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Representation of reality by irrational numbers. In the world there are an infinite number of space/time positions represented by irrational numbers. I should think that all these positions are real, even though they cannot be precisely described mathematically. Does this mean that mathematics cannot fully describe reality? What are the philosophical implications of this?

I would question your assumption that positions, magnitudes, etc., whose measure is irrational "cannot be precisely described mathematically." Consider a simple-minded example: In a given frame of reference, some point-particle is located exactly pi centimeters away from some other point-particle. I think that counts as a precise mathematical description of the distance between the two particles, even though it uses an irrational (indeed, transcendental) number, pi, to describe the distance. It's true that any physical measurement of that distance -- say, 3.14159 cm -- will be precise to only finitely many decimal places and therefore will be only an approximation of the actual distance. But the description "pi centimeters apart" is itself perfectly precise, despite the irrationality of pi.

It seems to me that most theories involve postulated objects, and then various laws that describe how those objects must or can relate to each other. So, you might postulate an id, ego and superego, or genes, or electrons, protons and protons, etc. It also seems to me that there are at least two types of "simple" when talking about explanations. There's a brevity "simple" -- like a maths proof or a piece of computer coding with minimal steps. And there is also an ontological "simple" -- an explanation relying on as few postulated objects as possible. If it's true that there are at least these two types of "simple", well, does that render parsimony often difficult to apply, if you're committed to it as a good rule of thumb when deciding what to believe in? One candidate theory could be ontologically complex but brevity-simple, whereas the alternative theory might be ontologically simple but convoluted. Here are some things that worry me: (1) does appealing to deities lead to simpler explanations that...

Good questions. The philosopher David Lewis (1941-2001) rightly insisted on distinguishing two kinds of ontological simplicity or parsimony: quantitative and qualitative. Quantitative parsimony concerns the sheer number of postulated entities; qualitative parsimony concerns the number of different kinds of postulated entities. Lewis argued that only qualitative parsimony matters. It's not the sheer number of (say) electrons but the number of different kinds of subatomic particle posited by a theory that makes the theory parsimonious or not, compared to its rivals. (Maintaining this line required Lewis to treat "the actual world" as an indexical phrase and to hold that each of us has flesh-and-blood "counterparts" in nondenumerably many other universes.) All else being equal, then, theories that posit deities are qualitatively less parsimonious than theories that don't, because (I take it) deities are supposed to be of a different kind entirely from the phenomena that they're invoked to explain....

My question is: does naturalism lead to scientific anti-realism? From a naturalistic perspective, there does not seem to be any Archimedean point from which to get an objective view - there is no ultimate meaning maker who can offer a “God’s eye view” of reality. Therefore, if one assumes philosophical naturalism, one must also deny the ability of science to provide objective information about the world. To quote Hannah Arendt, from a naturalistic perspective, “man can only get lost in the immensity of the universe, for the only true Archimedean point would be the absolute void behind the universe.” I really don’t see any way around this. Science, if understood as the pursuit of objective knowledge, can only stand on the shoulders of theism.

I confess I don't see a skeptical problem here. It's true that any perspective I could occupy, no matter how broad, will be my perspective when I occupy it. But that truth is just a tautology: it's implied by everything, including by theism as much as by naturalism. It makes no difference to either of those positions. Importantly, it doesn't imply that I can't achieve objective knowledge. From my perspective, elephants are bigger than mice: I perceive them that way. The fact that I perceive things that way doesn't imply that elephants aren't objectively bigger than mice, i.e., bigger than mice regardless of anyone's perception of them. Nor does it imply that I can't know that they're objectively bigger. To the objection, "But how can you know that you know this about elephants and mice?" one can reply with one's favorite theory of knowledge, which will explain how one knows anything, including how one knows that one knows that elephants are bigger than mice. In short, I don't see...

For years, scientists like Stephen Hawking have made claims, maintaining that the awesome, sophisticated creativity of the world around us can be interpreted solely by reference to physical laws such as gravity. But could Hawking's claim is be misguided? He asks us to choose between God and the laws of physics, as if they were necessarily in mutual conflict. But contrary to what Hawking claims, physical laws can never provide a complete explanation of the universe. Laws themselves do not create anything, they are merely a description of what happens under certain conditions. What Hawking appears to have done is to make a category mistake and to confuse law with agency. His call on us to choose between God and physics is a bit like someone demanding that we choose between aeronautical engineer Sir Frank Whittle and the laws of physics to explain the jet engine. The laws of physics can explain how the jet engine works, but someone had to build the thing, put in the fuel and start it up. The jet could not...

