[crimsonalucard]

Yeah so does mathematics itself. Right? Mathematics is applied everywhere and is even used to calculate the trajectory of nuclear bombs yet it's utterly clear to most people that ethics and mathematics have nothing to do with each other.

The thing with computer science is that people are just confused because they use it as a more lego like artistic endeavor rather than a mathematical field. The reality is... Computer science is really just mathematics with axioms rooted in two isomorphic primitives:

Lambda calculus and turing machines.

[abdullahkhalids]

It is absolutely not clear to me that ethics and mathematics have nothing to do with each other. Let me give just one example. In statistics, there is a great debate about Bayesian methods vs frequentist methods. People in other fields using Frequentist vs Bayesian has real world consequences. For instance, medical scientists using frequentist statisics abuse the methods to publish cures that will not cure or help any sick people. This is not to say that the same scientists using Bayesian statistics would not attempt to abuse the system, but my belief (which could be wrong), is that the abuse will be less with Bayesian statistics.

So for me the math professor, who teaches pre-medical students frequentist statistics or the mathematician who creates yet another adhoc frequentist test for some specific situation, is doing something bad according to my ethics. They are making the world a worse place because of the particular kind of mathematics they choose to do.

[crimsonalucard]

I'm talking about the categorization of ethics with mathematics. You can tell some story putting them both together it doesn't make the category make any sense.

I think the bayesian way is more beautiful. Does that mean now I have to insert beauty into the description? No.

[dogcomplex]

If you want to make an arbitrary categorization of what is mathematics (or computer science) to divorce it of perspectives of ethics, beauty, etc, then go for it. But those perspectives are there (and valid), and good luck coming up with a robust definition that successfully divides them without dramatically limiting your ability to say things about math/csc. (e.g. you may not be able to favor any representation of one formula/program over another without creating a definition of beauty, which leads you down the rabbit hole again).

Point being: categorization is fuzzy. Ethics, beauty, etc are fuzzy but foundational and applicable to pretty much everything - like any other perspective. Denying them a place in CSC/Math/etc because they're seen as too "hard science" is a dead end road, because meeting your own bar of using only logical truth while still expressing anything useful about a subject is (probably) impossible - which is the general consensus in modern philosophy (as I understand it).

[crimsonalucard]

Philosophy is the arbitrary categorization.

Usefulness has nothing to do logic or mathematics. Math and logic is statements, axioms and theorems. Usefulness is an arbitrary judgement that depends on context. It's "fuzzy" like you say.

Math and logic aren't fuzzy, ever. Categorizing things that are fuzzy and aren't makes sense.

[dogcomplex]

Even if math and logic were fundamentally without fuzziness, their applicability to the rest of the world is inherently fuzzy. Their invention has inescapable, inevitable repercussions which have ethical consequences - so yeah, those need to be considered by someone.

But I wouldn't even be that generous. The amount of inherently human decisions that go into the design, representation, learning, educating, and yes - categorization of math is far from a perfect un-fuzzy logical utopia. We inherently add our own human ideals of what we consider a beautiful (elegant, easily understandable) formula/proof/concept/whatever, and every time we do we affect the perception of subsequent discoveries. Any computer scientist who has developed a sufficiently complex system knows that it is is impossible to make something "purely rational" without making arbitrary categorizations, which another programmer might do completely differently to produce a similar result with far-reaching effects down the line. Likewise, Math as we know it is taught the way it is because of the specific way it formed historically and the way it's best understood by its human students. The fuzziness runs deep.

Maybe you want to escape to fundamental concepts with rigorous self-consistent definitions only, with no applicability to the real world. Just cold hard formulas - the "real math". 1+1=2. Well then I hate to break it to you, but unless you have mathematical definitions of elegance and complexity to replace the human ones, you have no choice but to treat every tautology the same. Even selecting which proofs and axioms we care about is inherently human. So 1=1 and 46332688=3+211+7774+... Oh, and forget base 10... Or for that matter, why we even choose to define particular operators... Or explaining the proofs of any of this in english without some self-bootstrapping rigorous definition of the proof language...

My point is just that to completely remove the human fuzziness you have to cut out a LOT. You have to sacrifice understandability, brevity, and conceptual usefulness, amongst many others. And even if you could make a perfect self-bootstrapping logic box (something famously proven to be impossible by Godel Esher Bach - no system can perfectly define itself, it can only be defined by its parent) then there's still the problem that whatever the discoveries of your self-contained system are, they'll still have an impact on the rest of the world - which we then judge the effects of through Ethics.

