/lit/ - Literature

[Anonymous No.15672871]

>get told to study analytic philosophy
>see this

WTF? Explain yourselves, anal-cels! How is this philosophy?!

[Anonymous No.15672885]

>>15672871
Are you so much of a brainlet that you can't follow the argument in the excerpt you posted?

[Anonymous No.15672908]

>>15672871
>How is this philosophy?!
You've clearly never read Aristotle's Organon. Take an elementary logic course before attempting to read *any* work in the philosophy of language -- from Aristotle to the present day.

[Anonymous No.15672938]

>>15672871
Lmao imagine using your life to study this

[Anonymous No.15672940]

>>15672871
The linguistic turn, or: the greatest manufacturing efficiency of toilet paper ever seen in the academy

[Anonymous No.15672962]

>>15672871
post the rest of the article. I need to see if there's a point to all this. it seems to be about the disquotationalist theory of the truth

he's basically calling someone out for using quotation marks wrong. this reads like some asshole on stack overflow except those people do it for free. this is what your student loans are subsidizing

[Anonymous No.15673001]

>>15672962
If you're just going to make shit up, go back to /b/ with the rest of the illiterate subhumans.

[Anonymous No.15673019]

>>15672938
Mathematics is even more autistic and abstract. Rigorous thought is certainly not for everyone.

[Anonymous No.15673027]

>>15673001
what the fuck? did you forget to take your meds today?

[Anonymous No.15673028]

>>15672871
It's sense and reference. You should be acquainted with the word 'cat' vs a cat (over there). I don't think it's well interpreted (such as does one precede the other) but it is real. I'm not sure how important the distinction is considering in any debate it never comes up as a point of contention

[Anonymous No.15673029]

>>15673001
take your meds

[Anonymous No.15673031]

>>15673027
>>15673029
Unintentionally ironic posts of the day.

[Anonymous No.15673040]

>>15673028
One is a 'token' of the other is how it's explained

[Anonymous No.15673050]

>>15673031
no you've actually upset me. what was your problem with my post? explain yourself. I'm seeing more and more of these nonsensical replies on here lately.

[Anonymous No.15673051]

>>15673029
>>15673027
kek

[Anonymous No.15673069]

>>15673050
Take a deep breath. It's a lot easier to understand after you've taken an introductory logic class.

[Anonymous No.15673092]

>>15672871
Is there a point to this article? Is he just calling out someone for using quotation marks wrong? holy fuck this is autistic

[Anonymous No.15673110]

>>15672871
This is symbolic logic. I'd hesitate to call it exclusive of the analytic. It's really a field as old as Aristotle.
I don't know where this is from, and I know some writers will use symbols differently, but if you understand what the symbols mean it makes more sense and isn't different from many other works of philosophy, in looking at language and abstraction. Though the writer's argument doesn't seem very interesting at all.

If you don't know, the triple bar symbol, ≡, means "if and only if" in philosophy, as the text mentions.
So x ≡ y means that x ⊃ y and y ⊃ x.
"⊃" mean an "if, then" statement, with the if on the left and then clause on the right.
x and y are statement variables for a premise.

[Anonymous No.15673114]

>>15673069
esl detected. now it all makes sense.

[Anonymous No.15673118]

>>15672962
>>15673050
>implies the entire field of Logic should be abolished
>gets upset when he receives pushback for being an anti-intellectual
wew

[Anonymous No.15673119]

>>15673092
Overview:
https://plato.stanford.edu/entries/reference/
Slightly deeper dive:
https://plato.stanford.edu/entries/types-tokens/

[Anonymous No.15673144]

>>15673050
I thought it was just me noticing the increase in nutters.

[Anonymous No.15673155]

>>15673110
>I don't know where this is from
It's from a book by the logician Peter Geach.

[Anonymous No.15673177]

>>15673144
You wouldn't even be communicating on the internet right now if people weren't absolute 'nutters' around a century ago about the distinction between types and tokens, and use and mention.

[Anonymous No.15673480]

>>15672871
>Tom loves Mary. I shall call this Hob.
kek, based

[Anonymous No.15673484]

Well, analytics? Your response?

[Anonymous No.15673561]

>>15673484
See “An Alternative Theory of Nonexistent Objects" by Ed Zalta.

