>>16901226
listen here logic guy. the realm of possible logical statements is like very infinite.
most of these statements are useless trash.
define barglo as bloblo with kogogaga then if barglo then kogogaga. here is your logic bro.

mathematicians only look at what's interesting. numbers, sysetms, probabilities and shit.
a logicist wastes time looking at empty of the universe space while mathematicians look at earth and planets and cool shit

Logic people are cs people larping as math people.

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>>16901234
>while mathematicians look at earth and planets and cool shit
That would be physicists and engineers. Mathematicians are too busy trying to divide impossibly huge numbers, looking at made-up sets of imaginary numbers, and developing increasingly obtuse jargon to do anything useful.

>>16901246
Other way around. CS people are Logic people creating an environment where they can benefit from the work of Pure Logic without having to try as hard to justify the usecase. Logicians playing with alternative foundational models of mathematics would otherwise have to deal with number theory retards screeching about their nonsense tower getting knocked over. At this point CS has become completely meaningless though because of the degree mill economy. A good filter for this is asking a CS graduate about System F-omega. If they don't know what that is, you can safely discount them as an irrelevant fungible labor unit.

meanwhile the fact that people get hangry proves that existence proceeds essence
check m8 platonist delusion

>>16901226
Trvke

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>>16901226
>Mathematics is downstream of logic
The most basic form of argumentation is the syllogism. A syllogism needs two premises. How do you know that there even ARE two premises in the world, huh? How do you know there's two of anything? How do you know 'two'? Check-mate, logicians.

>>16901311
Actually a syllogism is agnostic to that, and both it and premises are not primitives, but built up out of relations, conditions and classifications. By the time you're considering quantity and counting, you've already had to establish the entirety of reason. Reason itself is also quite a bit broader than you may think. For instance, we can have a system of reason where the law of identity does not hold. Can you formalize your argument in such a system? I think you'll find counting becomes quite hard without comparison.

>>16901333
>Actually a syllogism is agnostic to that
A what? Define it for me, please.

>>16901226
and both are downstream of physics

>>16901340
Physics is merely downstream from biology.

>>16901226
infinitary logic necessitates of mathematics to even be posed

>>16901262
>looking at made-up sets of imaginary numbers
heh, logiccel filtered by nomenclature, bet that at most you got a B in math, lmao

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>>16901338
In pure relational terms? A statement characterized by a transitive relation of a condition upon a condition.
No counting required. You can of course count the things here, produce semantic equivalents involving counting. But before you get your knickers in a twist, let me blow your mind here: Semantic equivalence doesn't refute the argument. Our structure isn't contingent on a notion of counting.
In fact, by relying on counting you end up running into problems with logics where syllogistic structure isn't predicated on having exactly 2 premises (oops, Plato!)

Here's a fun brain teaser for you to understand the importance of relational structures:
[math]
A \rightarrow B \rightarrow C \vdash A \rightarrow C
[/math]
Under the logical model you're most familiar with, this is the definition of a syllogism holds iff the arrow is predicative, which isn't necessarily the case for material implication. Can you guess why?

>>16901379
You're a wrong and excruciatingly boring pseud.

>>16901226
Mathematicians hate logicians.
Mathematics wanks itself incessantly over being built on unassailable logic. But its practitioners then go on to create absurdities in a group wank fest of unfathomable gayness, creating abominations which have no foundation other than "We said so! Tee Hee Hee!" They lick up each other's jizz and then they stack a house of cards upon their assumptions, tittering uncontrollably as their creation reaches dizzying heights of mutual masturbation.
When logicians call out these absurdities, point to the inconsistencies, the massive gaps between approximations and absolutes, the mathematicians are reduced to quivering jellies of indignant outrage. How dare anyone disrupt their sperm exchange sessions! So they resort to black magic and conjure up all sots of band aid fixes to conceal their weaknesses, resorting to such "logical" retorts as "It just is!" Like small children incapable of justifying their thought processes. Pathetic.
In a sane world these subhumans would be dragged out of their beds late at night, securely bound and stripped nearly naked, hung upside down from a nearby tree, hosed down with cold water, and then soundly savagely thrashed with polyethylene pipes. Salt is rubbed into their open wounds and they are then left to dangle for a few days while local folk are invited to poke at them with sharp pointy sticks and children are given rotten food to throw at them. It would give them time to reflect upon their crimes against logic.

>>16901226
two sides of the same coin when you know both of them.

