Thank you for putting in so much effort to this niche topic, you do not go unappreciated!

@AtticPhilosophy

Жыл бұрын

I appreciate that!

You got it. Logic is a procedure or set of procedures for determining the truth of a statement based on the truth of other statements. That's the simplest description I can think of. Logical necessity is a contradiction of a contradiction. You can prove a statement is necessarily true by showing its contradiction is a contradiction, an impossible situation.

Super! It's like entering the channel that presents you exactly what you are thinking about at the moment. 💙💛

Thank you Mark for answering the question and for the great video!!! Mathematical truths are based on logical necessity. If this necessity is not found in the physical world and does not represent the structure of reality then mathematics is just a game of concepts based on man-made arbitrary rules?

@AtticPhilosophy

Жыл бұрын

You’re welcome! I didn’t mean to imply that logic is merely based on rules we made, like a game. I don’t think logical truths could have been otherwise, although our rules & concepts could have been. Similarly, 1+1 has to be 2, whatever rules we might have. A different way to put it: there are abstract operations, like CONJUNCTION and ADDITION, which our concepts describe, but which aren’t part of the physical world. Logic and maths codify the workings of those operations. I’m not sure if that description makes much sense put so briefly!

Great question and answer! Perhaps it could be said then that logic represents reality within a limited dimension? Much in the same way that a pilot manual represents physics through the dimension of the normative rules of aircraft flight - or a mercator projection represents the Earth? Oh, and happy holidays, if that's allowed to be said on KZread... (I don't know the rules)

@AtticPhilosophy

Жыл бұрын

Yes, if by “reality” you include normative rules, you could say that logic represents normative reality. Happy Christmas to you too! And thanks for all the support & discussion this year.

Makes me think about logic as a model of reality (simplified complex thing with just enough features of the real thing that it still has explanatory power). "all models are wrong, some are useful" - I hear that a lot, don't hear much effort in formalizing what is meant by useful.

@AtticPhilosophy

Жыл бұрын

Yes, some people say that. The analogy is usually an architect’s model of a house - partly inaccurate but useful, eg in visualizing what the house will look like, or how light will fill it throughout the day.

you are underrated , keep going !

@AtticPhilosophy

Ай бұрын

Thanks!

Awesome.

How necessity is baked into logic: It's a monad. A closure operator. A monad on a poset is a closure operator. N(N(x)) = N(x) and similarly for P(x).

How about a non-classical logic like para-consistent logic? Is the latter still about representing the normative structure of its logical concepts (e.g. that of a contradiction)?

@AtticPhilosophy

Жыл бұрын

You can think of it that way, but with a different understanding of the logical concepts, or perhaps a different understanding of the truth-values those concepts interact with.

I'm loving your channel! Just I little suggestion If I may, if you are reading a script from some device, move it up so you won't need to look down, it's a bit strange otherwise. But it's just a unimportant opinion. Thank for your content!

@AtticPhilosophy

Жыл бұрын

No script, all made up waffle - but you're not the first to say this! I wonder what I'm doing?

@yuli3873

Жыл бұрын

​@@AtticPhilosophy Oh! My bad then, sorry. It might be that you are looking at a camera monitor or a secondary camera instead of looking at the main camera lense, perhaps? I'm not a KZreadr, though, so I couldn't know what to suggest, but I find it strange and somewhat uncomfortable because we look at your eyes but you're not looking at us, I think. Anyways, thank you for your content and for your reply, cheers from Argentina! (forgive me if any mistakes with my rusty English)

Whenever this question came up while I was at uni, it was usually a much more humble one: is there anything disallowed by formal logic that we can find in the world? Can we encounter "live paradoxes" out in the wild? Some people seem to think quantum mechanics provides for such, but then we have LL and QL to capture those. So I guess it just boils down to WHICH logic one uses. Are there any living paradoxes that defy ANY logical capture? I don't think anything can be said about that question, because if there "was" such a thing, it would escape any linguistic expression and we couldn't speak non-contradictory sentences about it.

@AtticPhilosophy

Жыл бұрын

That's an interesting (but different) question: does any phenomena break the rules of (classical) logic? Most people who disagree with classical logic think there is: perhaps statements that are neither true nor false, or true contradictions. As you say, this boils down to: which is the right logic to use?