[Anonymous No.15673566]

>>15672871
>like math
>be too dumb for it
>turn your life into this instead of getting any other hobby
loving every laugh

[Anonymous No.15674039]

>>15673484
Frege had a good analogy but in particular to numbers. Existence is prior to anything or you're stuck necessitating whichever object predicates existence in order to talk about existence.

[Anonymous No.15674194]

>>15673566
Logicians are dumber than (other) mathematicians? What?

[Anonymous No.15674361]

>Modus Ponens

[Anonymous No.15674456]

>>15672871
Traditionally, quote marks are used to switch from using a sentence (or word or other linguistic string) to mentioning a sentence (etc). So I might say: ''Max Black' is eight letters long', and that would be true, but if I say 'Max Black is eight letters long' that would be false. Max Black (the philosopher) is not eight letters long. So that's the use/mention distinction. Now, normally people accept that truth is a predicate of mentioned sentences, not used sentences. You might say ''Snow is white' is true' but not 'Snow is white is true.' What Max Black seems to be doing, is identifying the quotation of a sentence with a name designating the sentence, which is why he uses the abbreviation 'Hob'. Seems okay at first glance. And again, you might allow ''Hob' is true' but not 'Hob is true'. But the author suggests: once 'Hob' is a name, it ceases to be the sort of thing we can say can bear the predicate 'is true.' That's because we normally don't say that names (which refer to individuals) are true or false. We don't say ''Max Black' is true,' 'Max Black' is a name for an individual, not a sentence. So I get the point the author is making here. I don't know what solution to give because it depends a lot on your theory of meaning and reference.

I don't know about you OP, but when I read difficult continental philosophy like Hegel's Science of Logic, problems similar to this one come up, and they're just as difficult to think through but not for that reason bad. If you want to be consistent, hate all of philosophy, but this is not an analytic-specific problem. And in fact it's what makes analytic AND continental philosophy worth taking seriously. If you get filtered that's not their fault, but yours.

[Anonymous No.15675334]

>>15672871
It's math for language. High iq stuff, but also you don't need it. It's nerd pointless stuff, but unlike physics you can't make money as an engineer besides teaching

[Anonymous No.15675396]

>>15672871
>>15672908
>>15672938
>>15672940
>>15672962
>>15673019
>>15673027
>>15673028
>>15673029
>>15673031
>>15673040
>>15673050
>>15673051
>>15673069
>>15673092
>>15673110
>>15673114
>>15673144
>>15673155
>>15673177
>>15673480
>>15673484
>>15673561
>>15673566
>>15674039
>>15674194
>>15674361
>>15674456
>>15675334
>

[Anonymous No.15675634]

>>15672871
>"get told to study anal... "

[Anonymous No.15675832]

>>15675334
>It's nerd pointless stuff
All higher education is basically pointless nerd stuff.

[Anonymous No.15676721]

bump

[Anonymous No.15676763]

>>15673566
This, analytic philosophy is fake math for retards who can't handle real math

[Anonymous No.15676908]

I guess it's important on occasion to study philosophy of language and logic but building an entire school of thought based on mostly these two fields just seems beyond autism. Only the Anglos could have come up with it something so tedious.

[Anonymous No.15677189]

>>15676763
>>15676908
Logiclet cope.

[Anonymous No.15677320]

>>15674456
The problem isn't that it's hard, it's that it's so autistic.

[Anonymous No.15677467]

>>15677320
Reality is autistic, anon. Get used to it.

[Anonymous No.15677473]

>>15672871
itt keyboard warriors dismantle Logic and academia is never the same

[Anonymous No.15677480]

>>15677467
>>15677189
Autist cope

[Anonymous No.15677485]

What the anti-science christcucks ITT don't realize is that Peter Geach is one of their own. He literally founded modern Thomism.

[Anonymous No.15677488]

>>15677480
I'm more of an artist than an autist. But I'm sorry to say, reality doesn't care about your feelings.

[Anonymous No.15677492]

>>15672871
this is like programming with a lot of waste comments

[Anonymous No.15677498]

logic is gay haha

[Anonymous No.15677507]

>>15677492
learning logic is like learning programming but even more useless

[Anonymous No.15677509]

>>15677492
Programming didn't exist when this was written. Computer science is an outgrowth of logic.

