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Attic Philosophy
United Kingdom
Приєднався 27 січ 2014
Attic Philosophy is all about bringing you free, high-quality, university-level education on UA-cam. As a lecturer, I see the benefits of a university education every day, and I want more people to have access to those benefits. With videos covering metaphysics, language, logic, and social philosophy.
Learning philosophy can be really hard, whether you're studying it at uni or not. Academics often seem like they're speaking a different language. On this channel, I discuss some of the big ideas in philosophy, and show you how to get to grips with logic.
You can support the channel and help it grow by contributing on my Ko-fi page:
Ko-fi.com/atticphilosophy
Ask me a question in the comments! I'll try to get back to you. Or get in touch on social media:
Twitter: PhilosophyAttic
You can find out about my academic philosophy work here: www.markjago.net
Many of my academic publications are available freely here: philpapers.org/s/Mark%20Jago
Learning philosophy can be really hard, whether you're studying it at uni or not. Academics often seem like they're speaking a different language. On this channel, I discuss some of the big ideas in philosophy, and show you how to get to grips with logic.
You can support the channel and help it grow by contributing on my Ko-fi page:
Ko-fi.com/atticphilosophy
Ask me a question in the comments! I'll try to get back to you. Or get in touch on social media:
Twitter: PhilosophyAttic
You can find out about my academic philosophy work here: www.markjago.net
Many of my academic publications are available freely here: philpapers.org/s/Mark%20Jago
Axioms in logic
You can request a video from me by starting an AbleBees petition: www.ablebees.com/team/atticphilosophy
You can support the channel and help it grow by contributing on my Ko-fi page: ko-fi.com/atticphilosophy
00:00 - Intro
01:57 - Why use axioms?
03:56 - Typical Axioms
06:42 - Axioms vs schemes
08:03 - Axiomatic systems
08:35 - Proofs
09:18 - Different axiomatic systems
10:39 - Example: the identity axiom
15:04 - Working out axiom instances
15:34 - Example: explosion
19:25 - Difficult case: permutation
20:33 - Proof recipes
21:25 - The Deduction Theorem
If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Twitter: PhilosophyAttic
#logic
You can support the channel and help it grow by contributing on my Ko-fi page: ko-fi.com/atticphilosophy
00:00 - Intro
01:57 - Why use axioms?
03:56 - Typical Axioms
06:42 - Axioms vs schemes
08:03 - Axiomatic systems
08:35 - Proofs
09:18 - Different axiomatic systems
10:39 - Example: the identity axiom
15:04 - Working out axiom instances
15:34 - Example: explosion
19:25 - Difficult case: permutation
20:33 - Proof recipes
21:25 - The Deduction Theorem
If there’s a topic you’d like to see covered, leave me a comment below.
Links:
My academic philosophy page: markjago.net
My book What Truth Is: bit.ly/JagoTruth
Most of my publications are available freely here: philpapers.org/s/Mark%20Jago
Get in touch on Social media!
Twitter: PhilosophyAttic
#logic
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Thank you, philosophy-David Tennant!
My thought listening to this is that the argument could take a hint from epistemology in science. Falsehood exists and we can make the infinite lists of falsehoods. Possible Truth is everything not on that list, so a two value logic of False and Maybe and it is just a list of sentences of the chalkboard again. Paradoxes can go in the maybe column.
Thanks , keep up the great work
Is this semantic tableaux (like in the Kelly book)?
Yes, same thing.
So why the double negation of q at 6:26? I was expecting q,r,~p.
It’s the negated conclusion. q&r->p is a premise - don’t negate that.
@@AtticPhilosophy Thanks! I was confused about what you were doing. I thought you were somehow trying to prove q&r->p by assuming q and r and applying impl-intro. Now I see you were actually proving ~q from q&r->p, r, and ~p. Makes complete sense!
How about undecidable?
That’s not a good contrast term to true/false, since some sentences are true/false but also undecidable. “Undetermined” would be better.
Music is distracting. It's like having music over the PA while in class or a band playing in the next classroom while the teach is speaking. Some people might like that. I pose you could get more views by having a music/no music option.
There’s no music in recent videos - have a look there.
Dialetheism is an important response to this issue - & works well.
Limits of incompleteness would be helpful as a contextual & philosophical limit to these smaller statements.
Nominalism’s antithetical is Platonism rather than realism.
