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Can you coherently consistently imagine a universe where laws of thoughts are false?

If by "laws of thoughts" you mean laws of logic, then no. No coherent (that is, self-consistent) situation can violate any law of logic. Even philosophers, such as Graham Priest, who claim to be able to imagine situations that violate the law of non-contradiction concede that those situations are not self-consistent.

In a reply to a question about the sorites paradox, Professor Maitzen writes: "Logic requires there to be a sharp cutoff in between those clear cases -- a line that separates having enough leaves to be a head of lettuce from having too few leaves to be a head of lettuce. Or else there couldn't possibly be heads of lettuce." However, there is no justification that clearly leads from his premise to his conclusion: obviously we can have heaps of sand without knowing exactly how many grains of sand are required to distinguish a "heap" from a pile of individual sand grains, or else there would not be a so-called "paradox" in the first place! The premise as he presents it sounds like a tautology, not a logical argument. What makes a "heap" of sand is not only how many grains of sand there are, but also how those grains are arranged. If you took a "heap" of sand and stretched it out in a line, you would have the same number of grains, but it would no longer be a "heap." You could take a head of lettuce...

What makes a "heap" of sand is not only how many grains of sand there are, but also how those grains are arranged. If you took a "heap" of sand and stretched it out in a line, you would have the same number of grains, but it would no longer be a "heap." Agreed! Even so, there must be a sharp cutoff between (a) enough grains to make a heap of sand if they're arranged properly and (b) too few grains to make a heap of sand no matter how they're arranged. An instance of (a) would be 1 billion; an instance of (b) would be 1. Why must there be a sharp cutoff between (a) and (b)? Because otherwise (a) can be shown to apply to 1 (which clearly it doesn't) or (b) can be shown to apply to 1 billion (which clearly it doesn't). That's what the sorites argument shows. ...obviously we can have heaps of sand without knowing exactly how many grains of sand are required to distinguish a "heap" from a pile of individual sand grains, or else there would not be a so-called "paradox" in the first place! You seem...

Is the Sorites paradox really a paradox, or is it more properly considered to be a logical fallacy? By definition, the term "heap" is indeterminate. Yet the Sorites paradox tries to force a specific definition on what is by design an indeterminate concept: the very idea of defining the term "heap" as a specific number of grains of sand is fallacious, is it not? I don't see a paradox here as much as I see confusion about how terms are defined. How many grapes are in a bunch of grapes? How many leaves are in a head of lettuce? How many grains are in an ear of corn? How many chips are in a bag of potato chips? in each of the above questions, the answer will vary from one example to the next, the exact number is not particularly germane to the concept. So what makes a heap different from a bunch or any of the other examples?

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...

My understanding is that philosophers like Wittgenstein held that thought without language is impossible. I've seen many people reply that they have non-linguistic thoughts all the time, and my guess is that what they mean is that they often "think" in imagery rather than words. For example, rather than saying with their inner voice, "I should advance my pawn," they picture a chess board with a pawn moving forward. Does this demonstrate non-linguistic thought?

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....

For some reason, the sorites paradox seems quite a bit like the supposed paradox of Achilles and the turtle with a head start: every time Achilles reaches where the turtle had been, the turtle moves a little bit forward, and so by that line of reasoning, Achilles will never be able to reach the turtle. Yet, when we watch Achilles chase the turtle in real life, he catches it and passes it with ease. By shifting the level of perspective from the molecular to the macro level, so to speak, we move beyond the paradox into a practical solution. If we try to define "heap" by specifying the exact number of grains of sand it takes to differentiate between "x grains of sand" and "a heap of sand," aren't we merely perpetuating the same fallacy, albeit in a different way, by saying that every time Achilles reaches where the turtle had been, the turtle has moved on from there? If not, how are the two situations qualitatively different? Thanks.

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...

Given a particular conclusion, we can, normally, trace it back to the very basic premises that constitute it. The entire process of reaching such a conclusion(or stripping it to its basic constituents) is based on logic(reason). So, however primitive a premise may be, we don't seem to reach the "root" of a conclusion. Do you believe that goes on to show that we are not to ever acquire "pure knowledge"? That is, do you think there is a way around perceiving truths through a, so to say, prism of reasoning, in which case, nothing is to be trusted?

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...

Logic is supposed to be an objective foundation of all knowledge. But if that's the case then why are there multiple systems of logic? For example there's 'dialetheism', which allows for true contradictions, and 'fuzzy logic' in which the law of excluded middle does not apply. If people can just re-write the rules to create their own system of logic, then doesn't that make logic subjective and arbitrary? It doesn't seem like arguments would have much weight if I could simply just choose whichever system best supports the conclusion I want.

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...

Are all concrete objects contingent objects and all abstract objects noncontingent objects? Thank you!

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.

"Infinity" poses a ton of problems for both science and philosophy, I'm sure, but I would like to ask about a very particular aspect of this problem. What ideas are out there right now about infinitely divisible time and human death? If hours, minutes, seconds, half-seconds, can be cut down perpetually, what does this mean for my "time of death"?

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...

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