-Logic is celebrated abstract rewriting
-rewriting is the study of certain sequences in bounded arithmetic (FOL over binary relationship symbols = and <; operation symbols + x succ, usual operation axioms relating those and induction on bounded formulas; the distinction between classical and intuitionistic reasoning being next to insignificant because of double negation translation, a.k.a. we'll use classical reasoning).
-math has arithmetic among ts topic.

And we have come full circle.

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>>16901226
((Cantor)) destroyed mathematics with his anti logical set theory.
His fellow countrymen Fraenkel and Landau did the rest.

nothing could possibly be gayer or more limp wristed than participating in logic vs math arguments. you're all dumb small brained losers with no friends.

>>16901487
>two sides of the same coin when you know both of them.
One can never know the entirety of either, actually, and they're extremely heterogeneous.

Logic and reason are the study and application of relations, conditions and classifications. You can model inference as rewriting/substitution, but rewriting/substitution is it's own thing which is underpinned by logic.
>rewriting is the study of certain sequences in bounded arithmetic
Not really. You can model any variety of arithmetic in a rewriting system though, just like you can use it to model logic. But you can't have one without first having logic, and you don't need one to work with logic.

>>16901496
It was Hilbert actually. Frege and Russel only ever gave a shit about mathematics as an ingrown extension of logic. The formalists of the 20th century staged a coup and now we talk about things in sets, as though they could make any sense without identity, negation and relation.

We will not move forward until Logocentrism is restored, and the mathematicians are correctly identified to logic what the linear algebraists are to mathematics itself.

>>16901500
Maybe. But the fact you enjoy getting tag teamed ass fucked by both your grandfathers is much gayer.

>>16901226
>Mathematics is downstream of logic
you cannot define first order logic withiut set theory, so no

>>16903253
Well, i dont see how the computer implementations of first order logic use set theory. Maybe you are thinking of first order logic from the point of view of metatheory and not as a theory for the user

>>16903263
The moment you have to define what a property is, you need maths. It can be set theory or any other equivalent basis of maths, but you need it.

Software proof systems use type theory or other things, but they are maths.

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What a retarded thread. On one level, all you have here is arbitrary line-drawing between mutually arising comprehensions. On another level, it's effectively just historical revisionism wrt. the order of development of some formalisms, based purely on amateurish head canon, even though it takes 2 minutes to verify what actually came first (conclusively proving that mathematics is NOT downstream of logic).

>>16901226
>downstream
What "stream"?

>>16903253
Frege basically did. Type theory can. Combinators can.

>>16903310
>or any other equivalent basis
You've already refuted your own argument right here.

>>16903321
Feel free to demonstrate which part is fiction.

>>16904121
>Feel free to demonstrate which part is fiction.
Do you have any example of formal logic preceding arithmetic using symbols in any human culture?

>inb4 rhetorical slop about how everyone intuitively applies logic
Almost everyone also has an intuitive number sense. One is not formal logic just like the other is not mathematics.

>>16904128
>Do you have any example of formal logic preceding arithmetic using symbols in any human culture?
Mohism's Canons are a formalism of logic that precede anything equivalent for arithmetic in Chinese culture.
In the west, Frege's formal FOL precedes formal arithmetic. Keep in mind that though it is very common to see dialogue about Frege's work where set-theoretic framing is used, Frege himself did not work using sets, etc.
Engaging with pre-20th (and late 19th) century texts on math is fun, and I think underappreciated in these discussions.

A more interesting question to ask, can you name any organisms where informal arithmetic precedes informal logic?
Since mathematics is downstream of logic, we expect arithmetic to follow from logic and this indeed does seem to be the case. Interestingly, when the encoding is rather base and direct, the arithmetic is highly limited which also tracks with out expectations because organic chemistry isn't very good at the unbounded recursion needed.
Slime molds are a great example of an organism that can handle pretty complex problems of reason (for their biology), but we can't observe any behavior that indicates they can handle even simple problems of counting.

>>16904136
This post is written terribly I know, forgive me.

>>16904136
>Mohism's Canons are a formalism of logic that precede anything equivalent for arithmetic in Chinese culture.
Proof?

>In the west, Frege's formal FOL precedes formal arithmetic.
Ok, but this is completely irrelevant.


>A more interesting question to ask, can you name any organisms where informal arithmetic precedes informal logic?
I don't find speculations about unspecified "organisms" interesting. In most normal humans, basic number sense and intuitive grasp of logical coherence are both innate.

