You seem to be missing the point. Mathematical savants are not doing mathematics. But they are still mathematical savants. The point being that they can arrive at a ‘correct’ answer without following steps that appear to be coherent or rational. The only difference between what I described and a mathematical savant is that the conclusions of the mathematical savant are objective, while the conclusions a supposedly philosophical savant are subjective, which make it impossible to verify him or her as such.
Well, the word “savant” may mean different things to different people, or in different contexts. “Mathematical savant” does sometimes seem to be used in the way you are using it, to mean someone who just “knows” the answer to math problems without doing any calculations, but unless we grant that what they do really is magic, I think we have to accept that they are doing the requisite calculations somehow, even if they are remarkably efficient at it and they are somehow unable to introspect what they are doing.
Anyway, you are mistaken if you think philosophical positions are “subjective.” No philosopher would bother with philosophy unless he or she thought there was an actual objectively right answer to the problems they are concerned with. It differs from mathematical calculation (but not from creative mathematics) only inasmuch as we do not know an algorithm for obtaining the right answer beforehand, and probably do not know quite what form the answer should have. Philosophy is analogous to trying to prove new theorems, it is not analogous to trying to do calculations, and it is certainly not analogous to pronouncing unsupported opinions.
It is a myth, incidentally, that philosophical problems never get solved. Lots of what were once considered philosophical problems have been solved (although it often did take many centuries of frustrating work). The trouble is that once a philosophical problem gets solved, it generally gets reclassified and becomes, instead, part (often a foundational part, part of the conceptual framework) of science (or mathematics), or perhaps part of common sense. This is just a consequence of the way words like “philosophy” and “science” are used. “Philosophy” can refer to a process of inquiry, or to a theory that is proposed but has not been definitively established. “Science,” can also be used to refer to such things, but it can also be used to mean definitively established knowledge. (Indeed, the root word “scientia” always and only meant “established knowledge,” whereas “philosophia” meant the research process and its working theories and hypotheses. However, in modern usage, “science,” without losing its original sense, has expanded its purview to also include much of what was once called “philosophy.”)
If there were mathematical savants who could come up with new theorems without being able to prove them (as opposed to being able to calculate results that we already know how to calculate, albeit, perhaps, more laboriously), then that might be analogous to your notion of a “philosophical savant,” but, of course, we would not take the pronouncements of such mathematical savants seriously: we would not really count them as doing mathematics (or being savants) at all, they would just seem to be spouting random mathematical propositions of dubious truth. No more should we take your “philosophical savants” seriously. In philosophy, as in creative mathematics, being able to “show your work” (state your proof, and not just your result) matters as much, if not more, than the final result.
Again, I think you are completely missing the point. At the very least you seem to be setting up a straw man. You also seem to be confusing some of the tools of modern philosophy with philosophy itself. Give me an example of a philosophical statement (say, by Nietzsche) that is objectively true.
You also keep referring to “doing mathematics” or “doing philosophy”, as though the OP used that phrase. A mathematical savant generally does not do mathematics – he is able to produce mathematical theorems without proving them. Savants are so noted because, even though the theorems are not proved by the issuer, they turn out to be true – others can prove them. Of course they are not doing magic, but whatever process by which they generate their theorems is completely beside the point. It is quite possible that their process cannot be translated into a practical-sized number of symbols in formal logic.
I just re-read your post, and it makes even less sense than the last time, so I’m feeling the need to dive in point by point.
It is not sometimes seem to be used that way. It is usually used that way.
This is a naive view, considering that most high-functioning mathematical savants describe a pretty non-linear reasoning process, for example the synesthesia described by Tammet, where every number has a unique visual quality, and calculations are achieved through how numbers subjectively appear to fit together. No, it’s not magic, but Tammet certainly cannot “slow down” his calculations and write them down even if he wanted to.
Give me an example of a philosophical statement (say, by Nietzsche) that is objectively true.
If the term “philosophy” is so cripplingly nebulous (as I know it is), then why on earth are you taking issue with my perfectly valid use of the term? I’ll answer for you: you chose a definition to attack that suited your purpose of taking down a straw man.
Dubious truth? Not if others can prove the theorems. Here you seem to be contradicting your previous pronouncement that philosophy is not involved in the subjective. You can’t have it both ways. Would the philosophical propositions be of dubious truth or not? Would they be decidable or not?
