Humanities -> Philosophy -> Analytic Philosophy ->

Nice logical fallacy ;)

>>896247
wink
Also we're about 70fags from /sci/g/lit/
it's fun.

>>896260
>70
You are really fags
I'll stop by
[email protected]

Pretty interested desu

[email protected]

History of logic when

>>896284
>>896301
kewl
>>896323
that's a good idea m8eight

Okay.

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yo OP we got too much people in the slack group we should probably stop recruiting

>>896502
Just accounting for the inevitable number of users that go inactive over time in any online group.

>>896236
Sounds interesting
[email protected]

>>896559
>>896487
sent ;)

Can't wait until you guys eventually just reach the understanding of the Continentals with your logic.

>>896612
>understandings
>continental
I see a paradox here.

>>896618
For now you do.

>>896644
triggered by the intellectual smugness

>>896644
continental philosophy is just prose poetry really.
just aesthetics, nothing else.

>>896683
It's the end conclusion of logic as seen by individuals who do not need logic to reach it, hence the poetic style.

>>896696
>seen by individuals who do not need logic to reach it
Exactly, no logic, just emotions.

>>896702
Sure. But logic will reach the same conclusions eventually, so they are equally valid. Logicians are just slower at it.

>>896710
No, they wont reach the same conclusion.
They never have.

>>896718
They have and will continue to, but you're right, there's a point where they will branch off.

>>896738
name just one truth/knowledge continental philosophy produced.
What? you can't name? THAAHAAHAH

>>896696
Very elegant description of continental philosophy.

Kinda just repeating you here, but I'd add that Continental philosophers see complex logical patterns almost innately, and so extrapolate the consequences of these patterns on a level that most people can't follow directly.

Instead of spelling out A1->B1->C1.....->Z1 and A2->B2->C2...->Z2 they just say "So there's Z1 and Z2, and together they make A3."

>>896744
Nietzsche: Okay guys, so the Death of God is gonna lead to a collapse of the western worldview which will cause it to meander around with no direction. The West is eventually going to need to replace this with a new metaphysical or teleological outlook to revive its drive.

Analytics/Positivists: You didn't justify any of your beliefs with our own subjective method of attaining "truth." Therefore it is just wishy-washy bullshit. Checkmate, Continentals.

The Analytic/scientific worldview is on the cusp of a major paradigm shift bro. They hold a great deal of power that was built of off the enlightenment, industrial revolution and scientific advancement, but their inability to create a worldview/telos for society is becoming more and more of an issue. Continental/romantic thought is about to revive. There is no winner in this battle, its never ending pendulum

>>896236
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logic -> ¬faggy

>>896786

It's a tragedy worthy of the Greek poets.

You have an entire generation thirsting for some sort of meaning or drive: it's just normal and expected that once you get a teenage brain and can analyze the world in even crudely critical fashion you get an extenstial crisis. Western culture is in panic, swinging from trend to trend, distracting itself with entertainment, and unable to even gather the will to fight it's enemies anymore.

And what do the philosophers, those that are tasked with making sense of the world, and finding the unifying goal do? They sit around tinkering with grammatical nonsense about how "The current king of France is bald" doesn't make sense

>>896744
>name just one truth/knowledge continental philosophy produced.
name just one truth/knowledge analytical philosophy produced.

>>898425
Whether the current king of France is bold or not is an important question, since the answer yes will bring forth an ontological commitment, whilst the negative likewise; Russell opposed this dichtomy. If you however do not analyse the sentence you will end up with non-existent real entites, and a metaphysics akin to Platonism, Meinong, idealism or transcendental idealism; if such a realm exists, and if it is indeed transcendent, it can only be proved from analytic considerations of metaphysics, and thus straying away from Comte's historiography, becoming subsequently opposed to logical positivism and ultimately scientism.
If you cannot see the impact this sentence has, you are fooling yourself.

>>898503
Logical positivism is debunked and is for autists only.

Kant master race.

>>898503
>>If you cannot see the impact this sentence has, you are fooling yourself.
as long as you cling to your fantasy that there a some speculations which are more relevant than others.
Talking about this sentence shows already that you think that it is worth discussing, because there is something important about it, more important than what you feel and than your other inferences, but you are not even able to say why.

The first step of any rationalist is really to justify why he cannot stay away from his abstractions, why he thinks that his statements, formal or not, are relevant to his life, in connecting him to some reality which goes always beyond of what he is conscious. To any rationalist, What he is conscious of is never enough and he does not even know why.

>>898320
>>898380
ingore the continentalcucks and welcome

>there are people ITT who think continental philosophy is relevant to reality
>it's literally pedantic poetry

It's like saying natural science should be done without mathematics

Analytics only deal with 3% of what continentals deal with.

