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....

Why is the sorites problem a "paradox"? Isn't it fundamentally a problem of definition?

The sorites problem is a paradox for the reason that any problem is a paradox: it's an argument that leads from apparently true premises to an apparently false conclusion by means of apparently valid inferences. I don't think it's fundamentally a problem of definition, because the concepts that generate sorites paradoxes would be useless to us if they were redefined precisely enough to avoid sorites paradoxes. Take the concept tall man . In order to make that concept immune to the sorites, we'd have to define it in terms that are precise to no more than 1 millimeter of height, because a sorites argument for tall man exists that involves men who differ in height by only 1 millimeter. But defining a tall man as (say) a man at least 1850 millimeters in height would mean that in many cases we couldn't tell whether a man is tall without measuring his height in millimeters. Given the impracticality of taking such precise measurements in the typical case, we'd likely stop classifying men as "tall" and ...

Science claims that the cells in our bodies are alive, but the fundamental parts of the cell such as molecules and atoms are not alive. Does that mean our bodies are only partly alive?

Science also says that some of the cells in our bodies are dead. That already implies that our bodies are only partly alive, but only in the sense that not every part of our bodies is alive. If every part of a living thing must be alive, then the fact that atoms and molecules aren't alive implies that none of our cells are alive, and no bodies are ever alive. Both of those consequences are false. So we must reject the principle that every part of a living thing must be alive.

Recently, I noticed about sorites problem. I thought that problem is serious to all of philosophical endeavor, but my friend told me that is problematic when you assume some kind of platonism. Is he right? Or is it equally problematic when we assume nominalism?

I think that the sorites paradox is a problem even for nominalists. Suppose we line up 101 North American men by height, starting with the shortest man (who's 125 cm tall) and ending with the tallest man (who's 225 cm tall). Let's also suppose that each man except the shortest man is 1 cm taller than the man to his right. Clearly the shortest man is short. If 1 cm in height never makes the difference between a short man in the lineup and one who isn't short, then the tallest man is also short, which is clearly false. So there must be a tallest short man in the lineup. But who could that be? If we can't know who it is, then why not? I think I've managed to state the problem in terms that even a nominalist can accept. If nominalism, as such, evades the problem, then I'd love to know how it does.

Should the impossibility of reaching a definite answer for many of the questions that philosophy asks realistically lead one to stop asking , or even considering, these type of questions? Ultimately, is asking a waste of time and energy?

Philosophers are routinely asked these questions, whereas (say) physicists never are. I'm not sure that's fair. If the task of physics is to discover the fundamental laws governing the physical world, then there's no guarantee that physics can accomplish that task. For one thing, there may not be fundamental physical laws; it may be that for every physical law, there's a more basic physical law that implies it, without end. (The alternatives seem to be that some physical laws are not just physically but metaphysically necessary, which seems implausible, or that some physical facts are inexplicable and therefore not explained by physics.) Even if fundamental physical laws do exist, physicists can't reasonably claim to have discovered them given (for example) the ongoing disputes over how to reconcile general relativity with quantum mechanics. Are physicists therefore wasting their time? Some of the controversies in biology (e.g., abiogenesis; one tree of life or more than one?) seem just as...

Is it possible to employ a truth predicate or truth set (set of all true propositions) in ordinary first order logic?

To my knowledge, no. Ordinary first-order logic quantifies only over individuals (none of which are literally true) rather than over truth-valued things such as sentences or propositions. Thus there's nothing in first-order logic to which the predicate "is true" can apply. For that you need higher-order logic, which is a topic of controversy in its own right. By "set of all true propositions," I take it you mean "a set of all the true propositions there are," i.e., the extension of the predicate "is a true proposition." A Cantorian argument due to Patrick Grim concludes that no such set is possible. It works by reductio . Let T be any set containing all of the true propositions. If T exists, then it has infinitely many members, but that doesn't affect the argument. Now consider the power set of T -- P(T) -- which is the set whose members are all of the subsets of T. It's provable that any set has more subsets than it has members. With respect to each of those subsets in P(T), there is a true...

Mustn't there be a counterexample to any statement that's a generalisation, because if there weren't a counterexample the statement would be a matter of fact and not a generalisation?

It may help to distinguish between universal generalizations and statistical generalizations. An example of a universal generalization is "All swans are white," and a statistical generalization might be "Swans tend to be white." As it happens, that universal generalization is false, because some swans are not white, and the statistical generalization will be true or false depending on the context (in some parts of Australia, it may be a false statistical generalization). When people say things like "That's just a generalization," I take it they're talking about a statistical generalization -- a claim about how things tend to be, a claim about how things are substantially more often than not. The reason that we expect statistical generalizations to have exceptions, I think, is that if the person asserting a statistical generalization were in a position to assert a universal generalization -- a logically stronger claim -- then he or she would. That's why the universal generalization "All triangles have...

