic...logicians are philosphers...so, your point is straightforwardly contradictory.
In one of my many discussions I came across someone who suggested the thesis that logic, rather than being a discipline of philosophy, is a discipline of mathematics - a sort of a reverse of logicism. To begin with logic as a discipline remained largely unchanged since the time of Aristotle. It's development occurred as a result of mathematicians (philosophically minded ones, mind you) decided to utilize logic in order to solve problems in mathematics. Of course Aristotle's logic was entirely insufficient to deal with any problem in mathematics so it was up to the mathematicians (Boole, Peano, Frege, Hilbert, Russell, etc) to develop logic to a point that it could be used to solve problems in mathematics. He suggested that logic contained no more entities than mathematical entities and so could be thought of as a discipline of logic. I actually disagreed with him at the time (I generally disagree with everyone on any point but that is neither here nor there) but I do have some sympathy for that thesis. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 5:31:30 AM |
they_killed_kenny wrote:
There is nothing philosophy can do that science and art can't do better.
While I do agree this question may be stemming from ignorance, I wouldn't dismiss the question outright. I think there is a genuine question here. We might ask it this way: what is the subject-matter of philosophy?
If we take philosophy to be the "love of wisdom" (as the name implies) we might be tempted to suggest that anything pertaining to that is properly called philosophy. We certainly can put forth historical arguments with respect to philosophy giving birth to various disciplines (e.g. Newton's "natural philosophy" - physics). These seem to suggest that what the scientists are doing is genuinely philosophy. This seems to be the suggestion that x_file is alluding to (correct me if I'm mistaken.)
The one clear problem is this. Suppose there comes a time when every discipline within philosophy becomes specialized in the way that, say, physics and psychology have. What will be left of philosophy departments? Will they cease to exist? Will they become perhaps more like classics or literary departments in which the study of a "canon" of philosophical texts is done a la scholastics style? Or what of it?
Now I don't think that's x_file's full position. He has referred to philosophy of math and philosophy of science. There are two primary ways in which these disciplines go. On the one hand we have a more interpretative approach. Here in philosophy of science/math we interpret the activities, theories, etc and give them meaning. We try to figure out what it is that they are doing and discuss the overall implications of those doings and the theories and science produced and what they mean for us as human beings and what they tell us about our relationship with the world, etc. On the other hand we have "first philosophy" (I'm borrowing this phrase and usage from Stewart Shapiro.) What is crucial for "first philosophy" is that it's meant to be prescriptive. It means to provide a foundation by which science and mathematics is to proceed. To use names I mentioned in the previous post, pretty much all of those guys were doing "first philosophy" here. Another good example would be Karl Popper working on the demarcation problem. What counts as "good" science and what counts as "pseudo" science is a philosophical problem: a problem that it is the job of the philosophers to do.
These distinctive roles illustrate that philosophy has a particular relationship to other fields (e.g. "interpretive", "foundational", etc). The task of answer the question "what is the subject-matter of philosophy seems to be a carving out of what the philosophers role is respect to these other subjects but also what makes it distinctive from these other subjects.
In any event, this question of the "subject-matter" of philosophy is, I think, an important one. I think if we look at, say, Socrates, the answer might be something akin to ethical considerations and the caring of the soul. If we were to ask Descartes or Kant it might be to provide a foundation for the sciences. If we were to ask (the early) Wittgenstein or the positivists it might be a "critique" or "analysis" of the language we use. If our answer is not akin to the "love of wisdom" response in which many disciplines can be considered "specialties" of philosophy I think it's a significant question to ask what is it about philosophy that makes it distinctive from science, literature, etc? | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 5:34:03 AM | Bubonic plague aside (and it is still here...along with untold other unknown...new...recombined variants and such)
...many possibilities lie in wait, ready to challenge humanity again.....
Simply, i sense we have fallen from the agenda of true education..
teaching HOW to think instead of forcing all to accept WHAT to think.
...creativity, stifled; equality, sameness emphasized.
Be not assimilated....therein lies our only hope.
