Math applied to philosophy

[Anonymous No.14804793]

Was there any moder attempt to tackle a philosophical problem using rigorous mathematical theories?
Something like using Set Theory to prove ontological statement from certain suppositions.
If I remember correctly from high school, Spinoza tried something similar, but Math at the times was far from rigorous.

[Anonymous No.14804806]

>>14804793
Wittgenstein's 'Tractatus Logico-Philosophicus'.

[Anonymous No.14804865]

>>14804793
What do you mean by rigorous mathematical theories? If it's just logical rigor there have been plenty of attempts but they all failed either because you either front load your definitions with what you want to prove or logic is not able to get the results you want.

[Anonymous No.14804874]

>>14804793
One of my engineering lecturers said earlier this week:
>If you can't put numbers to it, you're a philosopher
>~Small pause~
>And we all know another name for one of those
Well I don't so w-what did he mean by that?

[Anonymous No.14804877]

[Anonymous No.14804923]

>>14804865
I was talking about that frontloading of definitions, possibly related to an axiomatic system. From the little philosophy I encountered, logical rigour alone can fail due to what is lost in translation between thought and loosely defined words

[Anonymous No.14804934]

>>14804793
Carnap - The Logical Structure of the World (1928)
Goodman - The Structure of Appearance (1951)

[Anonymous No.14804945]

>>14804874
Your engineering lecturer is an ignoramus.

[Anonymous No.14805408]

Freges "Begriffsschrift" was the prototype theory of an ideal language. Check Carnaps works, too.

[Anonymous No.14805415]

>>14804945
>>>14804874
>Your engineering lecturer is an ignoramus.

A typical STEMtard, yup.

[Anonymous No.14805421]

check out zalamea

[Anonymous No.14805430]

>>14804793
>want to do philosophy but am too brainlet for math
literature for this?
hard mode: nothing french

[Anonymous No.14805470]

>>14804793
Philosophy is not a science and will never be a science. Philosophy only clarifies concepts. Mathematics is not equipped to clarify concepts, since it does not work analytically but synthetically and since it does not process real experience but only numbers... Mathematics is necessary for the development of any science but philosophy is not and cannot be its territory.
In short, mathematics cannot be "applied" to philosophy.

[Anonymous No.14805479]

>>14805470
Wrong.

[Anonymous No.14805518]

>>14805470
Math is as analytic as it gets. All true mathematical statements are tautological.

[Anonymous No.14805554]

>>14805518
How? Mathematical formulae describe combination. They can do this because there are set rules for this combination and division. But explain to me how you are going to use mathematics to analyze anything, hmm? You only use mathematics after you have performed analysis (i.e. broken down an experience into simple elements which are then reduced to quantities).

[Anonymous No.14805581]

>>14805554
I don't know what that definition of analysis you're using is but the analytic/synthetic distinction you alluded to in the previous post is straight from Kant and Kant was very clear that mathematics was analytic a priori

[Anonymous No.14805601]

>>14804793
>tackle a philosophical problem using rigorous mathematical theories?
The term you're looking for is "Analytic Philosophy".
https://www.youtube.com/watch?v=w0UswnFUL8E

[Anonymous No.14805633]

>>14804793
Turns out to be the wrong approach entirely

[Anonymous No.14805644]

>>14805581
Kant thought mathematics was synthetic a priori

[Anonymous No.14805677]

>>14804874
Bro engineers are tards

[Anonymous No.14805697]

>>14805581
please read critique of pure reason before talking about kant

>>14805644
this

[Anonymous No.14805712]

>>14805697
1=1 is that synthetic? Is it a mathematical statement?

[Anonymous No.14805770]

>>14805712
Depends if you can prove arithmetic from first principles.

[Anonymous No.14805786]

>>14805770
If 1=1 is not analytic wtf is?

[Anonymous No.14805813]

>>14805786
I'm messing with you anon, obviously 1=1 is a tautology, but mathematics is always seeking higher levels of rigor, so you want to prove the system for describing the numbers is sound before actually doing anything with them. This is the difference between higher mathematics and the math you were forced to do in high school.

[Anonymous No.14805836]

>>14805712
The difference between mathematics and logic is that mathematics has an ontology -- that is, it requires the existence of sets, or numbers, etc. The rules of logic do not require the existence of anything.

[Anonymous No.14805844]

>>14805786
1=1 doesn't involve any combination. But its also not really an analysis, is it? The concept is not broken down into its constituent parts--its just a statement of equality. A number is used in the statement, but is anything added to it? No. Is anything inspected in it (i.e analyzed)? No. Is anything really asserted? No. We simply notice that does not contradict itself. If the statement were 1=2 you would not go about trying to show that it is false--instead, you could only assert that it is contradictory according to what is meant by equality.

