Thoughts on logic?
write it in latex or im not gonna read it
i've got a horizontal proof for you right here8[][][][][][]D -------- OP
>>83683470modal logic isn't second order logic, try harder
>>83683470im not autistic enough to understand this opsorry
>>83683482All second order is is quantitication over relations and predicates.
>>83683482modal logic is exactly second order logic.
>>83683477>8[][][][][][]D -------- OPThat's not a wff
>>83683470logic just means knowing what all the symbols mean, the rest is self-evident
>>83683497>thing logically entails itselfam i reading that right?
>>83683517By definition, yes. LolP->P is a tautology.
>>83683529i feel like basing your entire argument around disjunction and introduction is kind of basic and pointless, which logic anon seems to do anyway
>>83683536The exercise asked to show that []A&<>D |- []A&<>(D&A) in K. I converted a proof tree into a horizontal proof (with the help of natural deduction) to show that in K the hypothesis indeed entails the conclusion. I am currently working through a book on modal logic.
>>83683470yeah i like it. i played around with it quite a bit back when i was in school. wish it wasnt a mac only thing though. i dont want to get anything apple really, but i cant be bothered to learn anything else like fl studio.
>>83683470Don't show me something some bumbling retard mashed into the keyboard and then ask >Thoughts on logic?Your pic means nothing
>>83683559is a proof tree essentially a iterated truth table?
>>83683477spbp checked /thread
>>83683584Sorta, but it works more like a proof by contradiction. You assume the opposite of what you are trying to prove, and see if its leads to a contradiction. If it does then boom what you are trying to prove is entailed by the system you are working in. If it doesn't, then you can come up with a counter-model/counter-example and fill in each world in your counter-example with exactly what your propositions semantically entail.
>ask AI if a proof tree is a kind of truth table>it says no>ask if it's a collection of necessary truth relation>it says it shows truth values>header: is not
>>83683620This is a proof tree. You can convert it into a proof. It's a tool for proof finding.
>>83683664does the first thing in that diagram have its own rule? or is it trivial
>>83683668The negation of a conditional statement leads to a conjunctive statement which you can split into two statements.
Can someone explain natural deductions in propositional logic to me?
>>83683675i don't see the use for that really. but i don't know what the asterisk is doing here. i gather ~[]q is true if the other asterisk statements are true? and the non asterisk statements are always true? is that right?
>>83683705i guess i just don't get the jump from w0 line 1 to 2
>>83683742unless, of course, it's just a list of true statements
>>83683746oh i get it now.[]p and ~[]q contradict each other or something along those lines grip i don't think the board can grip harder than that though
>thing to prove>negation of thing>negation of implication and affirmation of conditionthe split is kind of confusing i might have to think more about that, but i guess it's just inverting to negate the condition
it sounds like w1 reduced back to introduction though
>>83683705Not sure why the author put the asterisks there desu. Anyway it's just the other side of the conditional. ~[]q=<>~q, which allows us to open a new world where we can stick ~q in. Since we have []p, we can move p into the new world. We also have [](p->q) which lets us move p->q in the new world. p->q=~p v q so we can split it into two cases. ~p contradicts p, and q contradicts ~q. We have found our contradiction which allows us to conclude that [](p->q) |= []p->[]q. :)
I've been meaning to get into thishow do I start?
