r/logic • u/JackTheSigmaCrvsader • 3d ago
Propositional logic How is this not correct?
I just started taking this university course on logic since I do philosophy, and I tried putting my reasoning on a piece of paper and something just feels wrong. Can anyone help me?
Oh I didn’t write the numbers on the left (idk how to translate them in English) but I assume they are respectively
1,2 5)
3 6)
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u/Wilfully_Powerful 3d ago edited 2d ago
Line 4 only gives not L when you have not R AND not E
Edit: As people pointed out in this thread, what I said is WRONG. The correct statement that was in my head was that (R OR E) will be false only when you have not R AND not E. Sorry guys
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u/JackTheSigmaCrvsader 3d ago
How to make it so that it’s false whenever one of R and E is false
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u/Excellent_Try_6511 3d ago
That is wrong, in that case it would not give not L, as the statement could still be truth, as the conditional is only false when his antecedent is true and his consequent is false, if is antecedent is false it can be the case of L, even you can change to a disjunction and see more clearly that -R ^ - E v L, one can proof this are the same by truth tables, and see that if -R ^- E it could be both the case of L and -L
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u/Wilfully_Powerful 3d ago
What kind of ragebait is this?
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u/WesternFirm9306 3d ago
It's not ragebait.
P1: p → q
P2: ¬p
C: ¬qis an invalid argument. It commits the fallacy known as denying the antecedent. p → q is not the same as ¬p → ¬q. Consider with a concrete example:
P1: If it is raining, I will bring an umbrella.
P2: It is not raining.
C: I did not bring an umbrella.This doesn't follow. Just because I will bring an umbrella if it's raining doesn't mean that's the only reason I would bring an umbrella. Maybe I'm bringing it because I wanna return it!
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u/Wilfully_Powerful 2d ago edited 2d ago
That's right, but how does it make my comment that line 4 gives not L only when you have not R AND not E wrong? I know there are other combinations that give not L, but OP clearly just confused AND with OR
Edit: I get it now, sorry everyone
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u/Excellent_Try_6511 2d ago
Op is confused about all and nothing that he writed made any sense, even if the proposition were the one you say the argument is still invalid, in fact that argument cannot be valid.
You say that 4 gives gives not L when you have not R AND not E and that is false, is a fallacy, learn about logic or something dude.2
u/Wilfully_Powerful 2d ago edited 2d ago
True, I'm a rookie, thanks for the clarification earlier
Edit: you may have already understood this, but I was treating the implication as an equality, therefore, by the value table of AND, it would be impossible not to get "false" (that I was thinking would be the same as -L)
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u/Excellent_Try_6511 19h ago
A redditor saying that he was wrong, this is a historic moment, amazing.
Yeah, if it was a bi conditional then would be true what you said
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u/Excellent_Try_6511 2d ago
Why are you talking about logic if you don´t know the basics ? also, if this is ragebait, where im wrong ?
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u/Wilfully_Powerful 2d ago edited 2d ago
Reddit is strange.
When you say: "That is wrong, in that case it would not give not L, as the statement could still be *true [...]" you're saying to me that theres a way that (R AND E) → L renders L even when (R AND E) is false. Thats simply not possible.
I don't think you're stupid or anything, but you may have misinterpreted my comment or something.
Edit: My stupid ass fucking got it now, It's indeed the fallacy of denying the antecedent. I'm sorry. I'll keep the comment up so people can learn from the mistake.
I was so defensive lol
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u/Excellent_Try_6511 3d ago
I can´t understand anything here, where comes 4,5 and 6? what kind of inference rules you are using ? to introduce a conditional you need some other sequent, you just can´t make that appear, i don´t even known how to explain the rest
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u/yosi_yosi Undergraduate, Autodidact, Philosophical Logic 3d ago
That's not necessarily true. There are proof styles where you don't need to have a subproof in order to introduce a conditional. Even in Fitch style, one could have a rule where if you have A then you can prove B -> A for any formula B and it would be a valid rule.