Nature, fate, a higher power....whatever....
status quo, though protected, is never permanent.
what is? it is....the will to live, self; unique.
where IS free moral agency hiding? | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 5:51:26 AM |
In one of my many discussions I came across someone who suggested the thesis that logic, rather than being a discipline of philosophy, is a discipline of mathematics - a sort of a reverse of logicism. To begin with logic as a discipline remained largely unchanged since the time of Aristotle. It's development occurred as a result of mathematicians (philosophically minded ones, mind you) decided to utilize logic in order to solve problems in mathematics. Of course Aristotle's logic was entirely insufficient to deal with any problem in mathematics so it was up to the mathematicians (Boole, Peano, Frege, Hilbert, Russell, etc) to develop logic to a point that it could be used to solve problems in mathematics. He suggested that logic contained no more entities than mathematical entities and so could be thought of as a discipline of logic. I actually disagreed with him at the time (I generally disagree with everyone on any point but that is neither here nor there) but I do have some sympathy for that thesis.
Aristotle is credited with formalizing the "syllogism" style argument. But his background was far more philosophical in the traditional sense than mathematical in the modern sense. For the most part, the distinctions made now between mathematicians and philosophers for example are artificial ones, the great mathematicians saw themselves as "philosophers". Leibniz has been massively influential for mathematicians, logic and analytic philosophy in general, yet we would hardly refer to him as anything other than a "philosopher". Aristotle obviously formalized the principle of non-contradiction as well. However, Aristotle saw his method of deductive argument as something that applied most directly to the immediate problems of philosophical inquiry, ethics, metaphysics, politics and so on. Clearly Socrates was interested in the deductive approach, and reductio ad absurdum arguments, again, like Plato, he was interested in how these methods could be used in fields beyond what the Pythogorreans and other noted mathematical schools were doing. Generally speaking, if one looks at where Russell and Frege are taught, it's in the same departments that Wittgenstein or even many of the Vienna circle/ logical positivists are taught. Logical positivism itself is a "philosophical school". | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 6:25:32 AM |
kirk763 wrote:
Leibniz has been massively influential for mathematicians, logic and analytic philosophy in general, yet we would hardly refer to him as anything other than a "philosopher".
Who is "we"? I've heard him frequently referred to as a mathematician. I'm sure both categories fit quite well. In any event, I was referring to Leibniz as the significant contributions to logic occurred with its formalization starting in the 19th century.
Generally speaking, if one looks at where Russell and Frege are taught, it's in the same departments that Wittgenstein or even many of the Vienna circle/ logical positivists are taught. Logical positivism itself is a "philosophical school".
Frege was trained as a mathematician; his dissertation was clearly a mathematical thesis. I'd have to look up Russell but I'm guessing he was trained in both fields. Wittgenstein was an engineer who became interested in mathematics and then foundation issues in mathematics and was pointed to the work of Russell (and subsequently read Frege.) His knowledge of philosophy was nonexistent prior to that (although he wasn't a mathematician either.) Russell decided to take him on as a student at Cambridge.
Which Vienna circle participants do you have in mind? Carnap had close ties with a number of mathematicians including Frege and Husserl. He was also studying physics early on *shrug*. Godel was a mathematician. His adviser Hahn was a mathematician. Much of their focus was on the philosophical contributions of Mach (a physicist no less) and Russell's mathematical program. In any event, I do agree that it was a philosophical "school" (or gathering/discussion group at the very least, I only point this out to disassociate folks like Godel who was a member of the Vienna Circle but certainly didn't subscribe to the positivism). I would also like reemphasize Godel. Though I didn't include him in the original list, I've only heard of two figures that have been championed as "the greatest logician since Aristotle" and those were Frege and Godel (obviously by different people.) I don't know what to make of that opinion.
In any event, as I said in my original response most them were philosophically minded (as are a number of great thinkers. Let's not ignore all of the other "non-philosophers" who had adequate knowledge of philosophy and that contributed to their overall contributions to their respective fields.) | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 6:48:38 AM |
kirk763 wrote:
Aristotle obviously formalized the principle of non-contradiction as well.