There are intermediate positions - neither nominalist nor platonist.
I have a question regarding this great video. Can you help me understand this a bit better? (¬B → ¬ A) → ((¬B → A) → B) I’ve tried substituting in some sentences for the variables, but it didn’t make sense so I must have messed up. This is what I tried B = I have a chessboard A = I can play chess From that I seem to get: If it is the case, that if (“if I don’t have a chessboard, then I can’t play chess”) → (“if I don’t have a chessboard then I can play chess”) → (“I can play chess.”) If it was (¬B → ¬ A) → ((¬B ∧ A) → B) Then I think I could get it to make sense. I know this is a lot to ask, but I would appreciate it very much if you could point out what I have misunderstood or misinterpreted. Thank you for a great video!
Think of it as saying: if ~B leads to a contradiction (A and ~A), then B is true. Written as a rule, it’s easier to understand: ~B -> ~A ~B -> A ________ B That’s one way to write the Reductio ad absurdum natural deduction rule, btw. So that’s basically what this axiom is doing.
Great video
Thanks!
I know this is old, but I just face a bit of curiosity enticing me. It seems that these modal symbols have to do with the relational states instead of the state itself, (ie. Describes something about the states around it that are accessible).
The symbols [] and <> aren’t really about states at all - they’re about the status of propositions, necessary or possible. They’re interpreted as quantifiers over related states. Not sure that was what you were asking tho!
How is the Liar paradox not a problem for any of the other theories? Assuming all these theories abide by binary (true vs false) logic.
It is, but (to me) the problem may be avoidable. For example, coherence or correspondence or whatever may allow exceptions to the t-scheme, whereas for deflationism, the t-scheme is built in to the definition of truth.
Jesus stayed out of human politics. His main theme in the gospel account was the kingdom of God. Which is separate from human governments and politics. Stop trying to conflate the two. He stayed out of the Jewish rebellion against the Roman empire. He fled to the mountains when the Jews tried to make him king. He commanded his followers to pay taxes and to be good citizens but never encouraged them to get involved in human politics. He told us to pray for the Kingdom to come.... So until the Kingdom of God comes his followers should be imitating the example he set. Jesus was neither socialist or capitalist. He viewed himself as a citizen of Gods Kingdom and his true followers would do the same.
Here’s a different way of asking the question: given the moral principles Jesus espoused, which political system best represents them?
The thing is Socialism isnt only bound to Marxism and every other ideology which forwarded it. Theres so many schools of socialist thought which arent marxist at all like Gandhian socialism. So Jesus was definitely a socialist. Just not a marxist. Hope that makes sense lol
I really appreciate your work especially your logic series
Thanks!
Do you have a podcast?🥰
Afraid not
Since this is about axioms, I’m going to leave the axioms for a logic that I call “Weak Negation Logic”. This is for anyone to see and use. (A→B)→(C→(A→B)) (A→(B→C))→((A→B)→(A→C)) ((A→B)→C)→(¬C→¬B) ¬(A→A)→B (¬(A→B)→B)→(A→B) (A∧B)→A (A∧B)→B (A→B)→((A→C)→(A→(B∧C))) A→(A∨B) B→(A∨B) (A→C)→((B→C)→((A∨B) →C)) (A∧(B∨C))→((A∧B)∨(A∧C)) From A and (A→B), infer B. P.S., you can distinguish between positive literals and meta-variables, in which case you can change the first axiom to A→(B→A) where A is a positive literal or A=(C→D). I call this modified version “Non-Intuitionistic Logic”. These are both basically propositional S4, but with some modifications.
Will you be treating Critical Rationalism (Karl Popper's epistemoloogy) too ? It solves most of the problems with justified true belief epistemologies
Probably not, philosophy of science has moved on quite a lot since Popper.
@@AtticPhilosophy How ?
Every axiom can easily be shown to be a tautology by truth tree or RAA. As always, sentences with 100 arrows can be more easily handled by applications of the Deduction Theorem, that is the "meanings" become far clearer when the forms are reduced to their Deduction Theorem equivalent sentences..
Of course - you don’t want axioms that aren’t classically valid!
