# There is an infinite number of words - "ONE", "TWO", "THREE"... etc. Every word has a definition. Every definition consists of letters. There is a finite number of arrangement of letters; thus there is a finite number of definitions. Thus there is at least one word that doesn't have a definition. Paradox?

### There is a finite number of

There is a finite number of arrangements of letters; thus there is a finite number of definitions. Is that true if we're allowed to use each letter an increasing number of times? If our stock of letter tokens increases without limit, then can't the number (and length) of our definitions also increase without limit? Certainly the names of the numbers will tend to get longer as the numbers they name increase, and those names will reuse letters to an ever-increasing degree.

# I wonder about the nature of modal concepts such as necessity and possibility. When I say "It is possible that this page is white" or "it is necessary that two plus two equals four" I use modal words in my speech. Where do these concepts belong to? Are they in my mind or I receive them from the objects themselves?

### It's a good idea to

It's a good idea to distinguish between epistemic uses of modal language (which have to do with our knowledge) and alethic uses (which have to do with truth independently of our knowledge). When you say, "It is possible that this page is white," you might be wearing tinted glasses and simply admitting that, for all you know, the page that looks amber to you is in fact white (i.e., it looks white to normal observers in normal conditions). That use of "possible" would be epistemic. Or, instead, you might be saying that the page, which in fact emerged a mottled gray from the unreliable paper mill, could have been white had the mill done a better job. Or you might simply infer from the fact that the page is white that it's possible that the page is white: what is true is of course also possible. Those uses of "possible" would be alethic. Where do alethic modal concepts belong? I'd say that they belong to logic, in the sense that they are at the foundation of the concept of logical consequence. To...

# Could necessary truths like "red is a color" turn out to be wrong?

### Not if they really are

Not if they really are necessary truths. By definition, any necessary truth couldn't possibly have been false. It takes some care to state propositions in such a way that they really are necessarily true. For instance, Red is a color asserts the existence of something -- red, or redness -- that arguably doesn't exist in every possible world. If there are possible worlds in which nothing physical ever exists, then nothing is red or (arguably) even could be red in such worlds, making it unclear whether there is a color red in such worlds. By contrast, the necessarily true proposition Whatever is red is colored doesn't assert the existence of anything, so it comes out (vacuously) true even in worlds lacking any red or colored things.

# 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

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

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

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

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

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

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.

# Why is there no universal definition of philosophy?

### For a reply to a very similar

For a reply to a very similar question, see http://askphilosophers.org/question/24944.