# 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

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

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 (!),

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

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

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,...

### The analogy to printing money

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.

### Professor Westphal wrote: "If

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.

# Why do we need a contrast to recognize a sensation? For example -; Think of hearing the same sound since your birth and think that you are hearing it without any variations. We will fail to recognize that we are perceiving a sensation and we won't be able to recognize the sense organ. Iam only 15,Forgive me if my question is fallacious. Thanks.

Thanks for your interesting question. I don't think there's anything fallacious about it. But I do think that, at bottom, it's an empirical question -- one that we can't expect to answer just by thinking hard about it. What you say in answer to it seems plausible to me: If all that I ever receive at my auditory organs is a totally undifferentiated sound, no matter what I do, then it's hard to see what function my auditory organs are performing for me or why I would even be aware that I had them. But I think that a confident answer to your question depends on properly gathered empirical data. You might look into the psychology literature to see if anyone has investigated this topic.

# If God is the creator of the universe and all the living and non living things , Can he create or recreate himself ?

### Because I think it's seld

Because I think it's self-contradictory to say that God could literally create or re-create himself, I think believers in a Creator God must say this: God created all of the created things in the universe, but those things exclude God himself (and also Platonic abstract objects such as the laws of logic). For a bit more detail about why, you might look at my answer to Question 25260 .

# In my amateur philosophy club, my friend told me that modal ontological argument is false because its premise, It's possible that a perfect being exists, doesn't make sense. He argued that it is logically equivalent to say "it is possible that it is necessary", which means 'there exists at least one possible world in which all possible worlds have this objects in them.' So, according to his analysis, that premise make possible worlds in a possible world, which is absurd and makes a danger of infinite regress. But I think he misunderstood the argument. I think what actually that premise says is "there is at least one possible world that has a object which is in every possible world." I think this is implied when the argument says that "if something possibly necessarily exists, then it necessarily exists." Am I wrong?

### Excellent question. It's

Excellent question. It's great to hear that you belong to a philosophy club. As I see it, if the modal-ontological argument fails, it's not because the locution "It is possible that it is necessary" is absurd or ill-formed or meaningless. The opening premise of the modal-ontological argument can be expressed without using the possible worlds idiom: There could have been a necessarily existing God (where "could have been" is construed as consistent with "is"). The idea is that even atheists are supposed to concede that a necessarily existing God is at least logically possible: logically speaking, there could have been such a thing (even if, according to atheists, there isn't). Granted the possibility of a necessarily existing God, the argument then uses the modal principle "If it's possible that it's necessary that G, then G," letting "G" in this case stand for the proposition that God exists. Conclusion: God actually exists. In my view, the argument can be challenged for assuming (1) the above...

# Some people define some things (which they truly may be or are) Impossible. 'Impossible' has a humane meaning in itself. But... If 'something' is really impossible... then why can you think that? If something is impossible... then why did the neurons in your brain have that thought? It must've been impossible for them to think of something which is not possible.

### I'll assume, just for

I'll assume, just for simplicity, that by a "thought" you mean a belief and by "something impossible" you mean a proposition that cannot possibly be true . I hope my assumptions aren't off the mark. (I'm not a neuroscientist, so I'll say nothing about how neurons work.) If my assumptions are correct, then your question becomes "How can anyone believe a proposition that cannot possibly be true?" One answer is this: "Easy! For example, many people down through the ages believed that they had accomplished the famous geometric construction known as squaring the circle . But the proposition they believed cannot possibly be true, because squaring the circle is impossible, as was finally proven in 1882. Those who believed the proposition obviously didn't see the impossibility of the construction." An opposing answer is this: "They can't! Indeed, we can understand the behavior of those misguided geometers only if we attribute to them a false belief that could have been true, such as the belief that a...