As a side note, if you mean "formulated" I've often heard of this being attributed to Parmenides. If you mean "formalized" then I'm not sure how that can be done Aristotle's logic. Perhaps you can explain. I'm only familiar with his general syllogism forms which as far as I can tell don't permit statements such as "no S is P and S is not P" to even be formulated. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 8:02:52 AM | | I'm not terribly interested in the fact that Wittgenstein designed his sisters house or wrote a lexicon for school children when he taught kids in the mountains in Austria. These kinds of discussions are only a thread away from genetic fallacy style arguments. It really doesn't matter what Wittgestein's training was in. He taught with the department of philosophy in Cambridge. He considered his work, even the early Tractatus, PHILOSOPHICAL. Russell taught in the philosophy department. The fact that he worked with a process mathematician , Whitehead, or discovered his famous paradox as a young man, doesn't alter the fact that he considered himself a philosopher. Descartes and Kant who you mention above, were both philosophers. Leibniz was never a professional academic but some of his most famous works like The Monadology are philosophical. When Ayer made the discussions of the Vienna circle famous in the English speaking world (Language, Truth and Logic) he was a professionally trained philosopher and spent all of his academic life teaching in philosophy departments. Popper was erroneously described as being a member of that circle which irked him no end but he was always and ever a professional philosopher. And the circle itself, which was to have it's most lasting impact in analytic philosophy, as you correctly conceded, met to discuss what would generally be described as philosophical problems. And, as you may have noticed, we are only discussing one part of the 'tradition', namely, analytic philosophers who for fairly obvious reasons tend to work very closely with developments in mathematics and out and out logicians. The Continental tradition would not share anything like the same proximity typically. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 8:06:06 AM |
As a side note, if you mean "formulated" I've often heard of this being attributed to Parmenides. If you mean "formalized" then I'm not sure how that can be done Aristotle's logic. Perhaps you can explain. I'm only familiar with his general syllogism forms which as far as I can tell don't permit statements such as "no S is P and S is not P" to even be formulated.
This is a bit muddled! Can you explain what you mean? I think you might be conflating the low of contradiciton which was famously introduced "formally" as a rule by Aristotle in his critique of Heraclitus and the question of the form of argument he began to develop systematically, i.e., the syllogism. They are two separate developments in his work. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 8:11:27 AM |
If you mean "formalized" then I'm not sure how that can be done Aristotle's logic. Perhaps you can explain. I'm only familiar with his general syllogism forms which as far as I can tell don't permit statements such as "no S is P and S is not P" to even be formulated.
Aristotle is generally credited with having introduced "formal logic" and the syllogism as one of the central features of that endeavour. I am reasonably confident that that is not a controverial or unusual view. I'd imagine if you did a quick web search there would be plenty of entries that should state something to that effect. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 8:13:23 AM | There are great philospohers and scientists today, but you will not hear much about them. Hawkins is the big name today, but there are others who are just as good and not generally known to the public.
I don't think its fair to compare historical figures in a nonhistorical context. The Ancient Philosphers are known for 2500 years and are highly valued. How are we to determine if a 45 yo Harvard physicist isn't as valued? I think this is very subjective.
Second, a lot of knowlege has been lost. There are a lot of unknowns from ancient times, from engineering to metallurgy, and we have no idea who came up with these things.
Just my $0.02 | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 9:03:53 AM |
I'm not terribly interested in the fact...
You should probably reread my posts. You're referring to references in two different posts that said two different things. I never mentioned Descartes, Kant, or Popper in my response to you. I referred specifically to those people who actually developed logic, not Descartes, not Kant, not Leibniz. I did refer to Russell and I did grant he was a philosopher. I also mentioned the likes of Frege, Boole, Hilbert, Peano, Godel all of which were mathematicians although certainly philosophically minded ones.
The inference you wanted to draw was "these guys all studied in similar departments therefore these are all philosophers" or something to that effect. I don't see how it follows. This is why I specifically cited what they studied in detail. Of course all of these guys are going to get a strong background in liberal arts. I think back then you could get away with having a broader scope in study but with specialization the way it is today, that is not as feasible.
Secondly, the historical argument wasn't really the strongest point (or at least the more interesting point) of his overall argument which was to suggest that the sorts of entities logic use are all mathematical entities. (FWIW, I suggested that modal and deontic operators weren't mathematical entities but were both valid disciplines within logic.) | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 9:15:52 AM |
This is a bit muddled! Can you explain what you mean? I think you might be conflating the law of contradiction which was famously introduced "formally" as a rule by Aristotle in his critique of Heraclitus and the question of the form of argument he began to develop systematically, i.e., the syllogism. They are two separate developments in his work.
