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?

I’m reading Terry Pinkard’s “German Philosophy 1760-1860 The Legacy of Idealism”, and on page 113, he writes: “Signing a check, hitting a home run, making an assertion, shopping at a sale are all other examples of normative activities that cannot be captured in a purely physical or “naturalistic description of them.” I’m not getting why hitting a home rim cannot be described as purely physical phenomena. Can somebody explain it to me?

Could someone help me clear up a paradox? Let’s say there’s a woman who says “I cannot say no to you” and the woman she is speaking with responds “well then, say ‘no’”. Is this really a paradox? In my opinion it isn’t: When the woman says that “she can’t say ‘no’” there are one of two interpretations of that phrase. She either means “I cannot deny your requests” or literally “I cannot utter the word ‘no’”. If it’s the former, then asking her to just “say no” wouldn’t put her in a paradox, since simply uttering the word “no” isn’t denying a request, it’s just making an empty utterance. It’s like how saying “I declare bankruptcy” doesn’t actually do anything, it’s just making noise. If it’s the latter example, and she cannot “say no”, then she technically never said she cannot deny a request—she just can’t use the specific word “no” in her statement. She can still say “I refuse” or “I will not do that” and then not have to say “no”. Am I wrong about this?

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?

Should (intentionally) false speech be completely free? If so, on what basis? Such speech seems only to bring harm and spread misunderstanding.

I have recently heard that, according to physics, you can never actually touch anything. This seems clearly false and I feel it should be refuted with philosophy (if not physics). Can you comment on this? p.s. See for example https://futurism.com/why-you-can-never-actually-touch-anything which seems to claim that, according to physics, you can never actually touch anything

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

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...

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?

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.