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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...

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...

In the Stanford Encyclopedia the predicate "is on Mt. Everest" is given as an example of the sorites paradox applied to a physical object--where does Everest end and another geological formation begin? It seems to me that people who climb Mt. Everest (including Sherpas who live in the area) know that the base camp is where Everest begins. The millimeter objection in the article seems arbitrary. Why not an operational definition of "being on Everest is at or higher than the base camp used to reach the summit"? I have no problem accepting that as fact. Likewise, if I describe something as a "heap", and the person I'm communicating with recognizes it as such, what difference does it make how many units are in it?

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.

When you look at non-human animal communication, for instance birds and cats, you can explain what's going on simply in terms of cause and effect. Now, human language is more complex, but if you happen to have determinist beliefs, at some level you believe it's all cause and effect, right? So, when describing why and how people use words, would an ideal observer need to talk about the meanings of words at all, or would the concept of meaning drop out as unnecessary?

Since no one else has answered your question, I'll chime in. I confess that I find it hard to see how any explanation of human communication purely at the level of (say) sounds and scribbles, with no reference to the meaning conveyed by sounds and scribbles, could avoid leaving out something important. But I'm no expert on this topic, so all I can do is recommend reading the SEP entry on "Eliminative Materialism," found here . I'm going to read it now myself.

Do words only have the power that we give them?

By "power" in this context, I take it you're referring to the psychological, rhetorical, or political power of words. I can't see any source of such power except us humans. That isn't to say that the power is unreal, only that words possess no internal magic, contrary to what humans in general used to (and some still) believe. Nor is it to say that any individual can render words powerless simply by deciding to. A racial slur, for instance, might induce people to physically harm the person targeted by the slur even if the person targeted decides to regard the slur as having no power over him or her.

Do these two sentences mean the same thing?- a) If I feel better tomorrow, I'll go out. b) Unless I feel better tomorrow, I won't go out.

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.

I'm 16 and have been studying philosophy for awhile. My question is when does a statement reach the point of 'absurdity'. For example, of the two statements, 1) My dog ran around the yard. And 2) My dog ran around the block with a big purple hat and green trousers. Number 2 seems the most likely not to have happened or seems 'ridiculous' by those who hear it. At what point does a statement cross the line of making logicalls sense to pure ridiculousness?

All else being equal, "My dog ran around the block wearing a big purple hat and green trousers" is far-fetched and unlikely to be true. But I wouldn't classify it as absurd in the logical sense, i.e., as making no logical sense. On the contrary, I think I can imagine (i.e., mentally picture) that amusing scenario. Now, if you were to claim that your dog ran around the block wearing colorless, entirely green trousers, I would classify your statement as logically absurd in the sense that it's logically self-inconsistent: it's logically impossible for anything, including trousers, to be both colorless and entirely green. So I'd say that something like logical self-inconsistency is the mark of a statement that has crossed the line into genuine absurdity. It's great to hear that, at 16, you've already been studying philosophy. I hope you'll keep doing so!

Why is the sorites problem a "paradox"? Isn't it fundamentally a problem of definition?

The sorites problem is a paradox for the reason that any problem is a paradox: it's an argument that leads from apparently true premises to an apparently false conclusion by means of apparently valid inferences. I don't think it's fundamentally a problem of definition, because the concepts that generate sorites paradoxes would be useless to us if they were redefined precisely enough to avoid sorites paradoxes. Take the concept tall man . In order to make that concept immune to the sorites, we'd have to define it in terms that are precise to no more than 1 millimeter of height, because a sorites argument for tall man exists that involves men who differ in height by only 1 millimeter. But defining a tall man as (say) a man at least 1850 millimeters in height would mean that in many cases we couldn't tell whether a man is tall without measuring his height in millimeters. Given the impracticality of taking such precise measurements in the typical case, we'd likely stop classifying men as "tall" and ...

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