I'm distinguishing between "formulate" and "formalization". The former seems closer to your usage of "formally": to formally state, for example. A formalization I have in mind formal logic and this, to me, is largely associated with the projects of the 19th and early 20th century. I don't know to what extent "formal logic" is associated with Aristotle's syllogisms. My only point was you can't formulate P ^ ~P symbolically within Aristotle's logic (unless I'm mistaken. I haven't actually read Aristotle's original stuff on this; I'm only familiar with what they have in logic texts on it.)
Anyway, I was just side noting that it seems to have been formulated in Parmenides. I've read that poem and really didn't get much out of it so I'm just appealing to the people who actually took the time to study it. Just from one of the online translations, I believe it's referring to this line:
"That things which are not are, shall never prevail" (I'd post a link but I'm not sure how.) | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 9:47:48 AM | I think you might have missed the fact that Aristotle is credited with having introduced both "formal" logic and the syllogism and Aristotle was the first to give a formal statement to the law of non-contradiction. And I've read quite a bit of Aristotle and am reasonably confident about those statements. Those are more or less incontrovertible facts.
Part of what I took issue with was your tendency to only discuss philosophy's common language in tandem with developments in mathematics and the analytic tradition exclusively. And, moreover, to give the impression that most of the central figures involved in these 'developments' were mathematicians. Those 'developments' belong to a very specific, multi-disciplined movement which, for the most part, has been continued and worked on in philosophy departments and texts. The linguistc turn and logical positivism, for example, are philosophical movements.
Logic and the attempt to use it in philosophical arguments has been crucial to metaphysics, ethics, epistemology, philosophy of religion and so on since the inception of the Western tradition. And, again, for the most part, if you look up course offerings at University, it's people in our departments(philosophy departments) that teach all of the logic courses for both philosophy majors and those who need to pass logic for other reasons. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 9:55:59 AM |
'd have to look up Russell but I'm guessing he was trained in both fields. Wittgenstein was an engineer who became interested in mathematics and then foundation issues in mathematics and was pointed to the work of Russell (and subsequently read Frege.) His knowledge of philosophy was nonexistent prior to that (although he wasn't a mathematician either.) Russell decided to take him on as a student at Cambridge.
Wittgenstein went to study specifically philosophy with Russell. Russell quickly realized the brilliance of the Austrian and they managed to hurry through his Tractatus even though his committee were (a couple of them at least) skeptical. Some of his final work involved Lectures on Ethics. His writings and influence have been felt more in philosophy than anywhere and he employed logic to a "philosophical" end. In other words, it really doesn't matter what his background is. The fact is that he committed the majority of his intellectual life to what he conceived as "philosophical" problems. The idea that his knowledge of philosophy was non-existent before he met Russell is excessive. He was extremely well read. He even troubled himself to read carefully figures who Russell despised such as Heidegger. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 3:04:13 PM | I believe that great minds continue to exist, just as they have throughout the ages, and that the advancement in time did not create any kind of vacuum in knowledge. Most of the brightest minds can usually be found in major universities today. Unlike in ancient Greece, when philosophy encompassed science, art, math, politics; today all these areas of knowledge have been highly developed and compartmentalized, creating seperate disciplines that we know of today. Philosophers do not exist the way they did in ancient Greece anymore. The modern world, and this country has become a nation of specialists. This is due to the continued advancement of knoelege in every discipline there is. Advances in science; in technology; in business; medicine; ect...
Today, philosophers have been replaced by experts in every field. Professors, researchers, scientists, businesspeople, political pundents and commentators. Even artists can serve as philosophers. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 6/30/2008 7:47:51 PM |
This is why I now keep silence when personally asked about some issues. Yes, it would be tragic if your utterance of a great idea brought down upon you the wrath of...of...who was it that was going to do you in if you revealed your genius? | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 7/1/2008 6:11:59 AM |
I think you might have missed the fact that Aristotle is credited with having introduced both "formal" logic and the syllogism and Aristotle was the first to give a formal statement to the law of non-contradiction. And I've read quite a bit of Aristotle and am reasonably confident about those statements. Those are more or less incontrovertible facts.