I am puzzled about questions that ask if a Creator can create Itself. Look at a circle after it is drawn: at that point, it has no beginning and no end. Look at a circle while it is being drawn: during its construction, you can see it does have a temporary beginning. Only after construction is complete, does its beginning seems to disappear. If time is cyclical, then why couldn't a similar analogy apply? Maybe I'm not expressing myself as clearly as I could, I hope someone here can upgrade the quality of my observation to get at its essence and not be stuck with the poor quality of my language choices.

Speaking of recurrence (!), this topic has come up rather often on this site in recent months. My own answers appear at Question 25260 and Question 25648 . In reply to Question 25260, I conceded that we can tell a story featuring a causal loop in which -- allegedly -- X creates Y in 1900, with Y already having created X in 1800. However, because Y already existed (indeed, Y created something) in 1800, I can't see how X can create Y in 1900: I can't see how X can create something that already existed (indeed, something that existed even before X did). Instead, I'm inclined to describe the story as one in which X and Y come into existence for no reason at all, and not because either of them creates the other. As I interpret it, your analogy to drawing a circle is meant to suggest that the story might have an actual, unique starting point that we can no longer identify because the story has now come "full circle": the drawn circle is now closed. But that suggestion, I think, misunderstands the...

When you ask why people believe in logic, it seems to me that the commonest answer is, "It works." But that answer seems problematic to me; how do you know it won't stop working? I guess what I'm asking is -- are logical laws nothing more than empirical regularities, models of how things behave? Are logical laws any different from empirical laws? Is there any stronger reason to have faith in logic apart from the fact that it works and has always worked?

Yes: As I see it, logical laws are different from empirical regularities. Many of our empirical predictions come true, but some of them don't, and in any case it's not hard to imagine any particular empirical prediction turning out false. I predict that the chair I'm now sitting in won't levitate before I finish answering your question, but it's easy for me to imagine being wrong in that prediction. Indeed, I can even imagine that universal gravitation stops working in the way we've become used to. But what would it be to suppose that the laws of logic stop working? Would it be to suppose that the laws of logic stop working and continue to work exactly as they always have? If yes, why? If no, why not? (Presumably not because the laws of logic would prevent it!) So I'm not sure it's possible to entertain the supposition that the laws of logic stop working. Indeed, I'm not sure that there's any such supposition in the first place. In my view, the question "What makes us so confident that it will never...

I don't know if this a philosophical question or scientific question, So this is my question, If A create all things, is it logically safe to say that A is uncreated?

It's a philosophical question. No scientist, as such, will have any particular expertise for answering it. If A created all things, then it follows that A created itself , since presumably only a thing (rather than literally nothing) can do any creating. But the notion that A created itself seems to me to be logically inconsistent: in order for A to do any creating, A must exist, and in order for A to be created (i.e., to be brought into existence) A can't yet exist. So I conclude that it's impossible for A to create all things. However, if A created everything else , i.e., everything distinct from A, then I think it does follow that A is uncreated. Otherwise, A would have to create A's own creator(s), which seems to me to be logically impossible. I myself think it's impossible for anything to create everything else, because I think that there are abstract objects (such as numbers, or the laws of logic) that exist necessarily and that are necessarily uncreated. So those things, at least,...

Professor Westphal wrote: "If I create everything except myself, then of course it follows that I do not create myself. But...does it follow that I am uncreated? I can't see how it does. For one thing, there could be someone else who created me...." If I am created, then I have one or more creators, each distinct from me. If I am created and I create everything except myself, then I must create my own creator(s), which is no more coherent than self-creation. Hence I must be uncreated. See my original reply. Professor Westphal's interpretation of John 1:3 makes the verse at least possibly true, but at the cost of making it oddly redundant: "All made things were made by God; and no made things were made without God." The second clause comes so close to simply restating the first clause that it could hardly count as "evidence" in favor of the first.

The analogy to printing money fails. There's an obvious difference between (a) "I create everything except myself" and (b) "I print all the money except what's in my wallet." Given the impossibility of creating my own creator, (a) implies that I am uncreated. By contrast, (b) doesn't imply that the money in my wallet is unprinted. Maybe Professor Westphal assumes that it's possible for someone to create his/her own creator. Maybe he imagines a time-travel loop in which, say, X creates Y in 1900 and then Y goes back in time to create X in 1800. I think such a scenario is conceptually incoherent, because I think that "X creates Y in 1900" implies "Y doesn't exist prior to 1900." But I suppose others might interpret "creates" differently.

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