[Anonymous No.14805850]

>>14805836
No you don't get what math is about. You define sets or numbers to be whatever you want and those are the axioms there is no ontology to it. Unless you believe anything we imagine has some type of ontological existence like Meinong.

[Anonymous No.14805861]

>>14805844
This is the exact definition of analytic the truth of the statement being evaluated only through it's parts relations to each other.

[Anonymous No.14805867]

>>14804865
sad smol bwainer can't wuse wogic womp womp

[Anonymous No.14805888]

>>14805844
“The analytic/synthetic distinction” refers to a distinction between two kinds of truth. Synthetic truths are true both because of what they mean and because of the way the world is, whereas analytic truths are true in virtue of meaning alone. “Snow is white,” for example, is synthetic, because it is true partly because of what it means and partly because snow has a certain color. “All bachelors are unmarried,” by contrast, is often claimed to be true regardless of the way the world is; it is “true in virtue of meaning,” or analytic.

[Anonymous No.14805903]

>>14804793
I saw >>14804923, and it makes me think what you are saying is "geometrical", not mathematical.
right now methods of mathematics is enormously vast you can say every method mathematical. but when philosophy says it is "geometrical", it must be involved with axioms, definitions, and theorems.

if this is correct, then Frege's Begriffsschrift will be the case.
Frege failed to do that because that one paradox, so Whitehead and Russell made another one, called Principia Mathematica.
the co-author Whitehead quite changed his mind on this "geometrical method". He wrote some criticism(or lament) on this. Philosophers now don't believe this is possible at all, which would also be an answer to why they think so.

>The other form of overstatement consists in a false estimate of logical procedure in respect to certainty, and in respect to premises. Philosophy has been haunted by the unfortunate notion that its method is dogmatically to indicate premises which are severally clear, distinct, and certain; and to erect upon those premises a deductive system of thought.
>But the accurate expression of the final generalities is the goal of discussion and not its origin. Philosophy has been misled by the example of mathematics; and even in mathematics the statement of the ultimate logical principles is beset with difficulties, as yet insuperable. 3 The verification of a rationalistic scheme is to be sought in its general success, and not in the peculiar certainty, or initial clarity, of its first principles. In this connection the misuse of the ex absurdo argument has to be noted; much philosophical reasoning is vitiated by it. The only logical conclusion to be drawn, when a contradiction issues from a train of reasoning, is that at least one of the premises involved in the inference is false.

[Anonymous No.14805924]

>>14805861
>>14805888
Analyze means to "break apart" or to dissect. How is the subject dissected or inspected in "1=1"?
It is obvious that "All bachelors are unmarried" involves an inspection--one "looks inside" the concept and sees which predicates make it possible *as a concept* (without reference to experience). But in the statement "All bachelors are bachelors" i.e "1=1" nothing is analyzed--isn't it so? How is a tautological statement analytic, then?

[Anonymous No.14805929]

>>14805850
>there is no ontology to it
Wrong. If that were true, you couldn't prove within set theory the existence of a set with such-and-such properties because there are no sets to begin with. Read the axioms.

[Anonymous No.14805955]

>>14805924
Tautological statements are analytic because you don't need know anything about anything outside the statement to know they are true.

A tautology is a special case of what we might call analytic statements. These are statements that are true solely in virtue of their meaning. Here are some examples:

A bachelor is an unmarried man.
Anything that is large is not small.
Nothing that is running is still.

If a statement is analytic, then its truth depends solely on its meaning and not on any other empirical fact. Note that all tautologies are analytic truths, but not vice versa. A tautolgical sentence is a sentence that is true in virtue of the meaning of the logical words in the sentence. An analytic sentence is a sentence that is true in virtue of the meaning of the words in the sentence. The three examples above are analytic truths but not tautologies. Why? Take the first example, it is true because "bachelor" has the same meaning as "unmarried man", but the word "bachelor" is not a logical word. Unlike words like "and", "or", "if then", "not", it does not describe any logical connections.

[Anonymous No.14805964]

>>14805929
You ASSUME the existence of certain sets from the axioms. If you don't accept the axioms you don't accept the existence of those sets see axiom of infinity in ZFC.

[Anonymous No.14806026]

>>14805955
But I'm asking you to consider the meaning of the word "analysis."
If I have an object before me and I begin to inspect it, then obviously I am analyzing the object, i.e., breaking it down into parts, looking for characteristics, and so forth. But if I merely look at the object, have I analyzed it? Clearly not. Now if I look at any non-tautological statement like the one's you mentioned, one can say that i am inspecting some concept, looking at its parts and characteristics. It does not occur to me to say during inspection that it is "true" that some concept has this definition. What does it mean to say that it is "true" that a bachelor is an unmarried man? How can it be appropriate for me to say that it is true that i am looking at what I am looking at? I am merely recounting a definition--that is all, nothing true or false about it.