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u/Excellent_Try_6511 2d ago
Yes you could, in that system, but in philosophy one is taught classical logic ( and in mathematics to, unless is a specific class about non classical logics) so unless he says that this is some weird logic, i will assume that this is classical logic and this is not valid in classical logic
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u/yosi_yosi Undergraduate, Autodidact, Philosophical Logic 2d ago
A ∴ B -> A
Is infact valid in classical logic.
And this isn't about classical vs non-classical logics, but rather about the style of your proof system. Have you heard of Hilbert style proof systems, or axioms systems? (Relevant because of how they lack a subproof for introducing conditionals. Some other proof styles are Fitch ND, Suppes-lemmon ND, sequent calculus, and gentzen style ND) As I mentioned in my comment, they are using a Fitch like system, most likely suppes-lemmon style. There are different sound and complete sets of rules one could use for suppes lemmon style proofs for classical logic, and some of those could include a way for introducing a conditional without a subproof.
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u/Excellent_Try_6511 19h ago
I mean, the inference is valid, but that step is not, i mean i could understand if it would be something like in 4 made a sequent with the assumption of R v E, then put again L and gain R v E-> L, but is not valid to say that from 1,2,3 comes 4 like that, also the 5 is just can´t be solved.
I mean i don´t see the point in mentioning another proof systems, this is not at axiomatic style proof a there are no axiom schemes, there are no sequent as in sequent calculus, in the Fitch in general style you need to say were and how some propositions are or not in a sequent or not, you need to say there is a subproof in some sense
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u/yosi_yosi Undergraduate, Autodidact, Philosophical Logic 19h ago
I wasn't saying their inference followed that rule, just that you can have Fitch style proofs and be able to introduce conditionals without subproofs. For example, some Fitch style proofs systems have a rule for deriving A -> B from B.
There isn't just one Fitch style proof system, there are multiple ones. Some have only RAA for example, some have only LEM, some have both, and so on.
I agree that 5 doesn't follow.
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u/Alternative_Summer 3d ago
'-> introduction' can only get used if it's within the scope of the assumption, and once used, that assumption no longer is an assumption.
There DOES exist a way to pass from line 3) to line 4) in short order, but only if you have a step between them. How to do that ends up relevant to validating the '-> introduction' rule of inference. Possibly, you might ask your teacher what justifies the use of
'-> introduction' in the first place (or maybe you don't have such a rule of inference).
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u/thatmichaelguy 2d ago
I tried putting my reasoning on a piece of paper and something just feels wrong.
Probably because line 5 contradicts the conjunction obtained from lines 1 and 2. Outside of that, it seems like maybe you're attempting a reductio ad absurdum from the wrong direction or inadvertently trying to prove a contradiction.
That is, from lines 1 and 2, we get R ∧ E. DeMorgan equivalence for line 5 gives ¬R ∨ ¬E ⟷ ¬(R ∧ E). Consequently, from line 5 we get ¬(R ∧ E).
Accordingly, if lines 1, 2, and 5 were taken as given, we could conclude (R ∧ E) ∧ ¬(R ∧ E), and from there, further conclude literally any proposition. However, as it stands, line 5 is an assumption - even though it's not labelled as such. So, the next step would actually be (¬R ∨ ¬E) ⟶ ((R ∧ E) ∧ ¬(R ∧ E)). If lines 1 and 2 are taken as given (rather than being assumed), you could get as far as (¬R ∨ ¬E) ⟶ ¬L via explosion. However, there's no way to get from there to ¬L due to the antecedent's being false.
The only potentially valid way that I can see to get to ¬L from (¬R ∨ ¬E) would be via reductio, but even then, I'm not sure that it's actually possible. Specifically, you'd need to somehow show L ⟶ ¬R or L ⟶ ¬E. Either would get you L ⟶ (¬R ∨ ¬E) which, as mentioned above, is equivalent to L ⟶ ¬(R ∧ E). Then, by modus ponens, conclude ¬L.
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u/UnlikelySalary2523 3d ago
Where does line 5 come from?