>>83683800that doesn't really help me understand this better though maybe comment on my attempts to solve it myself
>>83683844start with ted sider's book on logic
>>83683844start with volker halbach's book on logic
>>83683854Ok start in w0 with the negation of what you are trying to show is semantically entailed in the system (in this instance K). So we have ~([](p->q)->([]p->[]q). Since an implication is the same as a conjunction with the antecedent negated (p->q=~p v q) we find that we have ~(~[](p->q) v ([]p v []q). Using DeMorgan's law we can distribute the negation to get [](p->q) & ~([]p->~[]q) where the right hand side becomes ~(~[]p v []q) which becomes []p&~[]q. ~[]q = <>~q. Now that we have the diamond symbol we can open a new world with this! So we open a new possible world where ~q is true. Since [] reads a "necessarily", and any thing that is necessarily true is true in all possible worlds that the world it is true in has access to, move everything with a box symbol in the front into the newly opened world. We can move p in and p->q into w1 since they are necessarily true in w0 and w0 has access to w1 (has an arrow pointing to it i.e. w0Rw1 i.e. (w0, w1) are members of R). We can split p->q into two cases, ~p or q and in either case we arrive at a contradiction in w1. This entails a contradiction in K. Since ~([](p->q)->([]p->[]q)) leads to a contradiction in K we must conclude the opposite is true by IP (Indirect Proof/Proof by Contradiction). Hence we can conclude that [](p->q)->([]p->[]q) is true. In other words |= [](p->q)->[]p->[]q. We can just pull out the right hand side as well and show that [](p->q) |= []p->[]q. This reads as "[](p->q) semantically entails []p->[]q." You can also construct a proof in fitch style natural deduction from this tree (and an equivalent horizontal proof). If this thread is still up I will show you how to do that later but I am currently busy. :)
>>83683844start with under pressure by logic
>>83683963>(p->q=~p v q)i guess that does make sense... huh
>>83683963i guess my issue is just not all of that is actually in the diagram
>>83684025>>83684010Here is the tree converted into a proof :)
I didn't realize robots were so smart. I have no idea what I'm looking at.
>>83684067that's kind of a step ahead of where i was
>>83683470Idk why but the only people that ever talk about or seem into this are the biggest of busybody do-nothings
>>83684087They aren't, it's meaningless performative pseud jargon you see the same shit on discord from first year philosophy students
>>83684808lol you have to deflect your retardation.
>>83684819Classic retort, I use raw IQ to body you twerps on the daily, hide behind your exclusionary terminology it's all you have
>>83683470>...,[], D |- Dlol
>>83684087logic is a language of its own. if you arent in cs philosophy or math, theres no reason to be taught it
Can you help me find a Logic Discord server? I haven't been able to find a good one since a dispute happened somewhere before. I'm particularly interested in Henkin semantics.
>>83684946doing logic in discord sounds hellish and it's not something people do in groups unless they're trying to pass a class by sharing answers
>>83683509Your mom wffed it down XD
How does one get to this level of logic?
>>83684067>Show that (~[]Falsum) is a derivable rule of K.Did I do it right? | [](A&B)| | ~[]A| | | []| | | | ~A| | | | A&B ([]Out, 1)| | | | A (&Out, 5)| | | | Falsum (Falsum Intro, 4, 6)| | | A (IP, 4-7)| | []A ([]In, 3, 6)| | Falsum (Falsum Intro "~[]Falsum" 2, 9)| []A (IP, 2-10)The Tree Rule Lemma seems to prove this also.
>>83685313Let *B = ~A and *B' = A&~A, then by the entailment lemma *B' |- Falsum so *B |- Falsum. Idk if that's right desu I'm still learning.
Why won't anyone fucking help me with logic!? Nobody on /sci/ seems to know this shit and I keep asking them and they won't help! :(
fee fees > logic
Oh wait I think specifically for ~[]Falsum it should be: ~[]A |- ~[]A&<>~A (where *B = ~[]A and *B' = []A*<>~A), but clearly since ~A is in our possible world, by introducing in A&B we get out contradiction, and hence if the child *B' entails a contradiction then so will its parent *B. I hope I'm getting the reasoning correct here for the proof. Been trying to carefully read through this to make sure I fully understand what's going on here but honestly I don't know for sure. I'm self teaching logic.
I just want to master correct reasoning to win debates on the internet. :( I'm going down autistic level rabbit holes here guys. I'm even reading an entire book on logic and have been studying logic to do this. I read an entire book on set theory for this shit! :(
>>83685447Logic cannot win debates, you want to study rhetoric instead. And rhetoric is the science of convincing people when you have no argument, more or less, as you will find out.Anyway, different cultures use pretty different symbols to express logic. ~ and ! are pretty universal for not, as are & for and and | for or, and falsum/verum are universal period. But other symbols can differ a lot, so to get the best discussion going you should always define the symbols you use.>>83685179This is just very basic math. Take real analysis and you'll go through much more complex proof principles. Or even a discrete math class or a mathematical statistics class would teach you all the basic proof techniques and would go beyond that.Actually I don't even like their choice of using a proof by contradiction. The intro part of the proof naturally leads itself to a constructivist approach instead, and is like 2 steps removed from a proof by induction. Both would have been cleaner in this case.
