ukj

39 ms·

361.
by ukj 6y ago
The crux of the matter is information. Symmetrical (equational) theories contain none. Information mandates asymmetry.
362.
by ukj 6y ago
Good question/intuition. You are correct in that I am appealing (exploiting?) the Liar's paradox [1]. The gist of which is that the truth-value of the proposition is undecidable. You could interpret my statement as a performative
363.
by ukj 6y ago
Löwenheim-Skolem doesn't hold for higher order logics such as type theory/Lambda calculus. Basically, it doesn't hold for any constructive logic.
364.
by ukj 6y ago
I am not sure how to even respond to this coherently... alas - I try. Do you think "logical implication" (whatever that is) is not bound by temporal order? That simply tells me that whatever you think "logic" is - it doe
365.
by ukj 6y ago
I don't exist. Or the Philosophical cliche... I freely believe in the absence of free will. Scott Aaronson has discussed this in more detail: https://www.scottaaronson.com/democritus/lec18.html
366.
by ukj 6y ago
I'd say ,given the nature and flow of reverse mathematics, conclusions are necessary but insufficient for premises. The erudite/formal lingo aside. Reverse mathematics is a nice metaphor for how justification works in practice.
367.
by ukj 6y ago
Well, obviously! That's by design.
368.
by ukj 6y ago
I hear you (and I obviously made a bad inference re: your background - apologies), but there is a distinction to be made between large-but-finite (computable? halting?) and infinite (non-computable? non-halting?) sets. We can't compreh
369.
by ukj 6y ago
You aren't hearing me. The difference is the order/sequence in which the events take place. Regular maths starts with premises then looks for conclusions. Reverse maths starts with conclusions then looks for premises. So in revers
370.
by ukj 6y ago
From your comment above I am making the (admittedly presumptuous) inference that you didn't study Quantum physics. https://en.wikipedia.org/wiki/Renormalization If giving up infinities allows me to understand The
371.
by ukj 6y ago
The finite axiom of choice doesn't suffer from paradoxes of infinity. It's mostly intuitive to computer scientists that infinities don't exist ;) And we are also in the habit of proving/realizing our choice-functions rat
372.
by ukj 6y ago
You are going too far! Reject the Axiom of INFINITE Choice. Embrace the axiom of FINITE choice! Become a Finitist (can I interest you in some pamphlets to tell you more about my religion?) https://en.wikipedia.org/wiki/
373.
by ukj 6y ago
You are disagreeing over the meaning of the word "the" in "THE axiom of choice". It's not only one - there are multiple formulations. There are the axioms of finite choice; and the axiom of infinite choice. Broadly
374.
by ukj 6y ago
Why do you assume that premises-to-conclusions is the "right way" to go about stuff? Why can't we go from conclusions to premises? https://en.wikipedia.org/wiki/Reverse_mathematics
375.
by ukj 6y ago
The way ZFC navigates around Russel's paradox is by adopting the axiom of restricted comprehension [1]. Here's a thought experiment: What happens if we allow for unrestricted comprehension [2] ? What happens if we say 'Contr
376.
by ukj 6y ago
Humanities may not be a science, but being human sure is empirical. Experience is all we have. At the bottom of all of these bouts is then “demarcation problem”. What is a science, what isn’t a science? I prefer Paul Fayerabend’s view: if i
377.
by ukj 6y ago
There is a distinction to be drawn between expression and evaluation. If I express “2+2” it could be evaluated to 4 (in decimal); or 11 (in trinary). If two evaluators disagree on the truth-value of 2+2=11 then one possible explanation is t
378.
by ukj 6y ago
Theoretical vs practical expressivity. You can always insist you were arguing for theoretical expressivity when people start throwing counter-examples at you. https://en.wikipedia.org/wiki/Expressive_power_(computer_sci
379.
by ukj 7y ago
Your question was answered before you even asked it. > It matters for people who find it valuable, the same way art, music or literature matters. Key phrase "the same way". There's nothing wrong with being wrong, yet you s
380.
by ukj 7y ago
It was loaded. It contains an unjustified assumption that “logic, the art of making distinctions, the study of critical thinking and the foundation of mathematics" and [other?] art belong in different categories. It also takes an incom
381.
by ukj 7y ago
You didn't make a point. You asked a loaded question. It backfired on you.
382.
by 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 discov
383.
by ukj 7y ago
If 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
384.
by ukj 7y ago
It'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.
385.
by ukj 7y ago
The answer is: "both". Where do Mathematicians look to discover Mathematics? In the depths of their own minds. The part where you "look and think deeply" is discovery. The part where you "express your discovery in
386.
by ukj 7y ago
This is not an SE. This is a 6S. I have a 6S. I want an SE.
387.
Language Aptitude Not Math Predicts Programming Skill(i-programmer.info)
18 points by ukj 7y ago|5 comments
388.
by ukj 7y ago
>I think you're assuming too much good faith on the part of the person making the argument. Naturally. I subscribe to the principle of charity and I practice it. If you are just using me as a pawn in your argument, shame on you.
389.
by ukj 7y ago
All the same - "obscurity" is determined by context. If you happen to be in the "obscure camp" (without knowing it) in which GC is a problem, not a solution - it sucks for you having listened to the OP.
390.
by ukj 7y ago
I was addressing this point: > I think a constructive rule of argument would be to state upfront when you happen to be standing in the "obscure" or "completely artificial" camps. Obviously it is "to me". On

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