The funny thing is, I never proffered that “philosophical savants” should be taken seriously in any practical, verifiable sense. Perhaps you should go back and read my post again; I was arguing the exact opposite of what you seem to imply.
This is irrelevant. The mathematical savant does not have to show his work in order to be considered a savant. His work just has to be judged correct by others.
No, you are missing the point. Philosophy is not a set of doctrines or factual claims, it is a process of research (and it always has been, since the time when the ancient Greeks initiated the discipline). As I said, once a philosophical claim is, to all intents and purposes, universally accepted as true it ceases to be considered philosophical (it is no longer subject to research, because it is now known to be true), and is rechristened as science (or, sometimes, as being obvious and trivial, even though it may not have been at all obvious to anyone over thousands of years of human history). So far as I am aware, none of Nietzsche’s claims are universally recognized to be true (some might happen to be so, but we don’t know it), which is precisely why they are still understood to be philosophical claims and not scientific facts.
Here, however, is a philosophical claim, that was explicitly made as a philosophical claim when it was first proposed, by a man who called himself (and was recognized by his contemporaries to be) a philosopher:
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed
That is Newton’s first law of motion, as published in his book Principia Mathematica Philosophiae Naturalis. We now call it science rather than philosophy because it is now effectively universally recognized to be objectively true, but the process by which Newton arrived at it was philosophical as he himself was well aware (he sure as hell did not arrive at it by the experimental testing of hypotheses). Newton’s laws of motion are a solution to the problem of understanding the nature of motion, something that philosophers had been wrestling with at least since the time of Zeno in the early 5th century B.C., and yes, Newton owed a large intellectual debt to Zeno and to many of the other philosophers who had worked on the problem over the intervening centuries, most certainly including those (such as, preeminently, Aristotle) who explored accounts of motion that eventually turned out not to be viable. Without Aristotle (and a lot of other, lesser known, philosophers) there could have been no Newton.
Newton himself was not rechristened as a scientist rather than a philosopher until the mid 19th century when the word “scientist” was first coined to distinguish those who were concerned with research in what was, up to then, known as “natural philosophy” from those concerned mainly with the more intractable branches of philosophy such as ethics and epistemology.
Modern scientists, or, at any rate, those who are attempting to advance fundamental theory in their fields, are also philosophers in the original and proper sense of the word (and many of them know it).
I do not really care what phrases the OP used, because my point is that the OP, like you, is confused about what philosophy is. Philosophy is not a matter of making claims (true or otherwise), it is a matter of attempting to provide rational justifications (in effect, proofs) for claims, something which savants, by their very nature, do not even attempt to do. Philosophers, even “great” philosophers, do not succeed in producing satisfactory proofs very often (the problems are very hard, and typically takes generations, if not millennia, to solve, if they are soluble at all) but, nevertheless, that is what philosophy is all about.
I am an aspergerian autistic, and I am not very creative but on the other hand, I am pretty good at novel spatial solutions.
For instance, while I am not very socially aware, the fact that I am not very lampshaded by body language means I see right through some ploys. In fact, because its possible to learn such things, I make out better than regular folks in limited situations.
So too if you have an autistic savant that is a memetic reproductionist, they can be so skilled as to put beauty into dry replication. There is beauty in photorealistic engineering.
See my previous post.
The ambiguity I am concerned with in the passage you quote is that in the word “science.” The word “science” changed (or, rather, greatly expanded) its meaning over the past couple of centuries. The word “philosophy,” not so much.
I am saying that your understanding of what philosophy is is plain wrong (although your mistake is a common one amongst those whose knowledge of philosophy is relatively superficial).
If others prove the theorem, then they have done the mathematics, not the alleged savant.
Yes, the philosophical propositions would be of dubious truth. All philosophical propositions are of dubious truth. Once they are known to be true, they cease to be philosophical.
We seem to be agreed on that point then.
My point was that mathematical savants who compute results whose correctness we can check via a known algorithm (all recognized savants, so far as I am aware) are not doing something that is at all analogous to what philosophers do.
If (per impossible, I think) there were savants who reliably produced true, previously undiscovered theorems (as opposed to results of computations), that would get a bit closer, but it still would not be right because they would still be failing to produce the closest analogs to what philosophers produce, the proofs. (Nearly all actual philosophical proofs are flawed, but that does not contradict the fact that the aim of philosophy is to provide proofs.)
