I see the sorites paradox as a very serious problem, not a logical fallacy that's easy to diagnose and fix. The paradox arises whenever we have clear cases at the extremes but no known line separating the cases where a concept applies from the cases where the concept doesn't apply. Clearly, 1 grape isn't enough to compose a bunch of grapes. Just as clearly, 100 grapes is enough to compose a bunch of grapes. So which number between 2 and 100 is the smallest number of grapes sufficient to compose a bunch of grapes? If there's no correct answer, then the sorites paradox shows that the concept enough grapes to compose bunch of grapes is an inconsistent concept. But inconsistent concepts, such as the concept colorless red object , necessarily never apply to anything, in which case it would be impossible for anything to be a bunch of grapes. One might reply, "Okay, fine. Necessarily there are no bunches of grapes. Life goes on." The problem, however, is that the sorites paradox applies to every vague...

I'm no expert on Wittgenstein, and I don't know the particular argument of his that you're alluding to. He does give a famous argument that anything properly regarded as a language must be usable (if not also used) by more than one person. But your question is about something else: whether a being can think without possessing language, or maybe whether a being can have thoughts with no linguistic content . I think the clearest reason for answering "yes" is given by the problem-solving behavior of non-human animals to whom we have no reason to attribute language. Mice seem able to solve mazes, octopuses can figure out and open screw-top jars, and so on, yet it seems a stretch to attribute language to them. When an octopus encounters, for the first time ever, a closed glass jar containing attractive prey, which linguistic resources or concepts must it use when it figures out how to remove the screw top? What sort of linguistic content is the octopus representing to itself? None that I can imagine....

In my opinion, the reasoning that generates the paradox of Achilles and the tortoise isn't nearly as compelling as the reasoning that generates the sorites paradox. The Achilles reasoning overlooks the simple fact that Achilles and the tortoise are travelling at different speeds : if you graph the motion of each of them, with one axis for distance and the other axis for elapsed time, the two curves will eventually cross and then diverge as Achilles pulls farther and farther ahead of the tortoise. All of this is compatible with the fact that, for any point along the path that's within the tortoise's head start, the tortoise will have moved on by the time Achilles reaches that point: that's just what it means for the tortoise to have a head start. It's not that the Achilles reasoning is good at the micro level but bad at the macro level. It's just bad. By contrast, the only thing overlooked by the sorites reasoning is the principle that a small quantitative change (e.g., the loss of one grain of...

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...

I'm inclined to say that all concrete objects are contingent. But those who believe that God exists noncontingently would likely disagree, because according to standard versions of theism God is a concrete object, since God has causal power. But I'm inclined to say that not all contingent objects are concrete. The Eiffel Tower is a concrete object, whereas the set whose only member is the Eiffel Tower -- the set {The Eiffel Tower} -- is an abstract object, as all sets are. The identity of any set depends solely on its membership: had any member of a given set failed to exist, then the set itself would have failed to exist. Therefore, because the Eiffel Tower exists only contingently, the non-empty set {The Eiffel Tower} itself exists only contingently. Indeed, any set containing at least one contingent member is itself a contingent, abstract object. Or so it seems to me.

I recommend that you read this and this and see if you think they imply each other.

One might mean either of two things by "infinitely divisible time." One might mean merely that (1) any nonzero interval of time can in principle be divided into smaller and smaller units indefinitely: what's sometimes called a "potentially infinite" collection of units of time each of which has nonzero duration. Or one might mean that (2) any nonzero interval of time actually consists of infinitely many -- indeed, continuum many -- instants of time each of which has literally zero duration: what's sometimes called an "actually infinite" collection of instants. I myself favor (2), and I see no good reason not to favor (2) over (1). Both views of time are controversial among philosophers, and some physicists conjecture that both views are false (they conjecture that an indivisible but nonzero unit of time exists: the "chronon"). But let's apply (2) to the time of a person's death. Classical logic implies that if anyone goes from being alive to no longer being alive, then there's either (L) a last time at...

Three points: 1. It's not clear that the project of eliminating all of our presuppositions even makes sense. For instance: Could we coherently try to eliminate our presupposition that eliminating a given presupposition is inconsistent with keeping that presupposition? I can't see how. Indeed, Descartes himself seems ambivalent about the possibility, or desirability, of eliminating all of our presuppositions, because in his work he frequently appeals to unargued-for principles that, he says, "the natural light" simply shows us must be true. 2. Your argument for the claim that "Answering skepticism should be [a] priority in philosophical research" relies on this premise: Descartes was correct to claim that no belief is justified if it can be subjected to any doubt. Most philosophers, now and in Descartes's time, would reject that condition on justified belief as far too strict. They would challenge Descartes to derive that strict condition from a recognizable concept of justified belief, rather...

The problem simply recurs with the phrase "at the base camp" in your definition: Which millimeters of terrain belong to the base camp, and which do not? At the limit, nobody knows. But unless there is a sharp cutoff between those millimeters that belong to the base camp and those that do not, the sorites paradox shows that the phrase "at the base camp" has logically inconsistent conditions of application, and therefore either nothing is at the base camp or the entire earth is at the base camp. I see no hope of solving the sorites paradox for one vague phrase, such as "Mt. Everest" or "a heap," by appealing to some other vague phrase, such as "at the base camp or higher" or "what someone I'm communicating with recognizes to be a heap." If only it were that easy.