>>899139
>>898956
>>898521
>>898520
You're all disgusting.
Science is the only discipline that created knowledge and dispelled almost all of philosophy.
Philosophy is by definition sophistry.

>>896236
[email protected]

have these lot even added anyone yet?

>>899565
I sent invs to all itt.
Wanna logic with us bby

>>896236
[email protected]

hey fag no one cares

>>900635
sexual orientation is a social construct.

>>899336
Nice bait

How do I show something is a model when it has infinite theorems.

>>901211
You don't?
If it has infinite theorems then it's not a model

>>901870
Then we just "add" theorems to our axiomatic systems while we find them?

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Got into a argument about something stupid about games with my brother and he pulls a burden of evidence facially,cheeky cunt! Will Hurley's intro to logic get the job done of are there shorter condensed books that do a better job?

>>902130
Those fallacies are not seen in a formal logic course. They are mostly just rule of thumbs for debating that people overuse to win shitty debate competitions, or show how niggers are subhuman.

[email protected]

Reminder that logic is not meant to prove existence, but only to formalize the various reasonings.

>>902337
And what about existential quantifieres?
Checkmate atheist.

>>901894
That's not how it works. A formal system is characterized by a finite set of axioms, and its theorems are defined to be the set of sentences constructable from finite sequences of deductions from those finite set of axioms, so a formal system has finitely many theorems by definition. If you want a formal system with infinitely many theorems you'll have to start out with infinitely many axioms, which will make the system inconsistent.

>>902993
I get that part, but what is then an example of a formalized axiomatic system that we use daily in mathematics? Considering we can construct the naturals in many of them, we could prove infinite theorems even if they're pointless.

>>896236
[email protected]

[email protected]

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>>903155
>>I get that part, but what is then an example of a formalized axiomatic system that we use daily in mathematics?
typically, ZF.

intuitionist type theory is a formalization of kant's doctrine

"Analytic and Synthetic Judgements in Type Theory", 1994
https://michaelt.github.io/martin-lof.html

and is used for computers
same thing with one formalization of Hegel's doctrine at nlab, which is in infancy.


The whole point is that mathematics is to formalize your concept one degree further than what you have in natural languages.
The typical concepts that people choose to love is the one of sets and numbers.

You have several degree of formalization, beyond the natural language, where you can cling to the notion of constructibility, or you can go fairly wild, wrt to constructibility, in adding axioms that you like.

The typical work of the theoretical scientist, who loves to mathematize anything he thinks of, is the one of inventing statements which deliver, once they apply they favorite rules of deduction, the concepts, the formal statements that they want.

Their task is also to continue to apply their favorite rules of deductions to the initial concepts and see what they can deduce form these.

so you have both ways:
-start with some concepts
-formalize these concepts
-invent new concepts which from which you can get the initial concepts
-deduce invent the theorems that you can get form your initial concepts

you can even mix the reasoning of deduction with the one of induction and formalize both.

>>903165
>>903223
check your electronic mail

>>902993
>so a formal system has finitely many theorems by definition. If you want a formal system with infinitely many theorems you'll have to start out with infinitely many axioms, which will make the system inconsistent.
be careful with the axiom schemes, which are justly an infinite amount of axioms disguised as one finite statement

>>902993
No, this is totally bullshit.
>A formal system is characterized by a finite set of axioms,
This is true in most cases but there are formal systems which define an infinite set of axioms recursively/inductively. But since the most pivotal proofs of arithmetic is provable with a finite number of axioms, such is usually the case.
> so a formal system has finitely many theorems by definition.
This doesn't follow, most formal systems actually do have a infinite numbers of theorems.
An example in mathematics would be:
2|6, 3|9, 4|12, etc.
Even though these theorems are possible to define by one theorem, all of the singular cases have their own theorems as well.
Even propositional logic has an infinite amount of theorems:
Take an arbitrary true theorem, name it P. Add P∧-P
Let the newly created theorem be the arbitrary P and restart the process. Thus you've created a consistent infinite amount of theorems.
The problem is indeed with the cardinality, but it is the other way around. In predicate logic we have a too small cardinality on our infinite theorems following from our deductive system.
The unprovable theorems are uncountably many and them provable theorems are only countably many, if I remember correctly.
>>903155
Most of modern mathematics is very pedantic, and I see several occasions where they directly refer to predicate logic etc. It is very useful since instead of referring implicitly to an argument it could be used to state it explicitly.
>>898521
>Talking about this sentence shows already that you think that it is worth discussing
Yes, this is my standpoint.
I didn't refer to anything in regards to the content of the sentence but rather its historical impact on different schools of thought, and thus, it has an importance merely from observing the consequences from discussing it.
If I am not allowed to argue the stance I take, and you infer from it some kind of performativ paradox or intellectual dishonesty, you've ruined any debate.