@tomholroyd7519

Жыл бұрын

Stop assuming formal logic is binary

I will show that numbers are built from images Example , 4 always represents 4 images, like 4 squares for instance. To be specific numbers are "labels" for groups of images 1. The main idea here is that maths is built from images (a) example , geometry is clearly made of images b) example 2, We claim numbers are built from images too, as say 4 , always represents 4 images, like 4 squares for instance. C) imaginary numbers are connected to images too , which is why they have applications in physics D) In general any mathematical symbol that comes to mind is connected to images too.

please tell me the hardest book on logic to study,

@AtticPhilosophy

Жыл бұрын

No idea what the absolute hardest is. A standard grad textbook with some advanced stuff is Boolos & Jeffrey, Computability & Logic. If you’re looking for punishment, you could try working through Principia Mathematica.

Logic allows logic users to craft models that predict the way systems evolve, but predictability seems to be a feature of some physical systems to a greater degree than others. Does the way logic relates to systems differ between a universe in which some formal systems are effective for predicting and one in which no formal systems are?

@AtticPhilosophy

Жыл бұрын

I'd say logic is more to do with reasoning than prediction of outcomes. Often, the outcome of a physical system isn't a logical consequence of its previous states - it might follow with a certain probability given the laws of nature, but that's not really logic's remit.

Reality -- what a concept.

@AtticPhilosophy

Жыл бұрын

I know! Where would we be without it?

The answer to the Question: Yes The Reason: Because it is necessary, which is to mean, that the opposite is Impossible. Look into the Eyes of Ananke and you will See.

As a computer scientist I've always been uncomfortable with metaphysics because I have trouble fitting infinity into the computer. I prefer to think of formal systems as collaborative games like Dungeons and Dragons -- social constructions! Great vid :)

@AtticPhilosophy

Жыл бұрын

Even computer scientists need infinity - eg computation defined using Turing machines with a potentially infinite tape. Mostly computer scientists appeal to *potential* rather than *actual* infinity - what a computer could do, left to run long enough. The distinction goes right back to Aristotle!

But at the same time the metaphysics still follows The logical rules

@AtticPhilosophy

Ай бұрын

Everything fits within the laws of logic, else they wouldn’t be the correct laws!

Formal Logic takes what is gray and turns it into black or white. Very useful.

@AtticPhilosophy

Жыл бұрын

As in, it makes things more precise? That can be both an advantage and a disadvantage. But I think its helpful to have precise rules about what constitutes valid reasoning.

@tomholroyd7519

Жыл бұрын

Binary logic is a straw man. You don't need to go far. 3-valued logic is already good enough. Way better than 2. There is a "Formal" logic that includes grey

I watched until 1:31 and get annoyed with the lack of answer. Hahahaha.

Classical logic isn't consistent with vague predicates°, and I'm not sure there are any non-vague predicates in the real world (sad foundationalist noises). °Think Sorities Paradox applied in a really annoying way - to everything

@AtticPhilosophy

Жыл бұрын

Good point. Whether vagueness is consistent with classical logic depends on your theory of vagueness. According to epistemicism, on which vagueness is an epistemic phenomenon, there’s no issue with classical logic. Since it’s up for debate whether that theory is any good, it’s up for debate whether classical logic is right for vagueness.

@platosbeard3476

Жыл бұрын

@Attic Philosophy , it may well be that our concepts have sharp borders that we can't access, but that doesn't really solve the issue. If we can't access these borders and we can't access non-trivial semantic properties (Tarski, Rice), it's of no practical use. As a tame example - 'if, and only if, it's raining when you leave the house, then take an umbrella' has a zone of practical vagueness. While it may be that there's a sharp border that we can't access, that doesn't allow us to actually assign solid truth values in the zone of vagueness. If I leave the house with an umbrella, and you leave the house without one, who's right? Can science answer the question?

To ask, where the necessity comes from, is a invalid Question, Just Like asking, when Time began. Invalid is to mean, that it presupposes a contradiction. This being Most obvious in the example of Time. It is Not, that one cannot understand These Questions, and that one cannot get an answer. It is Just, that they are already directed at Something, which is Not possible to reach.

@AtticPhilosophy

18 күн бұрын

Well, we can ask, why is a given necessary truth necessary? Generally, what is the *source* of necessity? That question makes sense to me.