@@AtticPhilosophy point is some are "obviously " valid (in the sense of being tautologies) while others are not. Im not quite clear on what you mean by "classically valid". If we are going to devise a test for "axiomatic validity" what should it be based on? Seems to me the axioms should be as few as possible and as simple as possible. I think most , if not all, axioms can be "validated" by truth tree construction but that adds a complicated and different layer to the axiomatic system.
@@pfroncole1 A list of axioms defines a logical system. They don't need to be obvious, but should be classically (truth-table) valid, and together define what counts as valid. In sub-classical systems, such as relevant logic, you drop some of the classically valid axioms to avoid things you don't want, eg the "irrelevant" p->(q->p).
I suppose p>(q>p) is "irrelevant " in the sense that it adds nothing to a system with p>p as an axiom. I've often wondered how the axioms are being selected apriori other than with the multi-valued truth table test for independence?
I suppose p>(q>p) is "irrelevant " in the sense that it adds nothing to a system with p>p as an axiom. I've often wondered how the axioms are being selected apriori other than with the multi-valued truth table test for independence?
Why people don't use another letter for p→p? For example, P. Or p². Or I, for Identity. This way you avoid making mistakes, I guess. The proof becomes: p→(I→p) (p→(I→p))→((p→I)→I) p→(I→p) (p→I)→I p→I I Also, there is a missing parentheses here: 13:27 . Hahaha. It should be ... ((p→(p→p))→(p→p))
That’s a useful trick, especially for abbreviating things more complex than p->p. Just got to be careful: I is neither a sentence letter nor a meta variable!
4:40 I don't read A→(B→A) like that. I interpret it like characterizing A as everything that implies A.
Ah, I was thinking of it as saying something about ->, not about A. So if you drop this axiom, what changes: A or -> ?
@@AtticPhilosophy well ... Both change. If you drop the axiom, you lose information about → AND you lose characterization of A as the axiom implies. I know it doesn't look like that's the case, but the modern understanding about Logic and Math says that. To be more precise, A may be the same, as a proposition, but it is not the same considering its relations with the other propositions. So, in some sense, A changes too. Hehe.
What do you think about Schrödinger logics?
I'm a philosophy teacher, did my master thesis on Wittgenstein, and I must say I never got the point of mathematical logic for philosophy (let alone the proof of p ---> p !). None of the great philosophical contributions I've read so far (including in contemporary analytical philosophy) ever needed heavy logical tools. I'm talking about classical philosophical topics: metaphysics, ethics, philosophy of action, philosophy of religion, etc. Should I feel, some day, that I miss all these technical tools, I'll invest some time in it, but until then it looks like a waste of time to me. Could maybe someone give a few examples of significant contributions in some classical fields of philosophical that wouldn't have been possible without axiomatic logic?
I suppose it depends on whether one deems it useful to make such axioms explicit . For example, the principle of non-contradiction was implicit all the way up through Plato. It wasn't useful to axiomatize it. Aristotle's formalization of the logical principle of non-contradiction was useful for him however when he decided to refute sophistical arguments that took advantage of ambiguities in grammar. Much in the same way Wittgenstein thought it was unnecessary to show how we use words until they are misused, in which case we require addressing their use explicitly in order to clear up the errors that come up from their misuse.
Most of the big 20th C analytic philosophers were also logicians - Frege, Russell, (early) Wittgenstein, Carnap, Quine, Kripke, Lewis. Much of their work relies on developments in logic. Later Wittgenstein is probably the exception here. You can definitely understand a lot of philosophy without much logic, but it's hard to do work in metaphysics, mind, language, especially without some basic logic.
Well, it definitely depends what you take under consideration. If you are doubtful about the entire formal logic project, I am very confused, as its use is quite obvious, showing that certain invalid arguments very similar to valid arguments are indeed invalid. Abstraction through formalization helps to capture each argument with the same form. On the other hand, if you are skeptical towards axiomatic proofs only, Mark said nicely at the begining of the video that natural deduction or truth trees are much easier for general use. The main use of axiomatic proofs was in philosophy of mathematics other than logic (a part of philosophy when I last checked). It is ok not to be interested in something, but it is not ok to say that something has no value just because you are not interested in it.
@@AtticPhilosophy Some basic logic, you're absolutely right: fundamentals of propositional, first order and modal logic. Nothing very fancy. But I find the textbooks of philosophical logic overly technical and little helpful to understand or elaborate real philosophical arguments. And I still don't get the point of proving that p --> p ! ^^
@@matepenava5888You're answering to a straw man. I don't say I'm "doubtful about the entire formal logic project". I just say I'm skeptical about the interest of those developments (at least most of them) for actual philosophy. It's not a pure intuition, but confirmed by what I know of current philosophical researches in various fields.
