browser32 wrote:If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). Since anything follows from a contradiction, it follows that the statement is true. Thus the statement is a member of the set of true statements.
Faust wrote:Firstly, FJ, anything does follow from a contradiction.
If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). Since anything follows from a contradiction,
Ah, so if you assume a contradictory statement is true then anything follows.
"Since anything follows [if you assume a contradiction is true]..." <- we don't assume that, so everything he said after that is based on an assumption that we're not making.
browser32 wrote:Consider the following argument:
If a statement is true, then it is a member of the set of true statements.
If a statement is false, then it implies a contradiction (as we find in a proof by contradiction). If A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes, and it follows that the statement is true.
A statement thus is either true and true only, or both true and false.
I'm going to replace "Anything follows from a contradiction" with what you said that actually means, since that's such a vague phrase. GOD I HATE THAT PHRASE
If A is both true and false, at the same time and in the same place, then truth values, as used in classical logic, have no meaning, so anything goes, and it follows that the statement is true.
Anything goes if A is both true and false, sure, but why do we assume that A is both true and false? We don't.
The context is given by the OP. You're saying the context is out of context...
I don't think it's useful to divorce logic completely from truth like that, because logic doesn't just exist in a vacuum. It's used to determine what's true and what isn't.
Truth and logic are inextricably linked, and if they're not then logic is pointless and self-referential (I don't think it is, but you seem to, which makes it extra-weird that you insist on keeping this convo about logic in itself and not about truth, as that would make the whole conversation likewise pointless).
Mind you, I understand that a valid argument doesn't necessarily provide a true conclusion, I'm not saying that logic is synonymous with truth, but I am saying that it's really kinda pointless to talk about logic if logic can't be used to determine what's true.
Faust wrote:...correct reasoning.
Flannel Jesus wrote:Faust wrote:...correct reasoning.
correct in relation to what?
reality
formal logic
Definition
Classical or traditional system of determining the validity or invalidity of a conclusion (inference) deduced from two or more statements (premises). Based on the theory of syllogism of the Greek philosopher Aristotle (384-322 BC) systematized in his book 'Organon,' its focus is not on what is stated (the content) but on the structure (form) of the argument and the validity of the inference drawn from the premises of the argument-if the premises are true then the inference (also called logical consequence) must also be true. The basic principles of formal logic are (1) Principle of identity: if a statement is true then it is true. (2) Principle of excluded middle: a statement is either true or false. (3) Principle of contradiction: no statement can be both true and false at the same time. Also called Aristotelian logic. See also fuzzy logic and symbolic logic.
i understand that, you misunderstood what i meant.
the reasoning itself is correct because it works in reality. i'm not talking about specific premises or specific conclusions.
the reason logic is even something people consider is because it can be used to take true premises and reach true conclusions in reality. if logic couldn't do that, nobody would give a shit about logic because it wouldn't mean anything or matter at all in reality.
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