Now tell me, does any analysis take place in a tautological statement? Does any verification take place in a tautological statement? If to both questions you answer no (which would be correct) why in the world should I call a tautological statement analytically true?

[Anonymous No.14806063]

>>14806026
You're arguing against Kant's definition of analytic. Using your definition of analysis and your stating that philosophy uses analysis how can anything be true in philosophy? Or rather if you don't think you can say that it is "true" that a bachelor is an unmarried man can you at least say it's not false?

[Anonymous No.14806112]

>>14804793
https://culture.vg/features/art-theory/on-set-theory-and-the-bastardization-process.html

Set theory applied to art demonstrating that videogames are the greatest artform ever, and that art is videogames.

[Anonymous No.14806201]

>>14806063
I was not quite clear in my previous post--let me clarify. I take it that there is analysis in experience, for instance, when I come upon a new object, or when I think upon my experiences. Now in these cases I really create a definition, based on the object I have come across, that is to say that I take an object as a unity and bring characteristics or predicates under its concept, or I continue the process of revising my knowledge. In other words I analyze an object (not a concept). Truth in this context is the agreement of my concept with the object, not the predicates of a concept with the concept (impossible, since the concept is nothing but a name under which I have brought characteristics). If I analyze the concept itself I can do nothing but look at the concepts under it--now what can I say as for truth except that it is really the case that certain concepts really are under a certain concept? To say then that "All bachelors are unmarried" is "true" as an analytically a priori statement is to say that it is true that the definition of a concept is what it is. To say that it is "false" that "All bachelors are married" is to say that it contradicts the statement "All bachelors are unmarried"--but which is actually the case? It depends on whether I have designated bachelors as married or unmarried. How else can we look at the issue? If I say that "all bachelors are married" is logically true, this is just to say that it does not contain any contradictions--but how should I know this without referring to the definition itself? And then I am merely comparing a defining statement with my (current) definition...

[Anonymous No.14806202]

>>14805964
>You ASSUME the existence of certain sets from the axioms.
What the fuck did I just say?

[Anonymous No.14806238]

>>14806201
And again this is what math is about. You take whatever definitions and axioms you want and then work out the consequences. When something is false in math it means it contradicts the axioms and definitions.

And as far as truth being agreement of concept with the object we are obviously not talking about some specific bachelor out in the world just from the qualifier all.

[Anonymous No.14806250]

>>14806202
But assuming the existence of something isn't ontology. If pigs fly it would rain shit is an analytic statement that makes no ontological assumptions. If the ZFC axioms are true the rest of set theory and modern math follows

[Anonymous No.14806254]

>>14804793
There have been attempts, but since it's a retarded fucking idea all have failed. Miserably.

[Anonymous No.14806272]

>>14805518
>All true mathematical statements are tautological.
Actual retard detected.

[Anonymous No.14806293]

>>14805518
No. Theyre synthetic, there is an intuition to them. Read Kant and Euclid.

[Anonymous No.14806315]

>>14806272
Tautological means true in all possible worlds. If you can show a mathematical statement is not tautological that means you can potentially come up with a counterexample. Common freshman error is to confuse circular reasoning with tautology.

[Anonymous No.14806335]

>>14806293
There is an intuition towards the axioms which is why they are half way understandable and not alien gibberish. But math is not choosing the axioms it's the logical consequences of those axioms. If I enter a room I am not outside is an analytic statement and in the same way if whatever axiomatic system you want is true then the mathematical consequences of that system are also true. Finding those consequences is math.

[Anonymous No.14806391]

>>14806315
That's not what tautological means.

[Anonymous No.14806419]

>>14806391
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". A less abstract example is "The ball is all green, or the ball is not all green". This is true regardless of the color of the ball.

As I mentioned tautology is sometimes confused with circular reasoning or a vacuous statement but when talking about math or philosophy at least the above is the accepted definition.

[Anonymous No.14806472]

>>14806419
Theres a wide difference between any possible interpretation and every possible universe, freshman. We presuppose bivalent truth. Specifically in math, in any sophomore proofs course you cover the law of the excluded middle. So it will be obvious to any non freshman that saying (P v -P) is not true in all possible universes, but in all universes where it's true (a tautology!).

It is completely plausible and valid to have a kind of Bayesian logic that allows for probabilities rather than truths or falsehoods.

A tautology is more or less a statement which collapses immediately into the assumptions of your logical system. But it's on a per basis and cant be defined for all possible systems.