@davsamp7301

18 күн бұрын

@@AtticPhilosophy thank you again. It is indeed a interesting Question, what necessity is, But to ask, which source it has, does Not only presuppose, that there is one, but also, that Something Beyond what is necessary, could beground it. For as Casual modality suggests, there is either necessity or contingency. Now, No contingency could ground, what is necessary. But If only what is necessary could ground what is necessary, what is there left grounding that is Not already? Really, Like a Professor of Mine once Said, If one does Not understand the necessity of the force of the LNC, Noone could possibly Help one, for it is Impossible to explain of ground it further, as it is already always implied. So, the mystery of necessity may lie in the Essence of the core of classical Logic and is of a perculiar and unique, but also incomperable clear and lucid kind. If i May, i would also already Stop you on the notion of necessary Truth, for it already implies Truth, that is somehow Not necessary. But either, it is true, or Not, If now false or neutral. What now is it ro mean, that a Truth, being true, is possibly false? For it is only necessary, that what is true, is true, Always. One can also come to the understanding of this by asking oneself Just once what even would ground only one contingency. Clearly No necessity, for from necessity only necessary follows. But also Not from contingency, for what is Contingent is it in virtue of Something Else, Rendering it either into a infinite Regress or plain contradiction, as then some contingency is posited as fundamental, meaning necessary. Now, Not every Infinite Chain May be wrong and a Problem, but this certainly is, for it undermines itself, as it Sets Out to start from somewhere, that is Not necessary, but this is Not acomplishable. Furthermore, all of the above is Not even needed, for it suffices when only one necessity exists. Now, there are Not only many, but at least one, namingly the LNC for example, or the entire 'Logic' by its Nature. Now, there is Just one 'Reality', and Not two exclusive Realities, for this is Not only contradictory, but would be more then Strange. Therefore, No ontological contingency is possible and to be found consequently. But as i already Hope to have suggested, there is a notion of what could be called contingency in the Conceptual/Epistemic perspective, where we can ask ourselfs, why a cat must be a feline but Not black, although it can be. The source or ground of that might very Well be to vast and shady for now, at least for me. Clear to me only seems the destinction between both and the invalid language of contingency in ontological modality. For indeed, Our language is so caught Up in it, that we dont even recognize it, for how could we so easily? I Hope i could clarify myself further and asses your Question sufficiently.

Too vague. I didn't understand a thing.

A big mistake is to call those logical entities "atoms". Because that's a loaded term, "atoms" are supposed to be indivisible, and that of course is not the case for "logical atoms" as they're applied to reality. By using this loaded term we're implicitly led to assumptions about reality that aren't true. Instead, those logical "atoms" are only *conventionally* indivisible at an arbitrary level of description of reality. They're indivisible only because we momentarily chose so, for convenience. Instead, it would make a lot of sense to replace the term "atoms" with "objects" or "things", and conceptualise them as made of other "things", in nested levels of description/explanation from which we can choose any to focus on, in a hylomorphical manner. NB: this objection refers to logic as overlapped onto reality. In reality the objects and processes are divisible in principle, while in abstract logic they aren't. But logic only supplies us with a general, formal pattern that we can apply to various perspectives on reality, over and over again, wherever it fits. It's a mistake to assume reality, in its vast complexity, shares the narrow limitations of a simple logical tool as it's applied locally.

@AtticPhilosophy

Жыл бұрын

Are we talking about the sentence letters p,q,r of propositional logic? They're often called atoms. In propositional logic, they're indivisible parts of the language: syntactically, they're basic. They're not objects or things in the usual sense, but sentences describing how things are.

it's lame to show your face if you dont look into the camera

@AtticPhilosophy

Жыл бұрын

Not sure which video you watched - I’m looking into the camera right through this one!

Well yes, but actually no

Your presentation of logical atomism doesn't seem very charitable. I'm no scholar of Russell or Wittgenstein, but I highly doubt that either of them would want to say that a sentence like "It's raining" expresses an atomic fact, even if it's not obviously complex in the sense of featuring connectives in it. I can't remember who the example comes from, but logical atomists might analyse a sentence like "The knife is on the table", which could be represented as an atomic sentence in predicate logic, as meaning something like "There's a knife handle on the table, and a knife blade on the table, and they're attached to each other in the appropriate way to make a knife". And the idea is that you could analyse each of those constituents further, until you eventually get down to metaphysical atoms, at which point you can't analyse the atomic sentences that they feature in any further. Of course, there's plenty of stuff in this picture that you could object to, but the objection you gave seems a bit of a strawman.

@AtticPhilosophy

Жыл бұрын

Maybe you're right. But I think at some point, whatever they might mean by 'logical analysis' gives out, and needs to be replaced by a combination of metaphysical and scientific analysis.

vacuous. Empty.

@YassinAlMasri461

2 ай бұрын

when i started diving in philosophy i hated comments like yours , now i think that what you said is completely correct , and i think you meant that this dialectic presented in the video is vacuous and empty .

No

"In the beginning was the Word, and the Word was with God, and the Word was God." John 1:1

Can logic be expressed without language?

@AtticPhilosophy

9 ай бұрын

Some relationships can, eg by a Venn diagram, and we often reason about models with diagrams (eg in modal logic). But by definition, logic involves reasoning with and assigning various values to sentences, so very hard to do without a language of some kind.