The problem is, this invariance "works" for predictive models and technological problems. The usefulness of the logic is then what matters. Also, there are fields I am sure, that take into account the variance you describe, and put back the subjectivity in the equation, such as quantum mechanics and relativity, etc. — schopenhauer1
Thus logic that is metaphysically composed of "natural laws" becomes logic that is creatures composed of the patterns, recognizing the very patterns they are composed of. This might be where Banno was coming from in his idea that logic fits too well- like questioning why a glove fits so well. This also leans towards the idea that logic and math is in fact discovered. — schopenhauer1
Remember, we usually need to verify our proofs via appealing to external facts, e.g. a calculator. — sime
So for example you ask why it might be important to tie maths to logic. To do so requires that you treat maths and logic as if they are distinct. But if maths and logic are much the same thing, it would not make sense to seek to tie them together. — Banno
But its the implicative consistency that makes it work. It not only doesnt need invariance, but belief in this concept holds back what our technologies can do, becasue they aren't designed to pick up on and take advantage of this natural drift in sense. instilling greater creative innovation in our machines will require that we explicitly tap into what we now only implicitly understand in our technological languages.
Invariance only works as well as its limitations allow it to, just as Cartesian philosophy 'works' only as well as its limitations allow. This is like saying that those who believe that truth is 'objective' can cite how wonderfully a non-relativistic approach to science solves problems. They cite the wonders of the hypo-deductive method and the linear progress of the sciences. But Kuhnian approaches to science(there is no objective truth), which believe that science is not a linear progression, and that scientific ideas change via revolutions rather than accumulation can argue that their way of understanding also 'works', but differently, and in a way that provides more options for creative advance of thought. This is because "truth is not objective" doesnt mean objectivity is false, it means the idea of objectivity is an island floating on a moving sea, but its adherents cant see past the edge of the island and so see only invaniance. Technologies used to build computing machines work wonderfully, but in a limited fashion.. In order to exceed these limits and accomplish what even the simplest one celled organisms are capable of in terms of intelligence , they will have to modify their vocabulary and methods.
Quantum mechanics and relativity dont question the fundamental basis of an objective causal logic, although they play around with applications of it in terms of specific mathematical models
Conway's game of life was small step in the direction i have in mind. — Joshs
Why must logic and maths be either discovered, or invented. Why not both?
Does the law of the excluded middle not count here? If not should we immediately stop saying “invent” and “discover” and instead say “disineventcover” or some such term? — I like sushi
And this. Why must logic and maths be either discovered, or invented. Why not both? — Banno
As I wrote in earlier posts, according to phenomenology since Husserl, you've got it exactly backwards. Existence is irreducible, and logic presupposes it. There are explanations which precede logic, of which logic is just a historical derivative mode , and not a necessary one. — Joshs
Differences and similarities are not opposites, they are both implied in every meaning. Invariance is not opposed to change, it is the effect of a constructive activity that maintains itself over time as the same differently. In order to be invariant, a meaning has to reflectively turn back on itself so that it can persist as itself. The effect of exposure to context guarantees that this reflexive move exposes any meaning to alteration of sense. Thus invariance is always the invariance of a meaning whose sense begins to drift at the moment of its turn back on itself in reflection. So the illusion is created of pure invariance only because this continual drift of sense of a meaning is subtle enough that most dont notice it. From this inattention to change within identity was born the concept of pure invariance and the law of non-contradiction. — Joshs
But what you likely would not have noticed is that the SENSE of the meaning of the object or word wandered very slightly over that period of time. — Joshs
Okay, we can say "evolution". But then what is it about evolution that allows for properties to work? Evolution works by way of differential survival rates. Thus, it may be said that it was advantageous for humans to think in these ways. — schopenhauer1
these patterns were prior to and independent of human conventionalizations of the best ways to recognize them. — schopenhauer1
It’s a whole other thread, but I don’t necessarily accept evolutionary accounts of reason. Which is not to say that humans didn't evolve, as we clearly did, along pretty clear (albeit complicated) lines. But when we get to be able to reason and speak, then those abilities really escape the gravity of biology, as it were. (I've been reading about an evolutionary theorist, Kenneth R Miller, whose book The Human Instinct: How We Evolved to Have Reason, Consciousness, and Free Will goes into questions like that. He's not an ID proponent, in fact has testified as an expert witness against ID in US court proceedings.)
I think there's this kind of unthinking assumption that reason evolves, like teeth or tentacles or whatever (to put it crudely) but what see evolving is the capacity to reason - the ability to grasp abstract truths. And I don't think that is accounted for by Darwinian theory as such, as it's not necessarily a question that's strictly biological. (Interesting footnote: neither did Alfred Russel Wallace, who broke from Darwin on this exact question.) So when we perceive necessary truths, etc, we're actually thinking and reasoning in a way that animals generally don't (notwithstanding bee dances, caledonian crows or puzzle-solving octopuses). Hence the Greek definition of 'man as rational animal', which, I think, connotes a genuine ontological distinction. — Wayfarer
Hence the Greek definition of 'man as rational animal', which, I think, connotes a genuine ontological distinction. — Wayfarer
You're still operating with naturalistic premisses when you say this which, again, you reinforce by re-stating that 'Recognizing patterns becomes the reason why humans can survive'. So, again, this implicitly subordinates reason to survival, (which I *think* is rather similar to what the Frankfurt school criticized as the 'instrumentalisation of reason'.) — Wayfarer
And one visible consequence of that is the diminishment of the sense of wonder, which, I think, is undermined, whenever we seek to rationalise our abilities in biological terms. — Wayfarer
Here's a question that I would genuinely want to get the views from people on PF. Hopefully people understand my question.
Let's assume that there would be an explanation to why we have Russell's paradox and the incompleteness results of Gödel, Turing etc. Hence there would be a central axiom in mathematics, axiom X, that without it we have get into paradoxes and incompleteness results, because we don't take into consideration axiom X, so our logic "breaks down" and we have to settle with ZF-logic or other kinds of logic.
Would there be any other problems with Frege's ideas (naive set theory) and the idea that mathematics is comes out of logic? Is the set-of-all-sets the only problem? — ssu
Let's assume that there would be an explanation to why we have Russell's paradox and the incompleteness results of Gödel, Turing etc. Hence there would be a central axiom in mathematics, axiom X, that without it we have get into paradoxes and incompleteness results, because we don't take into consideration axiom X, so our logic "breaks down" and we have to settle with ZF-logic or other kinds of logic.
Would there be any other problems with Frege's ideas (naive set theory) and the idea that mathematics is comes out of logic? Is the set-of-all-sets the only problem? — ssu
I think that there isn't any flaw in logic. Logic is perfect, we just are not.I think Russell's Paradox and Godel's Incompletness is one example of the flaw in the logic itself. There may be broader criticisms that this approach is erroneous to begin with. Math may not be subsumed in a broader logic. — schopenhauer1
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