[Anonymous No.15677516]

>he makes a sentence but like it’s algebra god daaaamn bro

Logic is a nice consolation prize for aspiring mathematicians who got filtered out of big boy math.

[Anonymous No.15677518]

>>15677516
Math is just an application of logic, kiddo.

[Anonymous No.15677522]

>>15677518
Try again, incel.

[Anonymous No.15677526]

>>15677522
Take a course in logic or the foundations of mathematics. You might learn something.

[Anonymous No.15677527]

>>15677526
You first, retard.

[Anonymous No.15677528]

>>15677527
I am a professional mathematician.

[Anonymous No.15677535]

>>15677528
Your clueless posts prove otherwise.

[Anonymous No.15677539]

>>15677535
Cite a post of yours that shows you have any idea at all what you're talking about. Dicking around and calling people names is not a measure of knowledge.

[Anonymous No.15677541]

>>15677539
Just as I thought, you have nothing to say. Clueless.

[Anonymous No.15677544]

>>15677488
But does "reality" encompass my feelings, and isn't my caring about my feelings also part of reality? Meaning that reality does care about my feelings?

[Anonymous No.15677550]

>>15677541
Still waiting for you to say something substantive. So far you've only made it apparent that you got filtered on page one of the Organon, and have never studied rigorous mathematics.

[Anonymous No.15677553]

>>15677550
Same to you "professional mathematician." AKA unemployed programmer.

[Anonymous No.15677556]

>>15677544
No, not at the fundamental level.

[Anonymous No.15677573]

>>15672885
>>15672908
>>15673069
>>15675334
Are you people serious? Can't you see that the considered topic is trivial?
I know that people who go for philosophy these days are more into humanities than math, but this is just dumb.

[Anonymous No.15677580]

>>15677573
Cope, brainlet. You have no clue what you're talking about.

[Anonymous No.15677593]

>>15677580
You have conceded defeat, incel programmer.

[Anonymous No.15677598]

>>15675334
and it all deserves to be shoved in a locker

[Anonymous No.15677602]

>>15677593
In your dreams, high-school dropout. You're not fooling anyone with your unmoored ad hominem attacks.

[Anonymous No.15677604]

>>15677602
Nice cope. Keep freaking out.

[Anonymous No.15677608]

>>15677604
Get an education, then talk shit.

[Anonymous No.15677611]

>>15677518
Math cannot be "just an application of logic" because math is largely demonstrative and logic is primarily dealing with truth statements and therefore language. You cannot prove any geometrical or topological theory without showcasing and constructing your prove with a demonstration on a blackboard. All numbers and operations are symbols of spatial relations, even in algebra.
If you're misled by the similar use of equalities in both math and logic then you're rightfully called "clueless".

[Anonymous No.15677613]

>>15677608
You first, brainlet.

[Anonymous No.15677617]

>>15677611
It sounds like you've never taken a rigorous math course in your life. Your post is a jumble of nonsense.

[Anonymous No.15677618]

>>15677556
>not subscribing to a neo-aristotelean ontology
Enjoy your unsolvable metaphysical problems that will eventually lead to you denying your own humanity and reverting to myth, but autistic myth without sex appeal

[Anonymous No.15677621]

>>15677618
Physics doesn't care about your (lack of a) sex life.

[Anonymous No.15677622]

>>15677617
>if I say "rigorous" in every other post nobody will notice I failed out of math

Embarrassing.

[Anonymous No.15677625]

>>15677617
How come it's nonsense? What is nonsensical in it?

[Anonymous No.15677630]

>>15677617
logic 3002 is not a rigorous math course, silly goose. >>15677611 is correct.

[Anonymous No.15677655]

>>15677622
Just admit it: you have not studied mathematics above grade school level.

>>15677625
To the extent that it can be deciphered at all, it is straightforwardly false. For example, FOL is sound and complete and therefore logical truth corresponds to demonstrability, whereas mathematics in general is incomplete and therefore its truths are not guaranteed to be demonstrable. So the exact opposite of what you wrote. It is not the case the "numbers and operations are symbols of spatial relations" -- not even close. To even suggest so is nonsensical. Etc. etc.

>>15677630
In your ignorance, you just threw your chips in with someone who has never studied mathematics. Nice going, pseud.

[Anonymous No.15677672]

>>15677621
It clearly does, since it compels me to fuck.