That's what you keep saying but it's actually not clear. I don't even know how to interpret what you're saying to make it remotely true. What do you mean by "formally"? I already pointed out that some consider Parmenides to be the first to formulate the law of noncontradiction. So it's not an "incontrovertible fact". I've also challenged you "who has read quite a bit of Aristotle" (I have read some, I simply have not read his texts on logic, the organon(sp?) as it's called) can't even tell me how to formalize the principle of noncontradiction in his formal schema. I know how to formulate statements like "Some apples are red" in his schema. It's not clear how to formulate a contradiction. (Can an operator akin to "and" even be used in his schema?)
Part of what I took issue with was your tendency to only discuss philosophy's common language in tandem with developments in mathematics and the analytic tradition exclusively. And, moreover, to give the impression that most of the central figures involved in these 'developments' were mathematicians. Those 'developments' belong to a very specific, multi-disciplined movement which, for the most part, has been continued and worked on in philosophy departments and texts. The linguistc turn and logical positivism, for example, are philosophical movements.
I'm pointing specifically to those who actually made contributions to logic. They were mathematicians. Are you denying this? You keep bringing up all of these other people but I don't know what significant contributions to logic they have brought. (If I'm ignorant then list their specific contributions but I don't actually think that's the case here.) You point to the "Vienna circle" but they were a multidisciplined group working on problems in the foundations of mathematics/sciences coming from philosophy, mathematics and physics.
Logic and the attempt to use it in philosophical arguments has been crucial to metaphysics, ethics, epistemology, philosophy of religion and so on since the inception of the Western tradition.
To an extent. Aristotle's logic was largely useless to do much of anything though. Philosophical logic didn't really become a realistic program until the advancements made, particularly the predicate logic of Frege.
And, again, for the most part, if you look up course offerings at University, it's people in our departments(philosophy departments) that teach all of the logic courses for both philosophy majors and those who need to pass logic for other reasons.
And mathematics. I study both philosophy and mathematics. If you have anything at all to do with mathematical proof (which is what the bulk of actual mathematics is concerned with), you're required to study logic and you don't have to take it in the philosophy department. This is all required stuff for mathematics. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 7/1/2008 6:18:43 AM |
Wittgenstein went to study specifically philosophy with Russell. Russell quickly realized the brilliance of the Austrian and they managed to hurry through his Tractatus even though his committee were (a couple of them at least) skeptical. Some of his final work involved Lectures on Ethics. His writings and influence have been felt more in philosophy than anywhere and he employed logic to a "philosophical" end. In other words, it really doesn't matter what his background is. The fact is that he committed the majority of his intellectual life to what he conceived as "philosophical" problems. The idea that his knowledge of philosophy was non-existent before he met Russell is excessive. He was extremely well read. He even troubled himself to read carefully figures who Russell despised such as Heidegger.
He was well read but he was more of a, say, "intensive" reader than an "extensive" reader (and here I mean he spent a lot of time with the philosophers he actually studied.) I do agree that he was concerned with "philosophical problems" but in some cases, I think they were a means to an end. I actually don't think most of his stuff on language really makes sense until you see as it as a means for discussing the foundations of mathematics (which he also wrote quite a bit on later on.) But this is all side stuff anyway...
I'm not sure what's the significance of Wittgenstein here. Apart from the truth tables, what would you suggest were his significant contributions to logic? He's hardly comparable to Frege, Boole, Godel, etc. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 7/1/2008 6:57:28 AM |
'm not sure what's the significance of Wittgenstein here.
You made tendentious statements concerning Wittgenstein which were in need of correction. He was a philosopher...again...that's not something that ANYONE would typically deny.
His later discussion of language and language games is far closer to the work of Quine than it is to foundational questions of mathematics. You keep overlooking the fact that he held PHILOSOPHY seminars, published philosophy books and taught more or less exclusively in the philosophy department. You're statements concerning Wittgenstein are wholly speculative and tendentious.
And mathematics. I study both philosophy and mathematics. If you have anything at all to do with mathematical proof (which is what the bulk of actual mathematics is concerned with), you're required to study logic and you don't have to take it in the philosophy department. This is all required stuff for mathematics.
