Linked Questions

10 votes
5 answers
1k views

Shouldn't statements be considered equivalent based on their meaning rather than truth tables?

Consider the following truth table, which serves to define the logical connective ⇔, P | Q || P⇔Q T | T || T T | F || F F | T || F F | F || T According to the above truth table, the logical ...
EthanAlvaree's user avatar
2 votes
4 answers
9k views

Why is it that when A is false and B is false, we infer that A->B is true?

Why is it that when A is false and B is false, we infer that A->B is true? If A isn't true then we don't know if maybe when it is true then B would be false. could be B would be true, could be it'd ...
barlop's user avatar
  • 291
5 votes
4 answers
3k views

Why do contradictions imply anything?

I got this from the thread Why are conditionals with false antecedents considered true? And this is what Stefan Perko answered. Suppose it is raining and it is not raining. Then it is raining. ...
MattaCuna's user avatar
2 votes
3 answers
4k views

In basic logic, if an argument contains a self-contradictory premise, how come the argument is valid?

I have started to attend the logic lectures. The lecture notes indicate that a "self-contradiction" is a statement that is always false. But why will it lead to a valid statement?
eric pang's user avatar
6 votes
3 answers
2k views

Intuitively, why are Universal Statements true in the Empty Universe?

Source: p 165. Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko. I read this on Math SE; please advise if it pertains to my simpler question.   One property of ...
user avatar
4 votes
4 answers
802 views

How can one intuit that P → Q ≡ ¬P ∨ (P ∧ Q)?

I have not succeeded in intuiting P → Q ≡ ¬P ∨ Q in the sense of imagining how one would conjecture or divine the equivalence without any "foreknowledge" of ¬P ∨ Q to invoke formal proofs or truth ...
user avatar
2 votes
2 answers
270 views

Can 'All S is P' ever be false if S is empty?

I'm self-learning logic, I'm stuck on an issue similar to this question: In modern logic, why does "All S is P" contradict "Some S is not P"? In the boolean interpretation 'All S ...
binarylegit's user avatar
0 votes
2 answers
250 views

Do mathematicians take Modern Logic to be an appropriate representation of our sense of logic?

What examples do we have of mathematicians who explicitly and publicly expressed their personal confidence that mainstream modern logic, as used in mathematics, either as object of study in itself or ...
Speakpigeon's user avatar
  • 7,502
-2 votes
6 answers
194 views

If false imples true then you can't make statements about real life? Confused [closed]

I might have rushed into this and have insufficient knowledge about logic, however i have yet to see anything online go against this. Though i am not foolish enough to believe I have 'broken' logic, I ...
Rolf Haugaland's user avatar
0 votes
0 answers
19 views

Tautology of p implies q and not p or q [duplicate]

I'm learning about tautologies right now. I see that a tautology is when two propositional statements have the same truth values. But I'm struggle with the truth table my professor provided about the ...
Lex_i's user avatar
  • 101