>>83685376what do you need help with, dunno too must myself but i may be able to help
>>83683470I'm in my thirties and I did all this stuff in my teens and I could try to remember it but it really hasn't done any good for me after learning it the first time so why would I bother learning it again?
>>83685447>I just want to master correct reasoning to win debates on the internet.The absolute state of debate culture makes it not worth it. You could actually have a better argument but even if it was face to face, with a moderator, it devolves so fucking fast and the average person is so fucking retarded that even if you wrote out a flowchart of everything that was said more or less, circular reasoning and straying off on tangents will occupy most of your time.
>>83685801>This is just very basic math.No it's not.
>>83685801>Logic cannot win debatesEven sophists valued and taught logic
>>83685801>Logic cannot win debates, you want to study rhetoric instead. And rhetoric is the science of convincing people when you have no argument, more or less, as you will find out.How do I learn rhetoric?
>>83683470I just wrote an exam from this bullshit and i am glad i never have to think about it again
>>83687835I have mine in two weeks, I've been having fun with it though
>>83683470formalised logic syntax is something i've never been introduced to nor would find any use for in how I currently live my life. That's not to say that this fact couldn't change, but right now I'm looking at OP's wall of gibberish with no desire to extrapolate the meaning behind it because I would need to take a crash course in the semantics of the language used to describe it, and then run my brain through mental gymnastics to test, retest and validate whatever he's trying to prove.I'd say it's useful if you're into analytical philosophy over continental philosophy (e.g. dealing with numbers and symbols over concepts, etymology and semantics). It's also useful in computer science/ai training if i'm not mistaken, and abstract mathematical theorem.Where the gap is for any savvy student on their way to becoming a doctor is to understand the concept and be able to explain it wtih examples that relate to continental philosophical rhetoric and artisans who used proto-logical syntax in their essays. There's a few philosophers to look at in this regard apparently, chatGPT tells me Wittgenstein evolves towards this kind of syntax driven rhetoric, Kant uses formal structure but writes prosaically and anyone at the top of the foodchain in modern AI research would probably use elements of logical syntax in their whitepapers. Unfortunately I can't draw from any examples because like the hedonistic avoidant I am, I'd much rather turn this brain off via porn, weed and vidya than consume philosophically dense texts because I am extremely lazy and averse to effort in general.tl;dr this kind of logic is for specialists but there exists a gap where the type of human that can stomach this kind of mental torture can not sustain relaying the information back down the totem pole so that Bro Jogan tier conversationalists can have their way with its implications. Plug that gap and you might build a large audience.
superfluous to truth, always post hoc, so i never bother with it
>>83688456>superfluous to truth>always post hoccan you elaborate?
>>83688478no dumbass, that would completely defeat the point. learn to read
>>83688483gotcha so its not a real critique
>>83688680not the person you're replying to>>83688431he more or less said what i said here in that - it's useless to him in his current life because reasons, he just did it in about 5% of the characters that I used in this post.To explain my understanding of what he's saying, something superfluous to truth is something that is not necessary to utilise to arrive at truth, and that logic is applied after intuition makes the initial discovery. He's saying there's no place for backtesting philosophical intuition in any way that applies to _his_ life whilst refusing to elaborate any further. Par for the course on 4chan, it's really hard to get people to invest into philosophical discussion because of the arena in which we're operating in being tuned in a signal to noise ratio in which the signal of the board is aligned with less complexity and non-conducive to productive discussion.It's a learned sense of "i'm not going to bother elaborating for you peasants because it's exhausting and you're beneath me". Fine, if you want to be like that you can, but FWIW i personally get off on writing a lot and testing ideas in these arenas with real people.tl;dr man does not want to bother thinking right now.