Well I'm a philosophy professor and we are generally the department that is responsible for offering general, open logic courses to both philosophy and non-philosophy students, e.g., students that want to apply for law school and so on. Logic, at most academies, is considered a philosophical subject, surely you are aware of that if you study philosophy. And, from time to time, we have advanced courses for advanced students that are taught and attended by both philosophy and math students, usually taught by the top logicians in our department (Hintikka or Webb).
You point to the "Vienna circle" but they were a multidisciplined group working on problems in the foundations of mathematics/sciences coming from philosophy, mathematics and physics. I believe it was I who made this exact point. They were a PHILOSOPHICAL circle.
that's what you keep saying but it's actually not clear. I don't even know how to interpret what you're saying to make it remotely true. What do you mean by "formally"? I already pointed out that some consider Parmenides to be the first to formulate the law of noncontradiction. So it's not an "incontrovertible fact". I've also challenged you "who has read quite a bit of Aristotle" (I have read some, I simply have not read his texts on logic, the organon(sp?) as it's called) can't even tell me how to formalize the principle of noncontradiction in his formal schema. I know how to formulate statements like "Some apples are red" in his schema. It's not clear how to formulate a contradiction. (Can an operator akin to "and" even be used in his schema?)
On this you are quite simply wrong. I would submit that you don't know your Aristotle AT ALL if you are willing to make statements like that. Aristotle explicitly invokes what became known subsequently as the principle of non-contradiction in his critique of Heraclitus...look it up...he says that something cannot both be the case and not be the case at the same time depending on how the translator renders it. We get the "syllogism" DIRECTLY FROM Aristotle...look it up...surely all one would have to do is the most cursory of web searches to find 1000s of entires on this, it's common knowledge. The term "formal logic" is what Aristotle is credited with inventing...again...I'd invite you to do even a quick websearch if you're skeptical.
I'm pointing specifically to those who actually made contributions to logic. They were mathematicians. Are you denying this? You keep bringing up all of these other people but I don't know what significant contributions to logic they have brought.
What kind of arguments do you think Descartes uses in his Meditations for instance. Leibniz introduced a whole series of principles which are used to assess deductive arguments. When Aquinas makes an ontological argument for God's existence what do you think he used as his argumentative tool? When Mill writes his logic, what do you think he is discussing? You pose as though the way this old, old language was applied within a very specific movement, with little or no application beyond that rather blinkered movement, is the only way that matters. I think that particular posture along with a few others that characterized the Anglo-American analysts who perpetuated such views is utterly anachronistic now and is not taken seriously by many competent intellectuals.
If you have anything at all to do with mathematical proof
In other words, one very small and limited way in which the language of deduction is applied, that is not the whole of the story for logic I'm afraid! | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 7/1/2008 8:23:54 AM |
You made tendentious statements concerning Wittgenstein which were in need of correction. He was a philosopher...again...that's not something that ANYONE would typically deny.
Which one? I've never denied he was a philosopher. I'm not sure why you even brought him up in this discussion. He's not relevant.
His later discussion of language and language games is far closer to the work of Quine than it is to foundational questions of mathematics.
Ironically Quine was concerned with philosophy of mathematics as well... Have you read any of Wittgenstein's stuff on the foundation of mathematics? Have you noticed all of his frequent uses of mathematical examples in his philosophy of language stuff?
Logic, at most academies, is considered a philosophical subject, surely you are aware of that if you study philosophy.
Of course I'm aware of this. That doesn't make the thesis that it's a discipline of mathematics any less interesting...
On this you are quite simply wrong. I would submit that you don't know your Aristotle AT ALL if you are willing to make statements like that. Aristotle explicitly invokes what became known subsequently as the principle of non-contradiction in his critique of Heraclitus...look it up...he says that something cannot both be the case and not be the case at the same time depending on how the translator renders it. We get the "syllogism" DIRECTLY FROM Aristotle...look it up...surely all one would have to do is the most cursory of web searches to find 1000s of entires on this, it's common knowledge. The term "formal logic" is what Aristotle is credited with inventing...again...I'd invite you to do even a quick websearch if you're skeptical.
The problem is you haven't understood from the get-go. You acknowledged this in one of your posts. Do you understand what I mean by the distinguishing "formulating" and "formalizing" (your original word which I was challenging)?