>>16904136
>>16904143
You know what? Since you did write a relatively decent post, I'll put a bit more effort into explaining my point. I wrote "arithmetic using symbols", not "formal arithmetic", because the latter has a very narrow meaning, while I'm thinking of "formal" in the general sense of dealing with explicit abstractions using explicit rules, independent of context. It's at that point you are dealing with form. Intuitive human reason is mostly defeasible and contextual. It avoids outright incoherence but not in the systematized, abstract rule-following way. If you need to prove this to yourself, just observe what a huge difference it makes if you frame a logical proposition in terms of an everyday situation vs. using variables. In general, I observe that the more fundamental something is to the workings of the mind, the easier it is to take it for granted and the harder it is to treat it as an object of thought.

>>16904143
>Ok, but this is completely irrelevant.
How do you figure? You ask for an example of formal logic preceding arithmetic. Here is your example, Frege's formal logic preceding arithmetic.
>I don't find speculations about unspecified "organisms" interesting. In most normal humans, basic number sense and intuitive grasp of logical coherence are both innate.
I'm not asking for speculation about "unspecified "organisms"". I'm very much asking for a specific organism wherein reputable study shows they can solve problems of counting but not of reason.
Physarum polycephalum can solve problems of reason, but not counting. If they are truly unordered, then it stands to reason we can find examples of organisms which may solve problems of counting but not reason to complement my example of an organism capable of solving logic problems but not counting problems. A lack of such an example isn't necessarily proof, but it's certainly enough to hold the claim in suspicion.
You restrict the domain to humans, but I assert this domain is not enough to get the bottom of things in a way we haven't already covered.
As has been the central point, one can have a system of reason (however useless) without counting, but one can't have counting without a system of reason.

>>16904155
>Here is your example, Frege's formal logic preceding arithmetic.
What a lazy bait-and-switch. Dong arithmetic systematically using symbols falls under mathematics and it precedes Frege and "formal arithmetic" by ages. Either way, see >>16904154.

>I'm very much asking for a specific organism wherein reputable study shows they can solve problems of counting but not of reason.
This is trivial. The average American kid would be an example of just that. It's also irrelevant, because you're doing a bait-and-switch again:
>one can have a system of reason
>system of reason
Most people reason without a system of reason and they can count just fine.

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>>16904154
>I wrote "arithmetic using symbols"
Which is totally fair, and I will agree with it. I will 100% concede that this abstraction appears first in mathematics, and wouldn't hope to imply otherwise. Contemporary logic's representation does have its roots in mathematics' representation.
There are some interesting stipulations here. I think our current system stems from Diophantus circa 300BCE? Technically it's Francois Viete's work in the late 1500s, integrating work of the Islamic and Indic scholars, but IIRC these guys were themselves working off of Diophantus.
Symbolic arithmetic does technically precede Diophantus, but it's not really the same thing. Babylonian and Egyptian notation was just shorthand. Pre-iron age writing gets weird very quickly, thus I think it's cleaner if we ignore it, especially because these systems ended up orphaned anyways.

Interestingly in my example of Mohism, while it doesn't necessarily precede abstract symbolism for arithmetic in China, but it developed its own symbolic system in isolation. Mohism is weird in a lot of ways, I found it enthralling to learn about.

>It avoids outright incoherence but not in the systematized, abstract rule-following way.
I'm not necessarily sure about this, but as I'm sure you know, not a lot to say about it or analyze without intense speculation.

>Most people reason without a system of reason and they can count just fine.
For all intents and purposes, I generally don't draw a distinction here. I'm considering the base, intuitive and built-in sense of reason as a system of reason. This ends up just being uninteresting differences in semantics, though. See below.

>>16904161
I didn't see your post above, yeah. Not so much bait and switch, we're just speaking in different terms. I'm fully good faith here and understand we're operating in different mental frameworks.

>>16901226
No bro, the problem is you're reducing everything to individual entities.
You say that logical reasoning precedes mathematics, but they both work as a team. If that's not the case, then tell me, what do you define as reasoning?
Because perhaps that's where the misunderstanding lies.

As I see it, mathematics is the tool, and logic is the environment in which we apply it. If we modify mathematics, we'll have tools to modify logic, and in the end, it's the same chicken-and-egg dilemma. We know evolutionarily that the egg came first, but the individual isn't very far removed from that origin.

Did a dinosaur do math without needing logic? We don't know.