Sorry, but truly escaping the fuzzy swamp of human culture is pretty damn tough. Maybe it can be done, but I doubt it. All language is fuzzy, all understanding is fuzzy, representation is fuzzy, the choice to define one thing and not another is fuzzy, Mathematics and Computer Science as educational subjects are very fuzzy still (even as much as they believe they aren't). Fuzziness is the baseline, and the study of that fuzziness is Philosophy. Maybe there exists some pure kernel that is strictly without human fuzziness, but that remains to be seen, and even if it was - it would be very different from the subjects of Math and Computer Science as we understand them today.

[crimsonalucard]

Fuzziness is not baseline.

First off categorization and naming is a human endeavor. The logic that lies underneath is solid and independent of the nomenclature or any formal rigor needed to define the names. We understand math through using words and naming as tools, but the words themselves do not define the underlying structure itself which is as far as we know: Not Fuzzy.

Second our choice of what axioms and theorems to study don't make anything fuzzy. We are simply choosing a subset out of a set of all possible choices in which the subset remains not fuzzy. OUr arbitrary choices are human, but the logic within the framework of our choices still apply.

Godel Escher Bach is just a book. The incompleteness theorem you are seeking comes from Godel. Not only can a system not define itself, it cannot be fully provable and internally consistent at the same time. This does have a lot of interesting things to say about logic BUT it does not make mathematics or logic fuzzy and opinionated.

Fuzziness is not baseline. The baseline is unknown, but what we do know has been consistently observed to be not fuzzy.

Let's be clear, by fuzzy we mean things like ethics and religion. Things that are based on opinion and exclusive to the human experience. None of this type of fuzziness applies to science or math or computer science.

[TheOtherHobbes]

Yes, mathematics has ethics - in the sense that as soon as you start talking about something being "right", while other understandings are "wrong" you're making an ethical choice. That doesn't just imply right/wrong in a logical sense. It also implies that you may be choosing use an analogous process - possibly automated - to find right/wrong values in decisions of all kinds.

Philosophy is about understanding patterns, habits, and traditions of thought. You can look at the patterns from different angles, one of which is ethical.

If you don't think at this level, math just "seems right because it is" - obviously and self-evidently.

But that's exactly why you need philosophy - to understand why that's a superficial misunderstanding of how math works, how the foundations of math aren't as stable as they seem to be (see also Hilbert's Project), why empiricism cannot possibly be genuinely objective and only works up to a certain point, and why even something "obvious" like the concept of True/False is contingent and questionable.

Philosophically, any sentence that starts with "Obviously..." or "It's completely clear that..." turns out to be the product of a cultural habit of thought, not the absolute and immutable objective truth that it pretends to be.

If you have no experience of this you're going to find this hard to understand, and you may even deny it outright.

But that may be taken to suggest that you haven't learned to think outside the usual socially-defined norms, and therefore can't imagine anything outside of them - which is not in any way the same as having infallible knowledge that there is nothing outside of them.

[crimsonalucard]

I get it. Your saying philosophy is foundational. A framework that’s even lower level then logic. My argument is that at this low level, why is philosophy talking about high level stuff like religion and ethics?

My guess is historical reasons. People in the past could not delineate the dichotomy between the human experience and hard logic, but they saw a deeper meaning in many topics. Hence philosophy is a basically a relic from the past.

[dogcomplex]

Yes, philosophers argue "hard logic" is a subset of philosophy and the human experience, and its claim to truth is as unstable and fuzzy as the rest of said human experience - to the extent it can be applied to the real world at all. Moreover, the use of "hard logic" brings its own relative cultural perspective that steamrolls others without foundational claim to truth. Appealing to "hard logic" without awareness and acknowledgement of other arguments for claims to truth is thus seen as naive or arguably unethical, especially when imposed into systems that limit other discussions of truth.

That said, there are logical positivist philosophers that believe reality is consistent with a hard logic view of the world, and thus it is foundational. They are a minority these days as far as I know - falling out of favor since... Kant? (I forget my history).

But no, philosophy is not a relic of the past in the sense that it has been surpassed by logic/science/etc - not til those can lay claim to truth better than a bunch of old Athenians. Jury's still out.

[smhost]

nobody knows whether mathematics really exists "out there", independent of human minds, which is what you're talking about. people are generally more interested in how mathematics appears to humans.

the basic tools and methods we have of investigating mathematics is designed for human minds. what are mathematical axioms if not the attempt to discover the point beyond which human cognition can't go? if you truly believe that there is a mind-independent mathematics "out there", and you believe that humans are really that insignificant, then you must believe that the totality of mathematics is vastly beyond the reach of human minds. so then the mathematics that is available to humans as of today must be a very small part of mathematics in itself, and it's not a coincidence that we find it so useful.