[Anonymous No.15677698]

>>15677655
We have different notions of 'demonstrative'. By 'demonstrative' I mean that in order to do anything in, say, geometry, you have to construct your terms first in spatial figures and only then, by observing these figures, deduce anything. Nothing can be done in geometry without a spatial demonstration.
> FOL is sound and complete and therefore logical truth corresponds to demonstrability, whereas mathematics in general is incomplete and therefore its truths are not guaranteed to be demonstrable
Simply untrue. How is mathematics "incomplete"? What does it require for completion?
> It is not the case the "numbers and operations are symbols of spatial relations" -- not even close.
Okay, let's consider the following. Maths has any meaning and practical use only if it's applicable to our spatial world or, to be more precise, to our spatial form of representation of this world which is temporal and spatial. Therefore, all symbols in math have something to do with spatial relations or otherwise they are meaningless. Disprove that.

[Anonymous No.15677704]

>>15677655
This is your brain on first year logic. For all your bluster about him being "indecipherable" you turn a literal Logic 101 view held by nobody but undergrads into a meaningless jumble. He is correct. Like the other guy said.

You really are an unemployed programmer.

[Anonymous No.15677712]

>>15677698
good post. i’m in math too, what kind of math do you do?

[Anonymous No.15677719]

>>15677712
I do no math, all I did is just read Kant.

[Anonymous No.15677723]

>>15672871
Logic is a part of philosophy.

[Anonymous No.15677739]

>>15677698
>We have different notions of 'demonstrative'. By 'demonstrative' I mean that in order to do anything in, say, geometry, you have to construct your terms first in spatial figures and only then, by observing these figures, deduce anything. Nothing can be done in geometry without a spatial demonstration.
Are you still in grade school? That is not true at all. Geometry and topology beyond the very basics cannot be demonstrated visually.

>Simply untrue. How is mathematics "incomplete"? What does it require for completion?
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

>Okay, let's consider the following. Maths has any meaning and practical use only if it's applicable to our spatial world or, to be more precise, to our spatial form of representation of this world which is temporal and spatial. Therefore, all symbols in math have something to do with spatial relations or otherwise they are meaningless. Disprove that.
Utter nonsense. First of all, proofs in axiomatic systems operate independently of whatever the intended model is -- it could be numbers, sets, symmetries, operations, whatever -- it has no impact on proof or provability. Secondly, the intended model is generally not 'spatial relations'. For the Peano axioms, for instance, the standard model is Skolem arithmetic. Most mathematical models do not deal with anything so concrete as physical space or numbers.

[Anonymous No.15677755]

>>15677719
incredibly based. you fooled me. i’m a geometer and the other fellow is arguing disingenuously tbqh. your posts are pretty on-the-mark.

[Anonymous No.15677756]

>>15677704
The fact that you're throwing your chips in with this guy >>15677698 proves conclusively that you have zero mathematical background and have been talking out your ass this whole thread. Anyone who has studied mathematics or logic at the university level will know instantly who knows what they're talking about and who's full of shit in this thread. Enough said.

[Anonymous No.15677762]

>>15677755
>i’m a geometer
Lmao. You have never studied geometry in your life.

[Anonymous No.15677763]

>>15672962
>this reads like some asshole on stack overflow except those people do it for free
Excellent simile that brought a smile to my face.

[Anonymous No.15677768]

>>15677719
Not that poster you're replying to but have you ever read anything by LEJ Brouwer?

>>15677739
That poster's point already preempts yours, retard. His entire point is that our conventional symbolic and representational systems exist within our actual experience of reality which is spatial, temporal and linguistic. Any axioms or models we create must originate within experience, however abstract we make them. They ultimately refer back to the practical aspects of our experience like describing spatial manifolds which is the origin of geometry, and they then exist as discourses in language. However abstract they might become with meta-languages about "sets" they originated from and only make sense by referring back to practical experience, aka the description and manipulation of geometrical manifolds.

>>15677756
You're a first year logic student at most. Agreeing with >>15677755
that you are arguing disingenuously. Poorly too.