[Anonymous No.14806489]

>>14806472
Again you're not arguing with me you're arguing with modern logic that definition is the first line of the wikipedia article. You're definition is highly subjective and it's confusing how it could be applied to any mathematical statement.

[Anonymous No.14806507]

>>14806472
And you seem to be confused on what a universe is or what an interpretation is. The universes would all share the same logic if they didn't they would not be a possible world for an interpretation. Only the variables differ in the different worlds in one variable A is a cat and the other A is a dog.

[Anonymous No.14806532]

>>14806489
Imagine basing your entire argument on the first line of a wikipedia article. That's weak buddy.

You clearly haven't studied much logic. That's fine. The point is you're assuming certain things about logic as necessarily true in all systems which aren't. There is no reason (P v -P) must be true in every possible logic.

It's fine to define tautology only in terms of bivalent systems, but be aware that's what you're doing.

[Anonymous No.14806537]

>>14806507
>The universes would all share the same logic if they didn't they would not be a possible world for an interpretation.
Big fat wrong. You see assumptions as necessarily true when they aren't. Logic is axiomatic, freshman. You've simply asserted not necessary principles as necessary and claimed their universality.

[Anonymous No.14806565]

>>14806532
You're using possible without realizing it has specific meaning too. Possible world means possible according to your rules of logic if you assume the excluded middle no possible world for an interpretation can have that the excluded middle is false.

Wittgenstein in the Tractatus :
>4.4.6 Among the possible groups of truth-conditions there are two extreme cases. In one of these cases the proposition is true for all the truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.

[Anonymous No.14806589]

>>14806565
Yikes, citing the first line of wikipedia then citing Wittgenstein.

>Possible world means possible according to your rules of logic if you assume the excluded middle no possible world for an interpretation can have that the excluded middle is false.

Right, so your definition of tautology is a tautology and is therefore worthless. "Its true in all possible worlds", okay, which worlds? Ones with a specific assumption that actually structures what tautology means!

Your definition only works when the listener already accepts you're only permitting worlds wherein the LEM holds, and you're just glossing over that huge piece of information like it's nothing. You'd make a terrible logic teacher.

[Anonymous No.14806617]

>>14806589
My definition is the definition used in logic and math. Your definition is someone who misunderstand tautology to "and is therefore worthless". And you're exactly correct about the worlds under question namely in math only those worlds where the assumed axioms are true.

Discrete Math with Applications 4th Edition Susanna E. Epp pg. 34
>A tautology is a statement form that is always true regardless of the truth values of
the individual statements substituted for its statement variables. A statement whose
form is a tautology is a tautological statement.

[Anonymous No.14806642]

>>14804945
>>14805415
>>14805677
midwits COPE

[Anonymous No.14806671]

>>14805518
>>14805554
>>14806272
>>14806315
>>14806391
>>14806419
>>14806472
>>14806489
Imagine wasting your life """thinking""" about if math is """tautological""" or not. Get a life autists

[Anonymous No.14806740]

>>14806671
imagine wasting your friday night on 4chan. what a loser!

[Anonymous No.14806785]

>>14806740
I'm in austraila retard LMAO cringe loser spending his friday night on 4chan not even socializing with other midwits

[Anonymous No.14807129]

>>14806250
The point is that the axioms of set theory (or arithmetic) make existence claims. The rules of first-order logic do not.

[Anonymous No.14808468]

>>14806642
Engineers are the biggest midwits of all degrees

[Anonymous No.14808689]

>>14806617
How many times do I have to repeat that your definition used "in all possible worlds" you retarded faggot?

[Anonymous No.14808983]

>>14804874
Philosophy major here
I officially certify your teacher as based

[Anonymous No.14808996]

>>14806254
>Using an extremely precise and aseptic language to describe reality to reach meaningfull conclusions
>Retarded
Without going if it was sucessfull or not the idea, in itself, is anything but retarded.

[Anonymous No.14809363]

>>14804877
What’s wrong with this?

[Anonymous No.14809396]

>>14804877
that's funny

[Anonymous No.14809402]

>>14804877
to be fair men build cities to make women even more comfortable and have an easy life with easy casual sex.

[Anonymous No.14809427]

>>14805903
>The only logical conclusion to be drawn, when a contradiction issues from a train of reasoning, is that at least one of the premises involved in the inference is false.
i love how rationalists cling to this one. the best part is that they cannot deduce it and it makes them mad

[Anonymous No.14810161]

>>14808996
Man, if only I could move rocks with my mind! Let's try and figure out how!

[Anonymous No.14810196]

>>14808996
>>Using an extremely precise and aseptic language to describe reality to reach meaningfull conclusions
This is science, not philosophy