I have a few questions about logical consequences with regards to logic,
1) Is logical consequences(1) what governs the reader of the argument during study of premises? If so how does that relate back to soundness(2) as I was under the impression that soundness refers to the semantics of the premises(not their truth value per se, but the meaning and if it is fitted together nicely) or is a logical consequence the "result" of the total argument, the conclusion because that doesn't seem to be any different than the term "conclusion"
Also is entailment synonymous with logical consequences or is it a different concept all together?
1)http://en.wikipedia.org/wiki/Entailment
2)http://en.wikipedia.org/wiki/Soundness
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Q. Is entailment synonymous with logical consequences or... (not)???
A. Almost:- e.g. "This conclusion is a logical consequence of these premises." Or, alternatively:- e.g. "These premises entail this conclusion." 2 sentences are not "synonyms" but these 2 sentences mean the same thing. That is why I said "almost".
"Consequence" means "with-sequence". So the technically correct use of the term "consequence" relates to "antecedents" and "consequents", where the premises of an argument are the antecedents and the conclusion is the consequent. In sum, "entailment" and "logical consequences" are either corollary or almost identical "concepts".
Q. Is logical consequences (1) what governs the reader of the argument during the study of the premises?
A. Only if the reader is a logical person and governed by the rules of logic when s/he reads the premises. BUT, many beginners at logic find it difficult to disentangle premises from conclusions. So it is difficult for them to discern the logical (or illogical; a.k.a. fallacious) sequence (or "non-sequence"; also called a "non-sequitur") of any given argument, whether valid or fallacious. But, again, MORE DIRECTLY, logical sequence or consequence would govern a logical reader who studies premises. And they would say alternatively:- That follows (has logical sequence) or That does not follow (has no logical sequence) from these premises.
Q. If so, how does that relate back to soundness?
A. Soundness means not only that the SEQUENCE or ENTAILMENT "holds" [the argument is valid; the rules of logic hold] but also that the premises and conclusion are true. Soundness does not merely mean TRUE PREMISES and TRUE CONCLUSION, because, sometimes, even though premises and conclusion are true, an argument may not be sound, when/if it lacks logical validity or sequence. For example, the following argument seems to be a syllogism, but is a fallacy called the fallacy of an undistributed middle term. Every premise is TRUE as is the alleged "conclusion" also TRUE. But the conclusion is not a logical consequence of the advanced premises
Every cat is an animal (true) [major premise]
Every tiger is an animal (true) [minor premise]
"Therefore" every tiger is a cat. (true) [conclusion; which does not follow]
The middle term, "animal", is taken particulary or "undistributed" as the predicate of a universal affirmative proposition, according to the rules of logic. So there is no logical sequence between premises and conclusion. The argument is a fallacy with no logical sequence. The conclusion, though true, is not a logical consequence of the advanced premises. So "truth" does not guarantee "soundness" in an argument. But when you have both a valid argument and true premises, the conclusion is true and the argument is, then, "sound".
The fallacy of undistributed middle is far more evident in a similar argument.
Every man is an animal [rational animal] (true)
Every pig is an animal [non-rational animal] (true)
"Therefore" Every pig is a man. [false; fallacy of undistributed middle]
Q. (2) As I was under the impression that soundness refers to the semantics of the premises (not their truth value per se, but the meaning and if it is fitted together nicely) or is logical consequence the result of the total argument, the conclusion because that doesn't seem to any different than the term "conclusion"?
A. Validity deals with the "form", or "sequence" of an argument, including the meaning of the premises and the conclusion and how a conclusion "fits" (is a consequent of the premises) or does not "fit" (is a non-consequent or non-sequitur), to use your "fitted together nicely" phrase. Validity (logical argument structure) seems to be the term you are missing and deals with the "logical fitness" of an argument structure. So when you have both "fit argument structure" (validity) and true premises, then you have a "sound argument". But you can have a perfectly valid argument, without true premises, in which case your argument will be valid [following logical sequence] but UNsound.
eg. Every animal is a vertebrate (has a spine) [false; since worms are animals without vertebra]
Every cabbage is an animal [false]
Therefore every cabbage is a vertebrate [false]
But this argument is valid [fits logically] despite both false premises and a false conclusion. The conclusion does "follow" from the premises or, put alternatively, is a false "logical consequent" of the false "antecedent" premises.
Kevin
Soundness is PRECISELY the truth value, and has nothing to do with semantics. It has to do with "correspondence" to facts as they are known.
For example, I can make a VALID argument about the existence of blue unicorns, merely by following the rules that govern what is valid or not.
But obviously they don't exist, and therefore the argument is not sound.
In our common sense world, we use Aristotelian logic. That logic has very specific rules, and when followed, they always lead to valid arguments. (Not necessarily "sound" arguments--even some of Aristotle's own were not "sound", such as his astronomy.)
A person who says "the universe should not exist" is breaking the rules of logic. When you see contradictions, it means that one or more of the premises is faulty.
Formed properly, logic is always "valid". "Formed properly" is absolutely operative.
But to be "sound", the premises and conclusion must also be "true according to the fact of reality as known through the correspondence theory"--which is the basis of Aristotelian common logic.
This chart shows the true and false forms of all syllogisms--256 of them. No human can think outside of those 256, because no others exist. Aristotle found them all.
http://www.vaughns-1-pagers.com/philosop%E2%80%A6
If you can defeat an argument, then you have proved your own logic is "logical" (valid), and you have used "defeasors". https://docs.google.com/viewer?a=v&q=cac%E2%80%A6
What...? Soundness definitely have to do with truth value. And yes, logical consequence is what creates the proper understanding of the premise.
1), The eloquence of the Author to capture the readers attention and presenting something new that the reader has never read before.
2.) Real life experiences will be sure to capture the readers attention.
3.) There has to be a conclusion in every story and it is best that it be positive.