Thats NOT an arguemnt. Its a single statement.
As is your summary of your "argument".
That´s why I said it was the short version.
Well, it may be classed as an enthymeme (an argument wit absent premises) but I would like to see it reasoned through explicitally.
Well, I could follow your example and find some definitions that define my understanding of "meaning" correct - but I find that boring. For me it´s more about contemplating and investigating concepts than semantic proofs.
In any case (although I wuold still like to see your "collapse" argument in complete a more complete form)
I am afraid I can´t do that because the most basic axioms of logic are involved. That´s my very point. "A is not non-A" is the most basic axiom of logic. The explicit denial of this axiom throws you out of the realm of logic.
AFAIK in logic a contradiction
is regarded as being
false:
In any case AFAIK in logic a contradiction is regarded as being false:
"(Philosophy / Logic)
Logic a statement that is false under all circumstances; necessary falsehood"
contradiction - definition of contradiction by the Free Online Dictionary, Thesaurus and Encyclopedia.
Great, you have found one doctionary that says so. There are many philosoophies out there, and one single dictionary claim certainly doesn´t cover all the philosophical approaches that are out there.
Like always, you are more concerned with words than with content. If by all means you want to collect definitions that define "A=nonA" as false, be my guest.
To me such a statement is not meaningful. And I am trying to tell you why I think this is the more appropriate stance. You can hold all dictionaries against me but it won´t help you understand my point.
I am postulating that of two contradictory statements at least one must be false. The German Wikipedia entry "Widerspruch/Kontradiktion" e.g. starts with this very statement:
Kontradiktorisch (
widersprüchlich) wird eine Beziehung zweier
Aussagen genannt, bei der von der Wahrheit der einen Aussage auf die Falschheit der anderen geschlossen werden kann und – das ist wichtig – von der Falschheit der einen Aussage auf die Wahrheit der anderen.
Translation:
"Contradictory is the term for a relation of two statements in which from the correctness (truthfulness) of one of them can be concluded on the incorrectness (falsehood) of the other."
Later it emphasizes that logic considers the whole statement false
for merely formal-logic reasons ("aus formal-logischen Gründen"). This implies that the statement needn´t be understood/understandable or be meaningful for concluding that it´s a contradiction (an argument of mine that I have given you several times and that I happen to find supported here).
Personally, I think that declaring the contradictory statement merely "false" because one of the components is false may be formally ok, but it doesn´t catch the tragic of what actually going on here (and no dictionary entry will change my mind about that).
As far as I know, that is also wrong. See the
principle of explosion (logic).
Cool and interesting link. Thank you!
It pretty much confirms my thoughts about the issue. This "explosion" is what I was describing as the collapse of logic: everything can mean anything. And since the primary premise and purpose of logic is distinguishability (is that even a word?), the fact that everything means everything comes down to "everything means nothing".
This "explosion" also allows for the conclusion that true things are false, and thereby throws your criterion "truth apt" out of the window. It allows for "illogicality can be logical" and therefore throws logic out the window.
It is the destruction of the very formal system it employs (no matter whether you call it "collapse" or "explosion" into meaninglessness not only of the symbols used explicitly in the contradiction but also of any symbols of the formal system employed).
Now, you may be correct in that your link proves that this can be done (or that people have been trying to do that), but on the other hand the result of such an attempt proves exactly what I have been trying to say all the time.
On another note: Under "Addressing the principle" you find a great variety of approaches of dealing with this problem - and this variety demonstrates that your approach based on the definition you prefer is just one of several philosophical ways.
And just because it caught my eye: Under "see also" you will find
which is puts a huge question mark behind the definition of "proposition" you have offered: "This is black" cannot be true and not true ("this is not black"), and therefore (according to the the above definition "black can be non-black" is
not a proposition).
