Beginners question on deductive conclusions/analytic propositions
How can the conclusion of a sound deductive argument be necessarily true if it is also the case that only analytic propositions are necessarily true?
"Socrates is mortal" is the conclusion of a sound deductive argument but it would seem to be a synthetic proposition (as are the premises it is validly inferred from) its denial implies no contradiction and so must be contingently true.
What am I missing here?.
"Socrates is mortal" is the conclusion of a sound deductive argument but it would seem to be a synthetic proposition (as are the premises it is validly inferred from) its denial implies no contradiction and so must be contingently true.
What am I missing here?.
Comments (9)
Socrates is a Greek
Therefore Socrates wears sandals.
Clearly the subject term Greek does not contain in its concept the predicate term "wears sandals" nor does the subject term Socrates contain either the predicate term "is Greek" or "wears sandals".
The above argument is valid and if its premises were true its conclusion would be necessarily true. It is the case premise 1 is false but that just proves premise 1 is a synthetic proposition if it were analytic it could not be false.
I don't know where you are getting the "sound deductive arguments" are "necessarily true" from.
As you pointed out soundness uses synthetic propositions and therefore is "technically" never "necessarily true".
The most cheritable way of reeding the statement (assuming it's from a credible source) is that it tries to point out that every sound argument needs a valid structure.
Or it is persumed that there exist Premisses that are True since the syntetic basis for them is strong enough to claim it to be True. F.e. the premiss "I exist".
Maybe it is a good way to illustrate the second case with a counter example. If you assume there are no Premises that can justifiably be called True the concept of soundness falls apart.
Maybe it's helpfull to conceptualize it as synthetic Truths being held to a different Standard. If they meet this standard they are True. Once we have accepted the premisses as True it follows due to the validity that the argument is sound and that in this regard the conclussion is "necessarily True"(assuming the premisses are True).
Maybe one can further add that the Debatte if Premisses are not True and if there exist True premisses is not part of logic. So it introduces a further aspect that allows Logic to model more specific differences if one assumes the premisses to be True. Meaning if you actually believe Sokrates is a man, and that all man are mortal you necassrily have to believe the synthetic proposition that sokrates is mortal.
"Deductive reasoning goes in the same direction as that of the conditionals, and links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true".
The italicised part of the quote is a link which takes you to the logical truth page where it says,
"A logical truth is a statement which is true, and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement".
So it sounds like whats being said is a valid argument with true premises (ie a sound argument)s conclusion is necessarily true and that necessarily true propositions are analytic propositions.
I understand if the argument is valid then it is "truth preserving" ie true premises will always give true conclusions, I guess its just the use of the term "necessarily true" especially if we are to insist (correctly) only analytic propositions are necessarily true.
Re this: "A logical truth is a statement which is true, and remains true under all reinterpretations of its components other than its logical constants. It is a type of analytic statement," what they're referring to there is a tautology. "Logical truth" is a term of art for tautologies.
Btw: I forgot to mention in my last reply that the function of defining something as True can be done in a tatological system regardless of the synthetic truth.
Assume we define all man are mortal. Now let's say there is something x that is man'ish but not mortal.
In a system that puts the emphasis on the synthetic truth we would have to correct the definition to: man can be mortal or immortal. (Cmp. All swans are white example)
However we could also put the emphasis on the existing definition viewing it as analytical statement which in turn leads to the statement x is not a man since x is not mortal.
So even more synthetic seeming statements can under a certain framework be understood as analytic propositions that we call axioms. If all men are mortal and socrates is a man are axioms(maybe not the best ones) the conclusion is necessarily True since they are threated as analytic propositions (because they are definitions).
The trouble is that the notion of 'contained in' is never defined, and unravels into a chaotic mess when one tries to pin it down.
"Necessarily" is used here informally, as an amplification. This should not be confused with necessity in modal logic (which does not figure in this context). All this means is that given the truth of the premises the conclusion of a valid argument cannot be anything but true. This doesn't make the conclusion unconditionally necessary - the italicized condition still applies.