>>16903310
Syntax doesn't need mathematics. What you are talking about is semantics and there are semantics weaker than any standard set theory or type theory, so it is not that obvious thar those weaker systems are only math or only logic, this is source of academic debate

>>16904178
>I think our current system stems from Diophantus circa 300BCE?
>Symbolic arithmetic does technically precede Diophantus, but it's not really the same thing
The use of the abacus in Ancient Greece goes back to at least 500BCE and it's very much "symbolic arithmetic", even if it uses physical objects as symbols and physical operations to implement abstract arithmetic rules. Geometry predates even that and surely it falls under math. Now, proper systematic treatment of logic in Western civilization starts with Aristotle. I don't know enough about Mohism to argue anything about it.

>I generally don't draw a distinction here. I'm considering the base, intuitive and built-in sense of reason as a system of reason. This ends up just being uninteresting differences in semantics, though. See below.
It's demonstrably not just a difference in semantics. As I've already pointed out: people who can reason just fine start getting confused as soon as you abstract away the specifics of a logical proposition and replace them with variables. If intuitive reasoning was abstract and rule-based, it wouldn't have made a difference.

>>16904204
>what if you didn't eat breakfast this morning
By your logic, people being unable to parse this would imply semantics is different from itself.

>>16904216
I know you felt clever shitting that one out but you're not saying anything coherent and my point stands unchallenged.

What's your bottom line, anyway? You can say logic (formulated as explicit rules) is supposed to reflect the coherence of reality, and even animals with no number sense beyond "less"/"more" or "few"/"many" behave in a way that suggests an intuitive expectation of the same coherence. In that very narrow sense, you can say "logic precedes math". But if you're a functioning human, intuitive reasoning and basic number sense are innate and co-occurring. It's all hard-wired into the brain. The brain comes with both. One does not precede the other and one faculty is not neurologically separate from the other.

>>16903263
mizar; metamath

>>16901934
logic cannot exist without some metatheory: I've picked bounded arithmetic for that purpose.

>>16904121
>Frege basically did. Type theory can. Combinators can.
>You've already refuted your own argument right here.
No I haven't since none of those basis are logic.
>>16904192
>Syntax doesn't need mathematics
Sure, if you just want to syntax all you need is an alphabet or symbols. But is that what people mean when they say logic comes first? Are you saying that logic started without semantics?

>>16904371
They are examples of my point. Those are theories for the user and they in fact *develop* set theory. They are not build *on top* of set theory, the machine level implementation doesn't need set theory at all, only what any other programming language needs.

>>16904398
>Sure, if you just want to syntax all you need is an alphabet or symbols. But is that what people mean when they say logic comes first? Are you saying that logic started without semantics?
What i'm saying is that applying mathematics to the study of the semantics of logical systems is something very recent, late 19th century or early 20th. Even truth tables are a surprisingly recent invention. Logic started with basic linguistic semantics

>>16904204
>The use of the abacus in Ancient Greece goes back to at least 500BCE and it's very much "symbolic arithmetic", even if it uses physical objects as symbols and physical operations to implement abstract arithmetic rules.
But not a writing system and not in the line of descent for how we handle math today.
>Geometry predates even that and surely it falls under math.
And almost all of it was written in natural language.

>It's demonstrably not just a difference in semantics.
By semantics, I mean the semantics of the word "system", not the semantics of a specific system.

>>16904225
That's not me, btw.

>>16904191
>Did a dinosaur do math without needing logic? We don't know.
It would certainly be interesting if it were the case.
The point being, set theorists have argued ad infinitum for a century that mathematics is not a suburb of logic, and many take the exact opposite position.

>>16904398
Your claim was that they needed to be based in mathematics, then you go on to say that they can actually be based in any equivalent system. Thus, refutation. None of those are mathematics, and Frege's system is literally logic.

>>16904501
>Logic started with basic linguistic semantics
Were that the case, animals without language would not be able to solve problems of reason.

>>16905164
>Were that the case, animals without language would not be able to solve problems of reason.
When we talk about logic having syntax and semantics, we talk about the history of formal logic or symbolic logic, logic as a discipline and its practices (formal rules), because the syntax and semantics are aspects of logical systems as abstract technologies or devices, metalinguistic in nature. Language analysis. That's the usual sense of the term logic when mathematicians talk about it. Cognition is a more proper term for what you are calling logic. Human inference and animal inferential reasoning are other terms from the literature. Your use of "logic" in this uncommon sense strikes me as metaphorical. By all means, if it isn't unconmmons, name some example of its use