Recent content by drnihili

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    The essence of logic is to find out what argumentative structures

    Those are good points about the use of language. The question is whether they are in the realm of logic or in the realm of pragmatics. The standard answer is that they are issues of pragmatics. The seminal piece on this issue is H. P. Grice's "Logic and Conversation". If the issue interests...
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    The essence of logic is to find out what argumentative structures

    I statements do not generally imply O statemtents. To see this, consider making a statement about a group you only know a litte about. For example, I have a beard. On the basis of that, we can conclude that some contributors to this thread have beards. Notice that we don't first have to...
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    Runner's Paradox: Finishing the Race in d Metres

    As stated neither of your problems has an answer. This is because it is possible to remove an infinite number of apples from the basket and still have an infinite number remaining. In order to get a solution we need to assume that the apples are ordered, say by each haveing a label with a...
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    Runner's Paradox: Finishing the Race in d Metres

    No, I am not merely asking for a definition. A definition might be part of an answer, but it certainly wouldn't be an answer all by itself. At the very least it would require also demonstrating that Achilles' run could satisfy the definition. It would probably also require at least a prima...
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    Runner's Paradox: Finishing the Race in d Metres

    No, there's no question about whether Achilles can run from A to B. That is physically demonstrable. What is not demostrable is whether his run can be understood as the completion of an infinite sequence of shorter runs. Infinite divisiblity gives some reason to think that it can, but does...
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    Runner's Paradox: Finishing the Race in d Metres

    qed And I'll repeat my answer from before. I obviously can't give you an example of completing an infinite sequence as the possibility of doing so is what is at issue. In a finite case examples are easy to come by. Suppose that Achilles' task is to count all the integers form 1 to...
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    Runner's Paradox: Finishing the Race in d Metres

    Credentials have weight when the issue turns to the question of what the accepted view in a field is. Ideally, this thread should have stayed on the topic of Zeno's paradox and whether it is resolvable. However, it instead strayed to the topic of what the accepted view in a field is. For...
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    Runner's Paradox: Finishing the Race in d Metres

    Perhaps you should instead set out what mathematics you have used and read and what your basis is for saying that the logic is sufficent. I've given you references to the literature and provided the basis for my own claims to know what the field contains. Thus far all you've done is stated that...
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    Runner's Paradox: Finishing the Race in d Metres

    Let me just put it this way. As a person with a PhD focusing on Logic who has been empolyed teaching the same for several years, and as a person who has been doing active research on paradoxes for over a decade and who has been focusing on aspects of Zeno's paradox for about 5 years now, I can...
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    Runner's Paradox: Finishing the Race in d Metres

    Post deleted by the moderator.[/color]
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    Runner's Paradox: Finishing the Race in d Metres

    I'm guessing that you're restricting mathematical logic to a sort of standard first order logic as one might see it in a beginning logic course? If so I grant you that the Liar isn't stateable in that language, but so what? Remove the words "true" and "false" from English and it's not...
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    Runner's Paradox: Finishing the Race in d Metres

    All I can say is that the best of your knowledge isn't very good on this point. The Liar paradox continues to be an active area of research and there is no generally accepted solution to it. Tarski's hierarchical approach and Kripke's fixed point theories are perhaps the most commonly cited...
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    Runner's Paradox: Finishing the Race in d Metres

    Yes, I stated it correctly, but there is sufficient ambiguiity in the English to warrant further explanation. A lot depends on emphasis that isn't recoverable from text. I think you hold that 1-3 demonstrate that the series is completable, that by running one segment at a time Achilles can...
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    Runner's Paradox: Finishing the Race in d Metres

    Ok, as I understand it, your position is roughly the following. 1. The consistency of calculus demonstrates the consistency of an inifinite divisibility model. 2. Induction is sufficient to show that all of the ever decreasing segments lie on Achilles' path from 0 to d. 3. Since d is...
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    Runner's Paradox: Finishing the Race in d Metres

    Ah, since you quoted a place where I was talking about your position on science and math, I assumed that was the postion you were asking about. I'm on my way out the door now, so I can't say much more than that you think there is no contradiction involved. When I get back I'll try to give a...
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