>>83688774my issue with the first thing is that logic isnt about truth its about justification, saying things are true independent of our reason or that you could have a true belief without justification seems trivial. maybe the point is that you can have justification outside of deductive logic so why bother with it?i still dont get the second point about it being post hoc
I remember being given some basic examples of proofs when I took geometry, like proof by contradiction using a generic variable to show that if you can disprove an inverse example of the proof you're trying to make using said generic variables, that means it's true (or something like that).This is all in service to say it really rattled my brain not having done it before (and me sucking at math in general), and this thread hasn't remedied that.
>>83688431I mean basic logic is pretty damned useful for mathematicians. They operate mostly on first order logic though, what is in the OP is indeed kinda specialized but like any logic it has the same basic template and is mathematically rigorous. Actually I believe CS students dive into modal logic a bit too, it's actually kinda useful for designing AI because it lets you model beliefs and intelligence (I only have a cursory understanding of what CS students do with it as my background is mostly philosophical). But basic proof techniques is honestly something everyone should know. They need to teach this in school. It actually gives you a really solid foundation for reasoning. Without this kind of logic we wouldn't have the advanced math we have today and, consequently, our advanced scientific theories.
>>83689043if the logic isn't justifying a truth, what are you even doing?
>>83689043Logic is the science of what is true and what is false.
>>83689948youre being a bit vague >>83690075no lol truth is usually assigned by an interpretive function what youre figuring out with logic is if its valid or not. its the science of validity
>>83689317I always thought proofs were fun to write.
>>83690126interpretative desu
>>83690126>>83690139When I talk about what is true and what is false here what I mean to talk about are truth values, not what counts as "material truth". In logic what is true and what is false can be represented by the numerical values 0 and 1. If v(p)=1 then v(~p)=0 or vice versa and, if you have a consistent system, you will not find yourself with v(p&~p)=1. If you have a set of satisfiable sentences then your hypotheses and conclusion shouldn't result in a contradiction. Logic, formal logic anyway, which is what OP is discussing, investigates formal reasoning and is therefore not overly concerned with what is materially true. Hence why a simple syllogism like "All birds fly | Penguins are birds | Therefore penguins fly" is a logically valid sequence because the premises guarantee the conclusion! Aristotle was the first to systemically study logic. The syllogism above is a simple case of modus ponens, and this inference rule preserves truth between each of the premises to the conclusion. That is to say, for any arbitrary model M, if a set of sentences is sound in M, then those set of sentences will be true no matter which way you construct your model. This is what formal logic is the study of. Informal logic tends to be more devoted to things like discovering logical fallacies in everyday speech (ad hominem, bandwagon fallacy, begging the question, etc). It's a bit different from what formal logic does in that formal logic attempts to give a truly rigorous formalization of correct reasoning, and it turns out the best way to do that is through mathematics, hence why many logics are encapsulated through axiomatic systems like the various systems of modal logic (K, S4, S5, etc.)
>>83689317Proof by contradiction goes something like this.>Assume A. Assume ~B. *Shows ~B contradicts something about A. Conclude B is true. For example>If the earth is flat people would fall off the edge.>People do not fall off the edge.>Therefore the earth is not flat.Not everyone likes proof by contradiction though. Intuitionists in particular won't allow for it when it comes to indirect proofs because that introduces double negation which entails a weak form of LEM which intuitionists don't like because it allows you to do non-constructive proofs.
>>83690230with you on all that but the interesting part is the structure (from which we get validity) not whatever the interpretative function happens to assign as true or false
>>83690328Yes of course. That's the point. Formal logic studies the form of an argument, not necessarily its content. HOWEVER it is true that many philosophers do see formal logics as metaphysically significant. Many philosophers argue that the semantics of any logic, especially modal logic, have to be grounded is real material facts about reality, which is why you get stuff like "modal realism" from philosophers like David Lewis.
>>83690399havent started modal logic so i cant say anything about but i fully agree with the rest you said anon
>>83690422about itjeez
>>83690126how is that vague?
>>83690698anon gave a pretty great summary hopefully itll clear up any misunderstanding >>83690230
wow some robots are pretty smartmost are retarded tho