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>>896236
I'll give you a list of books to start with:
The Logic Manual by Volker Halbach, it is possible to find lecture slides on the internet.
http://logicmanual.philosophy.ox.ac.uk/
As an example.

Computability and Logic by Boolos, Burgess and Jeffrey.
The first part is the Turing proof of incompleteness, the second the more in depth (but not completely) Gödel incompleteness' proofs.
I recommend this book heavily, even though it can be very hard to get through. It is also possible to acquire without monetary exchange.

Greg Restall has a Vimeo channel which well accompanies the harder chapters of this book.
I would start watching them somewhere around this one:
Advanced Logic §8.1 Decidability: Deductively Defined Theories

For Modal Logic:
Modal Logic for Open Minds by Johan van Benthem.
Do the exercises and get through it.
I wouldn't recommend to go through all the applications of modal logic, but going through Deontic, intuitionistic, games, and provability logic is useful.
>>903230
>intuitionist type theory is a formalization of kant's doctrine
Could you give me an actual source on this, as a quote.
Since intutionistic logic is mostly defined by two aspects:
Having to provide an example, such as constructing a new prime instead of saying that "There exists a prime".
And claiming that --P<-/->P a priori (they disregard the principle of the excluded middle).

>>903262
Sorry, I meant P∨-P.

>>903282
Thanks for the recs meight.
So far wer're in entry level (posted in OP) thought.
When time comes we'll take into consideration your recs thenxks

>>903290
These are undergrad books. You can start with The Logic Manual.

>>903235
>be careful with the axiom schemes, which are justly an infinite amount of axioms disguised as one finite statement

Who brainwashed you into stupid things?
Have you ever heard about the forms?
Read a book.

>>902397
>>902337
Exactly, formal systems, mathematics included are the minecraft of intellectualism.

>>900389
>>899352
>>902174
>>903271
50 sent.

What's more rigorous than a formal system?

>>906595
Inductive reasoning is what creates formal systems.

>>896236
Is there any reason to get into Aristotles logic rather than reading a modern logic text?

>>908401
Only for historical/aesthetic/cultural gains.
It's like asking to read Pythagorean mathematics instead of modern math.

>>908401
No, not really. Aristotelian logic has already been incorporated into modern logic.

However, if by 'modern logic' you mean 'symbolic logic', and 'Aristotelian logic' means 'term logic' then Aristotelian logic might still have some use to train your reasoning in a non-autistic way.

>>908490
>Aristotelian logic has already been incorporated into modern logic.
And improved by modern logic too. Forgot to say that.

>>908490
>>908413
Thanks thanks, this saves some time.

>>908623
I am not >>908492
But it could be useful, or fun, to pick up secondary literature on the history of logic.
If you only study analytic logic you might wind up in the trap of becoming the douchebag analytic philosopher meme. There are viable and important systems which is contradictory to our formal logic (phenomenology to some part even though Brentano is the major hero of analytic philosophy of mind, Hegelianism, Kantianism etc.)
Also, as inductive reasoning is generally not applicable to formal logic it could be useful to see the attempts to formalise scientific reasoning (I do believe they largely failed as I side with Goodman).

Basically: the formal logic you will be taught isn't the only way to philosophise and having a general idea of what other people are doing is a good thing. Try looking up some secondary literature at least (some kind of summary), or keep an open mind.

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I saw these threads before, but I think my body is finally ready

>>896236
[email protected]

>>909454
>>909485
'vited
>>905144
>that's a bad thing
Although they aren't, that would be number theory
;)

Is the discipline of logic the purest form of rigor?

>>899336
Science is philosophy you mongoloid.

>>910251
WOMEN ARE MEN YOU MONGOLOIDS (except the "arbitrary" differences they have which I don't consider important)

>>910266
>Women are men

No, they aren't. But this clearly isn't relevant.

>>910299
APPLES ARE SHOES (except the way they are different)

seems interesting

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hi, I dropped logic after first year at uni but this seems neat, ty

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>>908641
Yes. What would be the most efficient way to go about digging deeply into kantian/Hegelian logic? They seem to require a lot of prior reading, and what is prior seems to be a series of dead ends. I could read scholastic philosophy to learn formal logic - but that would be less efficient than the step by step and naked proofs of formal logic.

I guess my question is -- is there text that presents proofs of kantian and Hegelian logic in a way that is similar to the way formal logic is presented in a text? A way in which a beginner can open the book and build upon defined axioms towards a larger picture? Do you have any recommend cations for texts?

