It's not clear to me what you're asking, but I'll do my best. Given a particular conclusion, we can, normally, trace it back to the very basic premises that constitute it. I doubt we can do that without seeing the conclusion in the context of the actual premises used to derive it. The conclusion Socrates is mortal follows from the premises All men are mortal and Socrates is a man , but it also follows from the premises All primates are mortal and Socrates is a primate . So which pair of premises are "the very basic premises" for that conclusion? Outside of the actual argument context, the question has no answer. I don't know what you mean by "the root of a conclusion," but you seem to be suggesting that any knowledge is impure if it depends on -- or if it was acquired using -- any reasoning at all. Perhaps the term inferential would be a better label for such knowledge. On this view, even if I have direct knowledge that I am in pain (when I am), I have only...

You've asked a very good question, and your final sentence makes a good point. Those who defend one or another non-classical system of logic (paraconsistent, dialetheistic, intuitionistic, fuzzy, quantum, etc.) insist that they're not simply choosing a system of logic on a whim or merely out of convenience. Instead, they say, we're forced to accept non-classical logic because (a) it's an objective fact that arbitrary contradictions don't imply every proposition; because (b) some propositions are objectively both true and false; because (c) some propositions are objectively neither true nor false; because (d) some tautologies aren't completely true and some contradictions aren't completely false; because (e) the data gleaned from reliable experiments don't obey the classical laws of distribution, etc. Having looked into them, I find none of their arguments for (a)-(e) persuasive. But what's most interesting, as various philosophers have observed, is that the defenders of non-classical logic sooner or...

Validity in an argument comes down to one question: Is it possible for all the argument's premises to be true and its conclusion false? If no, then the argument is valid. So, assuming it is impossible for Oscar to be both a whale and a zebra, the argument is valid. Even so, the argument is not formally valid, because the following is not a valid form: Octopus(Oscar) or Whale(Oscar) Zebra(Oscar) Therefore: Octopus(Oscar) Not all valid arguments are formally valid. Furthermore, assuming that Oscar is not both an octopus and a zebra, the argument is unsound despite being valid, because in that case the second premise and the conclusion are not both true. The same holds for this argument (on similar assumptions): Oscar is an octopus, or Oscar is a whale. Oscar is a zebra. Therefore: Oscar is a whale. Valid but unsound. So neither argument establishes its conclusion.

In my experience, philosophy courses take the explicit, self-conscious formulation and evaluation of arguments (i.e., reasoning) more seriously than any other courses of study, with the possible exception of those math courses that emphasize proofs. Moreover, the breadth and depth of philosophical problems exceed those encountered in math. Therein lie the advantages of philosophy courses as compared to, say, math or economics courses. If you pursue philosophy, I think you'll discover that the standards of argumentative rigor expected in philosophy courses surpass -- sometimes by far -- the standards of rigor expected in any courses outside of math, and again they're applied to a much more varied, and often deeper, set of questions.

None that I can think of, including none of the candidates that I've seen offered by "dialetheists" (i.e., philosophers who say that some contradictions are true). If you have any promising candidates, please let us know!

As far as I can see, the definitive property of the empty set is not nothingness but instead emptiness : It's the one and only set having (containing, possessing) no members at all. The empty set can be empty, in that sense, without itself being nothing. So I see no threat of contradiction here. Indeed, the empty set can belong to a non-empty set, such as the set { { } } , which couldn't happen if the empty set were nothing.

Does logic rule out the possibility that someone could travel into the past and affect events so that they turn out otherwise than we remember them? No, because our memory of those events could be mistaken. But: Does logic rule out the possibility that someone could travel into the past and affect events so that they turn out otherwise than they in fact did? Yes, so far as I can see.

As you suggest, all logical arguments (and hence all derivations) depend at least implicitly on laws of logic. So I can't see any way of deriving any law of logic without relying on other laws of logic. Nevertheless, we can derive every law of logic, provided we're allowed to use other laws of logic in our derivation. We needn't fret about our inability to derive a law of logic while relying on no laws of logic, because the demand that we do so is simply incoherent.

I'd say that they have different meanings. I interpret (a) as implying that your feeling better tomorrow is a sufficient condition (all else equal, presumably) for your going out, whereas (b) implies that your feeling better tomorrow is a necessary but maybe not sufficient condition for your going out. That is, (b) seems more cautious, more hedged: (b) allows that you may not go out even if you do feel better tomorrow. Compare: (c) If you feed your pet goldfish, it will flourish; (d) Unless you feed your pet goldfish, it won't flourish. Given how easy it is to overfeed a pet goldfish, (c) is doubtful: your pet goldfish may not flourish even if you feed it. Given that pet goldfish depend on being fed, (d) isn't at all doubtful.

Your question concerns the classical law of excluded middle (LEM): For any proposition P, either P or not P. Because logic is absolutely fundamental, ceasing to rely on LEM will have ramifications that are both widespread and deep. In classical logic, we can derive LEM from the law of noncontradiction (LNC), so to give up LEM is to give up LNC or the equally obvious laws that allow us to derive LEM from LNC. We should be very reluctant to do that. In my view, the alleged possibilities that you cite from physics are not enough to overcome that reluctance. First, they are possibilities only according to some, not all, interpretations of quantum mechanics. Second, even if we accept them as possibilities, rejecting LEM or LNC is more costly than (1) reconceiving "being dead" and "being alive" so that they name logically compatible conditions and (2) reconceiving "being here at time t " and "being elsewhere at time t " so that they name logically compatible conditions. It's less costly to mess with the...