[Anonymous No.15677770]

>>15677756
>mathematics or logic
teehee. i’d sooner eat my hat than throw these oft-referenced chips in with some asshole-clenching and insufferable logician who is hell-bent on venting his frustration on good faith anons. take the relaxationpill. you’re not the only stem-adjacent faggot on /lit/ and the fact that you think conceptualizations of math are so monolithic is strange. if you’d like to talk about math seriously and without calling me a pseud or a retard 50x i’d love to do that.

[Anonymous No.15677777]

>>15677768
Arithmetic is not about "geometrical manifolds", pseud. You're really not helping your cause (whatever the fuck that is) when you make such elementary mistakes.

[Anonymous No.15677780]

>>15677770
>stem-adjacent
Using the term "STEM" is the hallmark of the pseud.

[Anonymous No.15677783]

>>15677780
so you don’t want to talk about math. got it. BAAAAAASED RETARD!

[Anonymous No.15677786]

>>15677777
Set theory is not about manifolds either. Read before replying, first year.

>>15677770
If he doesn't reply politely to this I strongly advise you to ignore him. He doesn't want real discussion, he wants to snipe at people who know more than him from his very limited base of knowledge and always retreat to that base when questioned.

[Anonymous No.15677795]

>>15677783
With who? You? You have nothing to contribute to the conversation since you've obviously never studied the subject. Maybe if you would actually *listen* to what experts are telling you instead of sperging out and throwing around ungrounded insults, you might actually learn something.

[Anonymous No.15677801]

>>15677795
Half this thread is you repeating 'I don't want to talk to anyone' and calling people pseuds. While being mocked by everybody unanimously for not knowing what you're talking about.

I pity you that you don't know how to have real discussion.

[Anonymous No.15677802]

>>15677786
>Set theory is not about manifolds either. Read before replying, first year.
You literally just said:

>However abstract they might become with meta-languages about "sets" they originated from and only make sense by referring back to practical experience, aka the description and manipulation of geometrical manifolds.

[Anonymous No.15677815]

>>15677801
I'm the only one actually presenting knowledge here. All you do is throw insults at people who have devoted their lives to studying a subject you find too 'boring' to explore. The irony of you pretending to seek 'real discussion' is rich.

[Anonymous No.15677832]

>>15677815
>I'm the only one actually presenting knowledge here.
Says you. Let's take a vote, because according to everybody else, you're a pseud trying to punch way out of his weight class and embarrassing himself.

>devoted their lives
We already established you took a first year logic class.

[Anonymous No.15677837]

>>15677832
Thanks for proving my point. All you have is insults and lies, because you have no understanding of the subject on hand.

[Anonymous No.15677846]

>>15677837
to borrow from your lexicon, “Nice projection, pseud.”

[Anonymous No.15677847]

>>15677837
Have fun bumping your dead thread then. Another poster literally begged you to talk about maths and you declined. Switch to econ or some shit, the math is way easier and you will embarrass yourself less with your wikipedia knowledge.

[Anonymous No.15677850]

>>15677847
Cited without comment.

[Anonymous No.15677860]

>>15677580
I can't believe anyone takes this seriously.
Look at any modern paper in topology for example, then you'll see what a proof is.

[Anonymous No.15677873]

>>15677739
>Geometry and topology beyond the very basics cannot be demonstrated visually.
The principles of geometry and topology (axioms) must first be shown visually in order to be true. All further assertions in both sciences are only true if they are based on these 'demonstrative' principles. Therefore, if they cannot be shown in spatial relations (or be related to these axioms), they're simply not true. Show me at least one theorem in geometry that can't be demonstrated visually.
Inb4 trigonometry because it is an algebraic description of spatial relations and without this correlation it has no meaning. And I'm not even mentioning Non-Euclidean geometries which are all about space.
>https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems
Okay, that makes sense, but are you sure that maths is not "complete" in the same sense as FOL is 'complete"? As far as I understand this, these theorems have no applications outside of maths.
If you say
>FOL is sound and complete
then show us how FOL is complete in Gödel's sense of the word.
>proofs in axiomatic systems operate independently of whatever the intended model is
I'm not talking about proofs, I'm talking about correlation with space. Again, any method of proof can be as abstract as you want it to be and use whatever combination or language of symbols that you want, but it's axioms to which any proof refers to must first of all have a link to spacial relations.
Consider Peano axioms. They all are based on a mathematical notion of equality. The notion of equality itself is based on a notion of quantity. Quantity is basically a spatial relation. So, any assertions inferred from Peano axioms are statements referring to spatial relations.

