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    Arguments against materialism - how to refute?

    A popular way to accommodate pain within a materialist framework is to say that pain is a mental property: even if mental properties are not reducible to physical/materialistic properties, mental properties can be had by material objects. So materialism is unthreatened, so long as one...
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    Would the existance of an omniscient being prove that free will is non-existant?

    Although you cannot choose to do an action that makes 'A' not occur, I don't see how it follows that you do not choose for 'A' to occur. Perhaps the omniscient being's foreknowledge that 'A' will occur is the result of the being knowing that you will choose to do 'A'. If so, then if you had...
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    Proof of Poincare Recurrence Theorem

    yup. no luck.
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    Proof of Poincare Recurrence Theorem

    Does anyone know of an accessible reference that sketches a proof of Poincare's recurrence theorem? (This is not a homework question.) I'm coming up short in my searches -- either the proof is too sketchy, or it is inaccessible to me (little background in maths, but enough to talk about...
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    Philosophy of Mathematics

    More technical philosophers of mathematics -- those who address "foundational issues" -- also debate things like how to understand the set-theoretic hierarchy (is it iterative?). And another general question: what entitles one to accept mathematical axioms? Also, among those who accept the...
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    Create a mathematical expression using mereotopological theorem Perhaps reading this will be helpful.
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    Merit of meretopology

    Is a satisfactory answer to your question as simple as the observation that a tire is a part of a car? Whatever is part of a tire is also part of a car: tire parts are a proper subset of car parts. Express this fact in set notation, and you've got your mathematical relationship. There are...
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    Proposition Negation

    I disagree. "Some box contains 11 or more balls" should be translated as "There exists a box x such that either x contains 11 balls or x contains more than 11 balls." Then, when this is negated, we get: It is not the case that there is a box such that either the box contains 11 balls or the...
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    Philosophy of Physics

    Phil Physics vs. Phil Science Generally, inquiries in philosophy of physics concern foundational issues in the sciences. A "foundational issue" is a problem in the "foundations" of a particular science. For instance, the measurement problem is a foundational issue in quantum mechanics; the...
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    Help with an SD derivation

    Oops! Now I know...and knowing is half the battle.
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    Help with an SD derivation

    Rule of thumb: whenever you're trying to prove a conditional claim, the first assumption you make should always be the antecedent of the conditional. You didn't follow this rule; that's why you're having trouble discharging your assumptions at the end. And the argument is valid: I did a...
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    Frege proof.

    First, the use of "singular term" and "definite description" strikes me as odd: these are properties that terms can have (like nouns or pronouns). Better to say (1) as: "Propositions are not sentences; but they are domain indicators for sentences". This captures the fact that the same...
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    Paradox about Laws

    I think you're understanding -- the rest of the argument after step 2 is trying to show in a rigorous way that, given the further assumptions of claims I, II and III, these claims are contradictory. But I think that if one were to reject one of those other claims, (1) and (2) would be...
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    Paradox about Laws

    What if I make the claims about possibility more specific and say that I mean possibility in the sense of physical (nomological) possibility, so that the range of possible worlds I am considering are all and only those possible worlds that have the same laws of nature as this world? Also, I'm...
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    Einstein right = Newton wrong?

    How's this for a reason Newton was definitely wrong: mass is a frame-dependent property of objects. Newton's mechanics treats mass as if it is a frame-independent property of objects (cf. the second law). Therefore, Newton's theory is false. I don't see the point in saying that Newton was...
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    Peer review reviewed

    Perhaps the best reaction to problems with peer review in the medical profession is to do away with paper journals and publish everything online: let every voice have a say, and let there be the possibility of replying to every article (sort of like this forum, but "more professional"). If you...
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    Paradox about Laws

    Reply There is a typo in my statement of I. It should read: for any event e, if e occurs THEN it is possible that .... I don't intend claim I to be a possibility claim: I intend for it to be a claim about what is true in the actual world (or even in every possible world -- a necessary...
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    Paradox about Laws

    The following claims each strike me as intuitively plausible: I. For any event e, if e occurs that it is possible that the laws of nature made it the case that e occurs. (This is supposed to capture the intuition that it is possible for every happening to be law-governed. The laws of...
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    Axioms - the choice & meaning

    Why does one need to have a well-ordering of the rational numbers in order to perform a mathematical induction? Let me be more precise: Why does one need all of the rational numbers? Having the concept of successor requires, at most, some set theory -- e.g., Zermelo-Frankel axioms. I...
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    Axioms - the choice & meaning

    Well yes, but IN FC the theorems are derived from the axioms -- the axioms are primitive, the theorems are derived from them. Nowadays presentations of propositional logic starts with different primitive rules and derives the axioms of FC from those rules. What counts as primitive is relative...
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    Axioms - the choice & meaning

    One more thing about induction: Mathematical induction generally proceeds in accordance with the following sort of procedure: Find some way of "ordering" what you are taking about (e.g., by complexity of formula or whatever). Show that some property P holds of the first element in...
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    Axioms - the choice & meaning

    Special Note on the Deduction Theorem Yes, the deduction theorem is proven using mathematical induction. But mathematical induction does not involve the axioms of arithmetic or "math". (I'll substantiate this in a moment.) So there is no need to presuppose the Peano axioms in the proof...
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    Axioms - the choice & meaning

    Different Perspective on the Frege-Church Axioms Hello everyone- I think that I have a much more direct and accurate answer to the original question on this post. My answer comes in three parts, interspersed with (what I hope to be helpful) commentary. The axioms cited are known as the...
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    Can the Universe repeat itself?

    MF- I think you're on to an interesting puzzle. Boltzmann, one of the original people to think about how to account for entropy, encountered what is known as the recurrence objection to his attempt to derive something like the second law of thermodynamics from classical microscopic dynamics...
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    What cannot be philosophied about?

    For a brief report on a study of letters and their underlying logic, see;jsessionid=KRWZXIBGZXHJBQFIQMGCFGGAVCBQUIV0?xml=/connected/2006/04/18/ecalpha18.xml&sSheet=/connected/2006/04/18/ixconnrite.html Here is an excerpt -- sounds philosophical...
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    What cannot be philosophied about?

    Supplemental proof, as a response to Job's comment: Consider all the things, ideas, thoughts, etc about which we are ignorant -- and let this set include everything that happens to be unknowable in principle to us, beyond our powers of comprehension, etc (if such things there be). It is...
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    Can the Universe repeat itself?

    Nothing as elaborate as an infinite universe is required to substantiate an affirmative answer. Suppose (correctly!) that there are only finitely many particles in the universe. Then Poincare's Recurrence Theorem shows that, after a really really long time, the state of the universe at that...
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    How many rules are there in formal logic?

    Thanks for the welcome. There are (at least) two ways to think about the meaning of logical operators like AND, OR, etc. (What do I mean by "meaning of a logical operator"? I mean "what the sentences in which that operator occurs, mean. So, for instance, if someone said that "Jack goes to...
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    What cannot be philosophied about?

    Nothing. There is nothing that cannot be philosophized about. Here's the proof: Suppose "P" cannot be philosophized about. (Let "P" be whatever you want -- a thing, a topic, an idea, etc.) Then there would be something to philosophize about, namely, that "P" cannot be philosophized about...
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    Ross's Moral Theory

    A non-prima facie duty is a duty that one has no matter what. A prima facie duty is a duty that one has unless and until it gets "over-ridden" by some other duty. Prima facie duties are not absolute: they are defeasible. Example: We have a prima facie duty to not lie. But suppose we are...