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You think logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does?
by guerrilla 7y ago
You think logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does?
- inopinatus 7y agoI’d say they don’t matter nearly so much as art. The most cosmically significant export of humanity to date is Voyager’s golden record.
- guerrilla 7y agoGood thing the founders of modern science, mathematics, ethics and political theory didn't share the same opinion.
- inopinatus 7y agoRidiculous hubris, to claim to speak on their behalf, to claim to know the opinion of so many and diverse minds, and in such a crude misdirection to boot.
- guerrilla 7y agoGood thing they wrote volumes about it which have debated and summarized to the hilt.
- deleted 7y ago[deleted]
- inopinatus 7y agoThe summary is that without art, humans are cosmically uninteresting.
- iovrthoughtthis 7y agoI would like some stuff to read on this if possible.
- guerrilla 7y agoSEP contains dense summaries of every major thinker with extremely high quality references. Random example https://plato.stanford.edu/entries/leibniz/ https://plato.stanford.edu/entries/leibniz/
- DeathArrow 7y agoWhile art is certainly very important, I believe it doesn't have the same impact upon our lives as math has. And if you believe art is about creativity, you can find beauty and art in in mathematics and other sciences. Many great mathematicians were also art lovers, they appreciated music, they appreciated paintings and other forms of art. I don't think there's a dichotomy between art and sciences.
- inopinatus 7y agoI agree 100% with everything you say. However, I don’t believe that the “impact on lives” of scientific advances, whilst certainly being of tremendous interest and importance to the humans, carries into much universal significance.
- ukj 7y agoIt's the same kind of activity - creation. The significance of the creation (if it has any at all) is not necessarily the concern of the creator. Some people do Mathematics for its sheer beauty.
- guerrilla 7y agoYou could say the same about structural engineers.
- ukj 7y agoIf you buy into Wittgenstein's rule-following paradox. You could say anything about anything. > no course of action could be determined by a rule, because any course of action can be made out to accord with the rule If I had my own way of (mis?)interpreting him, I think he was alluding to what we now call "strict evaluation" in Programming Language Theory. A diligent rule-follower.
- guerrilla 7y agoStructural engineering the same kind of activity - creation. The significance of the creation (if it has any at all) is not necessarily the concern of the creator. Some people do structural engineering for its sheer beauty.
- ukj 7y ago[Scientific discoveries|Mathematics|Ethics|Political science] are the same kind of activity - creation. The significance of the creation (if it has any at all) is not necessarily the concern of the creator. Some people do [Scientific discoveries|Mathematics|Ethics|Political science] for its sheer beauty.
- guerrilla 7y agoYes, that's my point. It applies to anything that is creative and dismisses the original point through abstraction.
- iovrthoughtthis 7y agoYou think that art does not?
- morelisp 7y ago> the art of making distinctions, the study of critical thinking and the foundation of mathematics only matter in the same way art does? A major movement (or several, depending on how you slice it) in modern philosophy takes aesthetics as first philosophy - so yes, arguably they matter exactly the same way art does.
- voldacar 7y agoyou think too poorly of art
- guerrilla 7y agoI just think our quality of life would be much lower without the forementioned than without art. We'd be much worse off without any of them. My point is not to dismiss art but emphasize the utility of philosophy.
- andreareina 7y agoI think not the whole of logic, but this particular distinction -- what changes in the world if one is true versus the other? Is there even a difference that is manifest? It's like the question of what underlies quantum mechanics -- is the Copenhagen interpretation correct? Everett? Some flavor of deBroglie-Bohm? If there's no way to tell the difference, does it matter? It matters as far as the philosophy of it matters to you, but the concrete consequences of one way being true versus the other could very well be nil.
- miscPerson 7y agoCopenhagen requires an extraneous assumption — which may turn out to have practical implications. At the very least, we know it isn’t parsimonious, though that wasn’t clear until after it was developed (and the philosophical inclination to preserve locality was reasonable).
- Tainnor 7y agoThere is a distinction between logic, which is just the study of formal systems where you can prove theorems as in any other area of mathematics, and the philosophy of maths and particularly of mathematical logic. The same applies for set theory. The first one can assert that (in classical first order logic) e.g. there are uncountable models of the natural numbers; this is irrefutable. The second one asks things like "is classical first-order logic even true and/or adequate in an epistemic sense" (this is different from the more pragmatic question of "is classical FOL useful for the problem at hand")? Similarly, something like Gödel's incompleteness theorems are unequivocally true but the question of what they "mean" deep down is nothing that really affects mathematicians' work in general.
- guerrilla 7y agoIrrefutable and "unequivically" true if you take some classical FOL as a productive method of producing knowledge, a philosophical assumption. Philosophy came first, mathematical logic is just a formalization of that and the reason it was formalized at all and not somethimg else is epistemological. Your entire argument attempting dismiss philosophy is philosophy.
- Tainnor 7y agoI didn't dismiss philosophy. I said that as soon as you fix some axioms (such as those of classical FOL), the conclusions are irrefutable. This is where mathematics begins. The question where those axioms come from or whether they are "true" are philosophical. The two disciplines are related, but separate. Lots of mathematicians have different "foundational" beliefs from each other; some have studied or deeply thought about the philosophy, others may just speak to their intuition. However, this doesn't change the fact that they all come to the same conclusions from the same premises. E.g. a constructivist wouldn't be able to claim that a classical proof is "wrong", only that it's non-constructive and therefore unacceptable for some (philosophical or practical) reason; in fact non-constructive proofs can be seen as constructive proofs of some meaningless strings (e.g. the constructivist will maybe dispute the fact that there are discontinuous functions, but they will certainly accept the existence of a first-order derivation of the string representing "not all functions are continuous" from the axioms of set theory), the constructivist would just dispute that there is any meaning to these strings...