[Anonymous No.15677875]

>>15677860
All branches of mathematics and logic are based on proof. Some branches, like logic, just happen to feature more rigorous proofs.

[Anonymous No.15677883]

>>15677768
>LEJ Brouwer
No, I haven't. Is he somehow related to this conversation?

[Anonymous No.15677884]

>>15677873
>show us how FOL is complete in Gödel's sense of the word.
Godel did that proof, as well: https://en.wikipedia.org/wiki/G%C3%B6del%27s_completeness_theorem

[Anonymous No.15677910]

>>15677884
Wait-wait-wait, isn't Gödel's completeness theorem saying that in order for any axiomatic (deductive) system to be complete it must be fully expressed in FOL? Then of course FOL is complete.
>A deductive system is called complete if every logically valid formula is the conclusion of some formal deduction, and the completeness theorem for a particular deductive system is the theorem that it is complete in this sense. Thus, in a sense, there is a different completeness theorem for each deductive system. A converse to completeness is soundness, the fact that only logically valid formulas are provable in the deductive system.

[Anonymous No.15677965]

>>15677873
>Consider Peano axioms. They all are based on a mathematical notion of equality.
No, they are based on the concept of succession. The successor operation is the key to understanding how Peano conceptualizes arithmetic. There are a few axioms that define the equality relation, but that is not unique to arithmetic. It is used throughout logic and mathematics in the same way.

>The notion of equality itself is based on a notion of quantity.
No, equality AKA identity is simply the unique relation that holds between any object and itself. In practice, it is used to express that two definite descriptions refer to the same object.

>Quantity is basically a spatial relation.
No, what we understand as 'quantity' represents several distinct relations. The successor relation is one. The part-whole relation is another. The part-whole relation is the closest to what you might call space-like relations. It provides the basis for geometry, topology, and mereology in general. These fields don't require the existence of discrete, distinguishable objects as is required in successor-based fields like arithmetic, number theory, algebra, etc. The latter fields are generally not used to model spatial relations, but map more to our pre-theoretic concepts of counting, etc.

>So, any assertions inferred from Peano axioms are statements referring to spatial relations.
No, again. Peano axioms model a world full of discrete objects that occur in succession. The theory of closed fields would be an example of a better candidate for modelling space.

[Anonymous No.15677971]

>>15677910
>isn't Gödel's completeness theorem saying that in order for any axiomatic (deductive) system to be complete it must be fully expressed in FOL?
No.

[Anonymous No.15677985]

>>15677910
And yes, the original argument was about whether maths is an extension or application of logic. If maths can be expressed in a logical language, it doesn't mean that these are the same thing. If we consider the origin of both sciences then we shall see that logic originated from Aristotle who sought to find language formulas which can induce truth only by virtue of form (hence formal logic). Maths originated from geometry and its axioms are literally based on visual observations. You cannot prove the axiom that you can draw only one line between two points only from these notions themselves— you must first demonstrate it in space.

[Anonymous No.15677990]

>>15677573
>the considered topic is trivial
SOCRATES: The shoemaker, for example, uses a square tool, and a circular tool, and other tools for cutting?
ALCIBIADES: Yes.
SOCRATES: But the tool is not the same as the cutter and user of the tool?
ALCIBIADES: Of course not. ...
SOCRATES: Then what shall we say of the shoemaker? Does he cut with his tools only or with his hands?
ALCIBIADES: With his hands as well.
SOCRATES: He uses his hands too?
ALCIBIADES: Yes. ...
SOCRATES: And does not a man use the whole body?
ALCIBIADES: Certainly.
SOCRATES: And that which uses is different from that which is used?
ALCIBIADES: True.
SOCRATES: Then a man is not the same as his own body?
ALCIBIADES: That is the inference.
SOCRATES: What is he, then?
ALCIBIADES: I cannot say.
SOCRATES: Nay, you can say that he is the user of the body.
ALCIBIADES: Yes.
SOCRATES: And the user of the body is the soul?
ALCIBIADES: Yes, the soul.