> a => b b | F B T --+------ a F | T T T B | F B T T | F F T
4:52 weakening is invalid 5:10 that longer one is valid, and it's not an axiom, you can compute it quite trivially
Depends on the logic but weakening is valid in most logics, invalid in relevant logics.
What do you mean by "weakening is invalid"?
3:20 There's like a dozen "axioms" for RM3, and one of them is "mingle", where the M comes from, which they added because the mathematical structure they accidentally created already had that property. It's really much simpler than that. Modus Ponens is a theorem you can PROVE using Category Theory
Modus Ponens isn't an axiom, it's a rule! And you need to use it to reason with category theory (or any other theory) - just try without.
#RM3 conjunction is left adjoint to implication --- but "truth" is replaced with "validity" --- The Liar is valid, it is both true and false.
Thank you. Also, I liked the brief mention of the Logical Positivists at the start, although given your area is logic, might be good to also explore the limits of axiomatic, indeed the limits of all sentence statements as a result of Gödel & the Incompleteness Theorem in some future presentations.
It is precisely simple systems like syllogistic and propositional logics that Gödel's Incompleteness Theorems do NOT apply to! In order for a logic system to be subject to Gödel's Incompleteness Theorems it must be sufficiently expressive and consistent (e.g. peano arithmetic). There's even some arithmetics which are complete.
Please make some videos on Speech act theory 🙏🏻
His faith in logic rendered him dense. So sad.😊
Thank you so much, this really opened my eyes
Also, in regards to original sin as traditionally understood, Paul in Romans 5 seems to be talking about spiritual death (separation from God) rather than physical death.
Thanks a million for all your great videos! I appreciate the effort required.
ahhhhaaaaahhhhh!!
Sooooooo bloody helpful
🔥🔥🔥🔥
This channel is underrated.
In 1:50 you show a picture from Wittgensteins School, there are two persons marked. Wittgenstein to the left and Adolf Hitler to the right. Just wanted to mention this. How or if they influenced each other is very controversal but its interesting to think about it.
Hey, i know it have no relation with your video, but you have considerer talking about more rare or complex logic or authors, like Newton da Costa, and is paraconsistent logic for example, this guy is a beast, it will very interesting seen a video abaut it, i see very few people talking abaut it in anglo community, but in hispanic an latin lagic community, he is a big reference, or maybe de negationless logic of Griss, and the conception of negation in intuitionistic logic that is very interestinhg to, Greetings from Spain
I love you man
i feel like i now have a better idea of what ⊧ is, but what about A⊧B vs A⊢B? (sorry for abusing of your time but may i add the difference between the previous and A⊩B to this question?)
⊧ is semantic entailment: (in every valuation/model) if A is true, then B is true. ⊢ is about proof: B can be proved/derived from A. These are standard symbols with fixed meanings. ⊩ is sometimes used to speak about a sentence being true relative to a possible world, state, situation or whatever: s ⊩ A means that A is true relative to (world/state/situation) s. (Some people also use ⊧ for this.)
How is constituting somsthing not a cause for it? Im confused by this. Doesnt the brain confirgutation cause the mind to be a certain way?
Constitution is usually a relation between two objects: eg the piece of plastic constitutes the shampoo bottle. Causation is usually between events: striking the match (in the right circumstances) causes the flame.
I watched until 1:31 and get annoyed with the lack of answer. Hahahaha.
How would things be if Wittgenstein had access to category theory?
Who knows? But my guess is that his views would have been roughly the same.
@@AtticPhilosophy Probably, imo it might have added something
What is language? Language is under the highest genus of quality. It is sensible quality. It is sensible quality that is auditory in character. It is sensible quality that is auditory in character and significant of something. It is significant sensible quality thay is auditory in character, significant of something and whose to power to signify comes convention.
Meaning in th proper sense is a quality of language, for e.g. bank means inclined surface or financial institution; but it is also extended to mean what any sign stands for in reality, for e.g. the big cat like paw prints might mean there is a tiger near by.
love your work
Thank you!
This is brilliant and trippy
Thanks!