On the other hand, what real mathematicians do when they prove previously unproven theorems, is highly analogous to what philosophers are about.
Actually, I think it would be more accurate and perspicuous to say that mathematical research of this sort (research, not established mathematical facts) simply is a highly successful branch of philosophy (as, indeed, is fundamental research in physics and other fields of what is now called science). Other branches of philosophy, such as ethics and epistemology - the residue that is still pursued in university “philosophy” departments rather than “science” departments - have not had nearly so much success yet. (Perhaps they never will, but the issues are important enough that they remain worth pursuing.)
I appreciate that you are attempting to educate us about philosophy, but you are stumbling all over yourself here. How do you define “attempting”? It has such a futile ring to it. Is philosophy a mere attempt at rational justification? Might such mere attempts be guided by subjective precepts, often ultimately failing because objective truth does not always coincide with one’s aesthetic sense of how reality should be? Might the fact be relevant that many, perhaps most philosophical ideas are in fact unfalsifiable? What if a savant makes an inherently unprovable philosophical proposition? Is he still denied his philosophy? Or are only non-savants allowed to do so?
This is also true of savants. Plato says “mathematics is not created but discovered.” What is his argument? It is an unfalsifiable statement. No subjectivity is involved?
Genuine question: are you sure you aren’t just being defensive about a subject that is your trade or otherwise close to your heart. It seems like you are conflating formal logic (which is often taught as a component of an education in philosophy) with philosophy itself. Formal logic is just a tool that is used in many fields: mathematics, physics, computer science, philosophy. Formal logic is not the heart of philosophy – it is not inextricable – is an entirely separate subject. Formal logic is a tool; philosophy is the study problems. It is actually quite vague (I invite you to give a less vague definition).
Now you seem to be conflating our discussion of mathematical savantism with philosophical savantism. I’m not sure about the ultimate purpose of your point here.
Looking over the literature, that aim doesn’t appear to be of much value. What value is an aim if it does not produce a proof or a lemma? The savant would fit right in.
Again: a mathematical savant is not a real mathematician! He skips the proof step! —> So would a philosophical savant!!!
Okay…prod·i·gy/ˈprɒdɪdʒi/
–noun, plural -gies.
- a person, esp. a child or young person, having extraordinary talent or ability: a musical prodigy.
- a marvelous example (usually fol. by of ).
- something wonderful or marvelous; a wonder.
- something abnormal or monstrous.
- Archaic . something extraordinary regarded as of prophetic significance.
You do not need to be under the age of 30 in order to qualify for this position!
Just SPECTACULAR…in some special way
Again, if they are right every time then why must they “prove” anything to you? This is what bothers so many, but that is the essence of autism. They don’t need recognition like everyone else. When they do something spectacular, the knowledge that they are “right” is enough. If the technology and research weren’t already there to prove them right, you would not know that they are right. And they honestly don’t have time to waste explaining THEIR PROCESS to people who won’t understand. Your brain gathers and organizes information far differently.
Anyway…savants have PHENOMENAL MEMORY! Access to subconscious memory is mandatory to qualify for this title.
JUST FOR FUN!
There are many tests that can be done to check on “savantism.” Although there is no classic definition in the DSM IV, it is still acknowledged in many psych. circles. If you are testing a socially inept individual and they come up with high scores in: digit span, block design, Boston Naming Test, etc.–then you should be looking for Savantism. This isn’t sure fire, but it is good indicator.
Digit span: a test where the recipient is given up to 9 sets of alternating numbers and letters, verbally, and asked to repeat. example: 17, G, 27, O, 59, Z,
8, A…etc. You are asked to recite frontwards, and backwards. A high score here yields a big OOOOOOoohhhhahhhh…
Block Design: Many have seen or taken this test; random red and white blocks in various shapes and sizes are shown pictorally in already formed patterns that you must recreate with the blocks given. A high score here means EXCEPTIONAL pattern recog. and spacial awareness…a MUST for Savantism!
BNT(boston naming test) Here you are asked to name say…as many pieces of furniture as you can in 60 seconds–the idea being this…the more words you can come up with is in direct correlation to how early you started learning/memorizing words…a high score here is a big hoopla even though the test doesn’t seem like much.