If you can't see the non-trivial implications of apparently trivial topics you need to restart from the Greeks

[Anonymous No.15678032]

>>15677965
> It is used throughout logic and mathematics in the same way.
Equality in logic is a different notion than in maths.
> [logical equality] gives the functional value true if both functional arguments have the same logical value, and false if they are different.
>[mathematical equality] is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object.
> In practice, it is used to express that two definite descriptions refer to the same object.
In logical practice, not in the mathematical one. In maths equality is defined as equality of quantities.
> These fields don't require the existence of discrete, distinguishable objects as is required in successor-based fields like arithmetic, number theory, algebra, etc.
That was not my assertion in the first place. I was constantly referring to spatial relations, not concrete spatial objects i.e. bodies.
> Peano axioms model a world full of discrete objects that occur in succession.
Isn't succession a spatial relation? Your language betrays you.

[Anonymous No.15678034]

>>15677985
Mathematics and logic have advanced far beyond their humble origins in antiquity. Generally mathematics is the branch of logic devoted to modelling notions of 'quantity' in some sense. But the line is quite fuzzy. The main criterion used is that 'logic' involves axiom systems in which all truths are demonstrable, and 'math' involves those that are incomplete.

[Anonymous No.15678060]

>>15678034
>Generally mathematics is the branch of logic devoted to modelling notions of 'quantity' in some sense.
Aren't you just mistaking "mathematics in general" for mathematical logic? In that case it doesn't even matter what is an extension of what.

[Anonymous No.15678065]

>>15678032
>Equality in logic is a different notion than in maths.
No, it is not. Equality or Identity is the unique relation that holds between an object and itself. The object need not be a number of quantity. Any well-defined object will do.

>In maths equality is defined as equality of quantities.
No, not all mathematical objects are 'quantities' in any sense. For example, various functions, operations, structures, categories, etc.

>That was not my assertion in the first place. I was constantly referring to spatial relations, not concrete spatial objects i.e. bodies.
The point is, not all fields of mathematics are used to model space-like objects. Most, in fact, do not. Like number theory.

>Isn't succession a spatial relation?
No.

[Anonymous No.15678068]

>>15678060
>Aren't you just mistaking "mathematics in general" for mathematical logic?
No, *all* of mathematics -- arithmetic, geometry, topology, algebra, analysis.

[Anonymous No.15678069]

>>15672871
>explain yourselves!!1!
Burden of proof threads should be banned

[Anonymous No.15678117]

>>15678065
>Equality or Identity is the unique relation that holds between an object and itself. The object need not be a number of quantity. Any well-defined object will do.
Then your definition of equality is just more general than that of maths. Maths occupies itself with quantities, you just can't deny that.
>not all mathematical objects are 'quantities' in any sense. For example, various functions, operations, structures, categories, etc.
Because these are relations of quantities, no? No function has any use if it has no input.
>The point is, not all fields of mathematics are used to model space-like objects.
The point is, all mathematical objects have something to do with spatial relations. And logic isn't. Logic is concerned with the automatisation of expressing truth.
I don't mean to say that all mathematical objects are bodies. But they describe the world of bodies. Otherwise what is the appliance of maths, what is its use? To solve brilliant problems and receive prizes?
>No.
Well, it seems to me quite spatial. What is a succession? An act of following in sequence. What is a sequence? A set of things next to each other in a set order; a series. What is an order? If you haven't already noticed, all these notions are primarily spatial relations.

[Anonymous No.15678205]

>>15677875
You're not getting the point, dude.
It's not a question of rigorousness. These papers are just trivial. A freshman could think them up, perhaps a bright elementary school student even.
Proofs in mathematics require far more than this thing people seem to defend here and you need to learn far more learning to be able to pull them off.
Shit, I thought better of this board. Turns out it's just humanities people unable to get into more complex rigorous systems.

[Anonymous No.15678207]

>>15678117
>Then your definition of equality is just more general than that of maths. Maths occupies itself with quantities, you just can't deny that.
Mathematics is a lot more abstract then you may think. Structures can be identical, for example. Most mathematicians deal with abstractions far removed from concrete quantities.

>Because these are relations of quantities, no? No function has any use if it has no input.
A function can be a function of other functions. An operation can apply to rotations or abstract substitutions. Every object no matter how abstract must be given identity conditions in order for it to be an well-defined object.

>The point is, all mathematical objects have something to do with spatial relations.
The vast majority of mathematical objects have absolutely nothing to do with spatial relations.