At this point the best way seems to read through the philosophical cannon. (Which isn't terrible, just inefficient)

>>911662
No there isn't since their logic isn't formalised as strictly as modern logic.
The most important point here is though:
There is not only ONE logic, nor only one way to "do logic". There are a lot of aspects which Kant and Hegel have considered not covered within today's formalised logic.
Today's formalised logic is pretty much lacking of content except when it comes to Algebra, unless you use modal logic, or something else more obscure.
When someone says "X is logical" the appropriate question should be "In which logical system?"

I have sadly not been content with any second hand literature I have read of Kant nor Hegel.
Also, all you need to know is to learn their general ideas. The best way would probably be to look up different systems on IEP or Stanford Encyclopedia of philosophy.

>>911662
>What would be the most efficient way to go about digging deeply into kantian/Hegelian logic?
for hegel in reading this

https://ncatlab.org/nlab/show/Hegel%27s+%22Logic%22+as+Modal+Type+Theory

>Abstract While analytic philosophy famously rejected the speculative metaphysics of Hegel in favor of the analysis of concepts by means of mathematical logic, in particular predicate logic, recent developments in the foundations of mathematics via homotopy type theory offer a way to re-read Hegel as having useful formal meaning not in predicate logic, but in ‘modal type theory’. The essence of this suggestion has been made by Lawvere in 1991, which however remains largely unnoticed. Here we aim to give a transparent account of this perspective both philosophically as well as category-theoretically. We then further expand on Lawvere’s formalization of Hegel’s “Science of Logic” in terms of the categorical semantics given by cohesive higher toposes. We discuss how there is a useful formalization of a fair bit of modern fundamental physics, in fact of local gauge quantum field theory, to be found here.

for kant, ITT is a formalization of it, say Martin lof. >>903230

I think the confusion comes from schematic identification of logicism with realism, intuitionism with conceptualism, and formalism with nominalism, referencing positions in the old debate on the nature of universals. This is mostly right, but not quite: Hilbert is a nominalist about mathematical objects, but he is a conceptualist (Kantian) about mathematical symbols and their manipulation. "The subject matter of mathematics is... the concrete symbols themselves, whose structure is immediately clear and recognizable". The difference with intuitionists like Brouwer is that they were conceptualists about mathematical objects, not just symbols.

In fact, this was Hilbert's original innovation. He considered (idealized) mathematical symbols as objects of a priori perception in a way similar to Kant's view of arithmetic as a priori synthesis in time (hence their agreement against Frege, to whom arithmetic was analytic), and geometry as a priori synthesis in space. But Hilbert extends this to formulas of algebra, formal logic, etc., by merging both space and time into a joint medium of syntheses. These are the "logical concrete objects that are intuitively present as immediate experience prior to all thought", "a condition for the use of logical inferences and the performance of logical operations". A condition of the possibility of certain knowledge, also very Kantian. But Hilbert's extension of Kant gives much more: we can have synthetic a priori knowledge of logical consequences of all our axiomatic theories. Indeed, their proofs are analogous to Euclidean constructions in geometry, they are a priori syntheses of imagination, but based on symbols rather than figures.

>>912833

This Kantian in spirit view of symbolic manipulation explains the key goal of Hilbert's programme: establishing completeness and consistency of mathematics by finitary means. While there is no restriction on the nature of objects that we choose our symbols to represent there is a restriction on what we can do with those symbols. Only constructions of finite length, although potentially unbounded, are accessible to our Kantian faculties. However, should we reduce all our proofs to such constructions we will get the holy Grail -- a synthetic a priori certitude for all of mathematics. Alas, this optimistic hope was proved unattainable by Gödel.

Johan Georg Granström, Treatise on Intuitionistic Type Theory (2011).

>>912869
Is that a recommended read for beginners?

>>896236
add me please

[email protected]

>>912450
>not only ONE logic
Yes there is ONE logic.

breue

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>>914674
yes, it should be fine

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>>917376

>>916192
There isn't, if you think so, you haven't studied enough.
An example is that "truth" is a pivotal concept when defining the first axioms.
"A&B is true iff A is true and B is true."
That's the usual way of making it a totally meaningless platitude. However, there are other ways of analysing truth, and also thus totally different ways of analysing what it means.
If two theories are incommensurable, I would call them distinct, if they disagree on the nature of truth, they are most likely incommensurable.
Another example would be:
"A iff A is provable." as a first axiom.

>>917391
What's with all that nerd talk.
>believing in axioms
Literally theist tier.

>>918179
You can't have science without axioms/belief.

buop

>>910251
>science is philosophy

>>896236
I'm in.
[email protected]

>>922730
Sure it is.

Empirically prove the validity of the scientific method, if you don't think it is then.

>>923031
>Empirically prove the validity of the scientific method, if you don't think it is then.
It is self evident, I don't have to prove it.

>>924135
nice rigour& scientific spirit, undergrad

>>925996
what does that even mean?
What's more rigorous than concrete reality in front of you?
Fucking mystic.