There's a lot going on in your question, and I doubt that my response will cover all of it. But I'll say, first, that it begs the question against Hawking to demand that he explain "the awesome, sophisticated creativity of the world" if by "creativity" you mean something beyond the everyday creativity acknowledged by both sides of the debate (such as the creativity of human agents). Hawking doesn't accept the assumption that (for example) the laws of physics are the result of someone's creativity. Second, Hawking would likely question your inference from the premise "All created things, such as the jet engine, require creators" to the conclusion "The laws of physics require a creator." The premise is true, but it doesn't imply the conclusion. Third, it's not clear from your description of Hawking's view that he alleges a conflict between theism and the laws of physics. Rather, if I understand your description, Hawking claims that theism isn't necessary to explain what we observe. Now, if...

Why do scientists seem to dislike philosophy so much? (For example Neil deGrasse Tyson, Stephen Hawking and Lawrence Krauss). Even Dawkins seems to have joined the club (which is odd given he now seems to spend most of his time making what seem to me to be fairly clearly philosophical arguments). Is it simply that they are using different definitions of the word than philosophy professors? Are they generally attacking just bad philosophy and taking that unrepresentative sample? Do they mean philosophy as in "that thing taught in philosophy departments" or some more abstract notion about the relations of ideas? I really don't understand what their problem is with philosophy (and why they don't define their terms)...

I'm not sure why Tyson, Hawking, Krauss, Dawkins, Coyne, Feynman, et al. , express so much contempt for philosophy. But my best guess is that they're ignorant -- unaware -- of what philosophy is when it's done well, perhaps because they received little or no academic training in philosophy when they were undergraduate students. (By the time they reached graduate school in the sciences, it may have been too late for them to get that training even if they had been interested in getting it.) I don't think they're using different definitions, at least not systematically. Krauss does claim that physics has redefined the words "something" and "nothing," but I think he's deeply mistaken (see Question 4759 ). In general, I find that when non-philosophers, including scientists, reason about philosophical issues, they do so sloppily: making elementary mistakes in inference, conflating concepts that ought to be kept distinct, and so on. That's unfortunate but not surprising, since reasoning well about...

Does the acceptance of scientific naturalism commit one to the view that the universe is devoid of all meaning?

There are at least two ways to interpret your question: (1) Does scientific naturalism imply that no meaning at all exists anywhere in the universe? (2) Does scientific naturalism imply that the universe itself has no meaning? I think the answer to (1) is pretty clearly no . By "scientific naturalism," I presume you mean the denial of supernaturalism , i.e., the denial that any nonphysical minds or causes exist. On that reading, scientific naturalism is compatible with the fact that you meant something by your question (your question isn't meaningless) and the fact that I mean something by this answer to it. Nor does scientific naturalism imply that nothing is ever non-linguistically meaningful: it allows that an experience (say, of great music) can be meaningful to someone. What holds for the concept of meaning holds, I'd say, for the concept of purpose as well. I think the answer to (2) is pretty clearly yes . But what could it mean, anyway, to say that the universe itself has...

It seems to me that today's rationality is completely irrational in a sense that it attacks everything that is not rational. But who define what is rational? For example, many people like to back up their beliefs by scientific arguments or by pointing on the bad parts of religion. Yet in 19. century frenology was considered science. Today we call it pseudoscience. Is it lacking humility for most people or something else that they cannot accept that in 200 years people will laugh at our modern "science"? And, if we are so deeply influenced by beliefs of our times why wouldnt relativism allow for more open minded approach in a sense that it would allow people to believe anything they want (without the need for justification) instead of using relativism primarily for attacking "old" beliefs (example would be the view that christianity is obsolete)?

Your comment seems to be in tension with itself. You end it by suggesting that we adopt a version of relativism "that...would allow people to believe anything they want (without the need for justification)." Yet you begin your comment by apparently condemning, as "completely irrational," the beliefs of those who think pseudoscience or religion are irrational. I don't think you can have it both ways: relativism for their judgments, objectivism for your own. You ask, "Who defines what is rational?" I take it you have some definition in mind when you describe critics of pseudoscience and religion as "completely irrational." Relativism has an undeserved reputation for being open-minded. Those who think that they can "believe anything they want (without the need for justification)" should feel no pressure to keep their minds open to any evidence or arguments against what they believe.

Are empirical questions inherently non-philosophical? If answers to those questions can be determined by polling or science, should philosophers never address them?

Your question touches on a current debate within philosophy. You can find more about the debate by searching under "experimental philosophy" and "x-phi" on the web. Regardless of which side one takes, however, it's always important to know which kind of question (empirical, conceptual, logical, normative, or a mixture of those) one is trying to answer: the answer to "Which kind of question is that?" is a philosophical matter. In my experience, philosophers too often fail to recognize that the question they're asking has empirical aspects -- aspects that, as philosophers, they're not trained to investigate. If a question can be answered by polling or some other empirical method, then any philosopher who tries to answer it had better be properly trained in the relevant empirical method. Once the empirical results are in, the implications of those results are something that philosophers, as such, are well-equipped to work on.

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