>And logic isn't.
Not quite. Logic includes mereology which can be used to model spatial relations.

>Logic is concerned with the automatisation of expressing truth.
Not sure what you mean there. Logic involves rules of inference that preserve truth from step to step. But so does mathematics.

>I don't mean to say that all mathematical objects are bodies. But they describe the world of bodies. Otherwise what is the appliance of maths, what is its use? To solve brilliant problems and receive prizes?
That's how the mathematicians themselves see it, apart from the applied mathematicians. They are generally interested in mathematical truth in itself.

>Well, it seems to me quite spatial. What is a succession? An act of following in sequence. What is a sequence? A set of things next to each other in a set order; a series. What is an order? If you haven't already noticed, all these notions are primarily spatial relations.
That's not really how space as we know it works, though. There is not one thing, then the next thing. There is a continuous field of spatial coordinates with no distinct objects at all. Indeed, Euclidean geometry can be modeled without sets, let alone numbers. See:

https://en.wikipedia.org/wiki/Tarski%27s_axioms

That models fairly completely our intuitive understanding of physical space, yet there is nothing resembling a successor function. Just parts and wholes and spatial relations like 'betweenness' and 'congruence'.

[Anonymous No.15678213]

>>15678205
Stop pretending you read the book based on a screenshot of a partial page you don't even understand.

[Anonymous No.15678358]

>>15678207
> Most mathematicians deal with abstractions far removed from concrete quantities.
Yeah, definitely, because they deal with abstract quantities. Maths doesn't deal with two apples, it deals with "two".
>A function can be a function of other functions.
Well, some function better has some numbers or other kind of input in it lest it turns into an infinite regression.
>The vast majority of mathematical objects have absolutely nothing to do with spatial relations.
I think, we have a major misunderstanding here. See, our faculty of representation of any object is inherently spatial. And when I say 'spatial' I don't necessarily mean our concrete spatial world. I refer to a spatial form in which is tend to represent anything. We even represent time in space (look at a clock). And that goes maths as well. When I say "2 + 2 = 4", I don't imagine myself two concrete objects, say, apples. But I do imagine two WITH two. And that 'with' is a word designating a representation of a spatial relation. When I say A = A I JUXTAPOSE two objects. And juxtaposition is a spatial relation. Our whole faculty of representation is spatial and temporal.
> Logic involves rules of inference that preserve truth from step to step. But so does mathematics.
And which rules of inference did maths formulate? Why there is even a difference between the two?
Mathematical inferences do preserve truth, but do not produce the rules of truth preservation.
>That's how the mathematicians themselves see it, apart from the applied mathematicians.
We aren't concerned with psychology here. Why then maths is even considered science if it doesn't necessarily correlates with reality? How is it different from astrology then? Why do we call a mathematical truth 'truth' and not just mathematical non-contradiction?
>That's not really how space as we know it works, though. There is not one thing, then the next thing. There is a continuous field of spatial coordinates with no distinct objects at all.
And coordinate isn't an object? What is even the purpose of your argument if you still refer to spatial relations? Everything which finds itself in a continuous field is spatially related i.e. you can get from one coordinate to another.

[Anonymous No.15678375]

>>15678213

[Anonymous No.15678415]

>>15678358
>And which rules of inference did maths formulate? Why there is even a difference between the two?
E.g., mathematical induction.

>And coordinate isn't an object?
See Tarski's axioms. You don't need points. But even if you use points, there is no such thing as a successor since the field is continuous.

[Anonymous No.15678419]

Is this what passes as modern day "philosophy"? Absolute brainlet takes using trivial babbie tier logic you'd learn in the first 10 minutes of any logic class.

[Anonymous No.15678430]

>>15678419
I thought you were done posting in this thread?

[Anonymous No.15678435]

>>15678430
That was my first post ITT lmao, just came over from /sci/ looking for laughs. This board never disappoints.

[Anonymous No.15678439]

>>15678435
Nobody believes you. You tell the same lie over and over again.

[Anonymous No.15678442]

>>15678439
Take your meds schizo

[Anonymous No.15678451]

>>15678442
You literally are a schizo. You go into random threads with the sole purpose of disrupting them with obvious falsehoods and abuse. There is something seriously fucked up in your brain.

[Anonymous No.15678463]

all this logic hurts my head