First off, Aristotle was not the first to formulate the principle of noncontradiction. It was Parmenides. I already pointed that out. If you don't like his formulation then fine. I do agree that Aristotle formulated the principle of noncontradiction. I've read it in his Metaphysics. I've never denied that he did formulate it.
Second, I also agree that Aristotle developed the syllogisms and that these are examples of formal logic.
What I am objecting to is that the principle of noncontradiction cannot be expressed in Aristotle's formal logic. It can be easily expressed in the more contemporary sentential logic: ~(P&~P). That is what I'm looking for when I'm looking for "formalized". I think the term you originally meant to use was "formulate". I suggested that in my first response when you said it.
What kind of arguments do you think Descartes uses in his Meditations for instance. Leibniz introduced a whole series of principles which are used to assess deductive arguments. When Aquinas makes an ontological argument for God's existence what do you think he used as his argumentative tool? When Mill writes his logic, what do you think he is discussing? You pose as though the way this old, old language was applied within a very specific movement, with little or no application beyond that rather blinkered movement, is the only way that matters. I think that particular posture along with a few others that characterized the Anglo-American analysts who perpetuated such views is utterly anachronistic now and is not taken seriously by many competent intellectuals.
I'm not denying that they offered arguments. But none of them were really utilizing Aristotle's syllogisms (could they even be formulated in those? If so I'd like to see!) (As a side note, you either meant "Anselm" or "cosmological" but I'm sure that was an honest mistake.)
Guess what. So were the mathematicians! They were making arguments too. The problem, again, is that Aristotle's logic wasn't sufficient to deal with any of these arguments. That's what the benefit of these "new" logics are.
Let me be clear "argument" is not the same as "formal argument". The tools that Anselm requires are well beyond the scope of Aristotle's formal logic.
I do acknowledge Mill's contributions to inductive logic. | |
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| Philosophers and Great Minds Becoming Endangered Species???
Posted: 7/1/2008 9:04:45 AM | Aquinas had "5 ways", none of which was the ontological, slip of the mental tonuge I'm afraid, there were four others besides the cosmological argument however. There are however many variations on the ontological argument however beyond Anselm's seminal contibution.
I never said that logic begins and ends with Aristotle, that was actually the avowed position of certain logicians and mathematicians that resisted the 'newer' developments. I merely pointed out that "formal logic" as the term is still used today, is credited with having begun with Aristotle. He was the first thinker on record to look at inferences and to try and develop systems. It would be highly unlikely for Aristotle to have completed everything rather than set the ball in motion 2,500 years ago or so. As Jonathan Lear has argued "Aristotle shares with modern logicians a fundamental interest in metatheory his primary goal is not to offer a practical guide to argumentation but to study the properties of inferential systems themselves."
I take your concessions on Wittgenstein. Of course he was interested in the foundations of mathematics. But he ultimately rejected much of what was trying to be achieved there as futile. As for Quine, again, I take your concession that he is a thoroughgoing philosopher. It would be unusual for analytic philosophers not to say anything concerning related questions in mathematics...why wouldn't they...that does not delimit their intellectual endeavour however.
As for your comments on Parmenides, well I think this is where we get into a chain of infinite regression. We are bound to find echoes of all kinds of things in the presocratics, and further echoes probably exist before them. But if you do a web search right now for the Principle of Non Contradiction which has many formulations in the Aristotelian corpus, even beyond those offered in the Metaphysics, you'll find that the principle has been attributed by scholars and classicists to Aristotle. Again, it would be unusual for him to use the kinds of operators we would typically use today, i.e., -(p&-p) etc But these operators often simply reflect what is in the surface or deeper meaning of our utterances. Aristotle was obviously dealing with principles in long hand, but many of them 'convert'...look up some of the many other formulations available. A number of times he says the linguistic equivalent of it cannot be the case that p and not p are simultaneously true
You time and again tried to depict Wittgenstein in a way that was misleading...I initially mentioned that such examples can quickly degenerate into genetic fallacy type approaches...nonetheless, many of your comments concerning Wittgenstein have been straightforwardly refuted.
'm not denying that they offered arguments. But none of them were really utilizing Aristotle's syllogisms (could they even be formulated in those? If so I'd like to see!)
Descartes' arguments in his Meditations in first philosophy can pretty easily be reduced down to a series of Aristotelian syllogisms. | |
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