There are many “tests” used, but the above are just a few. They are fun to try 
so try them and see how you do!
After reading Einstein’s biography, he was definitely on the spectrum(asperger’s/high-functioning autism), and he EXPLAINED EVERYTHING. Of course his family to this day won’t acknowledge the syndrome, but the symptoms are profound; all that is necessary for a diagnosis…if he were alive.
Point of Interest: You DO NOT have to have autism of ANY KIND to have Savantism…thought you’d want to know…
A Savant is someone that has an amazing ability to constantly be ‘practicing’ even when to all appearances, they are doing nothing.–YEAH BABY! Just because a savant doesn’t tell you they are creative, their just being autistic, not LACKING creativity. Perfectionism as well. If it isn’t perfect in their eyes, they won’t show it to you!
We see, process, pattern search, and interpret human behavior far more than regular folk. Did you know that people’s eyes bulge ever so slightly when they lie? Your heartrate races, blood pressure increases and can make it “appear” like a protrusion, when really it’s very slight. An autistic person notices these things, others don’t.
What is also noticed is tone of voice & facial expressions(in correlation to mood), clothing, cleanliness, wardrobe, walk, etc. Taking all this information and finding patterns in human behavior is easy. Taking this information and using it to socialize is a far different animal.
Well, Saul Kripke comes to mind, although his philosophical research as a youth, focusing on logic as it did, verges on mathematics.
As an aside, in the 1950s, the Harvard mathematics department was recruiting faculty. On the basis of an article Kripke had written proving the completeness theorem for various modal logics, they invited him to apply for a position. The paper had been signed “Saul Kripke, Omaha, Nebraska,” so the department assumed he must be teaching at the University of Nebraska and addressed a letter there, which the university proceeded to forward to Mr. Kripke’s home. He responded, “Thank you for inviting me to apply for a position in your mathematics department, but my mother said I should finish high school and go to college first.” 
And my point is that in the case of the “philosophical savant”, it could be impossible to tell whether or not they are right. The mathematical savant can say that 38351 is a prime number, and the rest of us can go check that he is correct. A philosophical savant can say that “Death is not the worst that can happen to men” (Plato), but it is a vague, unprovable assertion, and no one can check whether or not it is correct.
Not sure if this is what you are looking for, but Temple Grandinsuffers from autism and came up with a bunch of new practices for the humane handling of livestock on cattle ranches and slaughterhouses. It’s not exactly philosophy (at least not human philosophy…maybe cow philosophy), but it’s certainly seems more abstract than counting cards and other feats of math.
I think you’re missing the point.
In math – yeah, we could imagine a hypothetical autistic savant who doesn’t explain how she reached her conclusions, and later a mathematician comes by to offer a step-by-step proof of why the sum of the squares of the other sides of a right triangle equal the square of the hypotenuse. She doesn’t know why it does; she only knows that it does; okay, fine, sure, whatever.
You’re putting the emphasis on the unprovability of philosophical conclusions to figure the same back-and-forth could play out between a savant and a step-by-step guy. Problem is, I think you’re missing the key shift in emphasis: so long as philosophical conclusions remain unprovable, the step-by-step stuff takes on a different kind of value: so long as you can’t be convinced by a philosopher’s conclusions, you can only ever be won over by the reasoning along the way.
We could imagine? This is not hypothetical. This is more or less standard.
I’m not sure what I’m “missing”, given that, as far as I can tell you seem to be arguing the same point I am. Perhaps you could elaborate.
So long as philosophy isn’t about disprovable conclusions, it’s solely about disprovable reasoning. Therefore a “savant” who offers philosophical conclusions minus the reasoning isn’t like a savant who offers disprovable mathematical conclusions minus the reasoning; it’s not merely that we can’t tell whether the philosophical conclusion is right or wrong, it’s that the reasoning is the philosophy.
First of all, you seem to be implying that the philosophical conclusion is not a part of “philosophy.” This is a severe and disabling disincorporation. Second of all, if the conclusions are not provable as right or wrong, then the reasoning in support of the conclusion can neither be proven right or wrong. If the reasoning cannot be proven right or wrong, then the reasoning is subjective in nature, which has been my thesis all along.
So?
Incorrect. A chain of reasoning can be – or fail to be – internally consistent regardless of whether the conclusion is disprovable.
That thesis is, of course, incorrect.