If God doesn't exist then what are the foundations of logic?

Same as they are if God does exist. The idea that God (if such there be) has control over truths of math and logic is one that a few philosophers have argued for (Descartes, for instance, if I'm not mistaken) but even staunch believers in omnipotence typically understand omnipotence in a way that doesn't call for the puzzling idea that God could change the laws of logic. Briefly, the view of many theists would that God can perform any logically possible task. One reason for saying that is that logical "constraints" help us make sense of what omnipotence might mean.Why anyone would want more is hard to fathom. Suppose someone asked God to light up a set of pixels on an infintely high-resolution screen so that these pixels made a figure that was perfectly round and perfectly square. What would count? Is there actually a genuine task to be done here? If not, then it hardly seems to be a limitation on God's power (or anyone else's) that s/he can't complete the task.

I am not trained in formal logic, so I was hoping you could help me with the moral argument for the existence of God, postulated as follows: 1. If God doesn't exist, then objective moral standards don't exist. 2. Objective moral standards exist. Therefore God exists. I don't really understand why the arguer is allowed to throw in premise 2. It seems that in order to prove that objective moral standards exist, you must first prove that God exists (because the objective moral standards come from God). Since the truth of premise 2 depends on the conclusion of the argument, it seems the argument collapses into a circle. I guess what I'm really saying is that any theist I know would concede that premise 1 is actually an if and only if statement (again, because morality is inextricably linked with God). After all, if you could prove that objective moral standards exist without appealing to God, then you've demonstrated morality's independence from the existence of God and thus nullified the argument. I...

Although I think the argument is fraught with difficulties, I don't think it simply begs the question. Suppose this hypothetical theist -- call her Thalia -- is arguing with an agnostic, Agatha, who nonetheless believes that there are objective moral standards. Agatha has real-life counterparts, and some of them are even sophisticated philosophers. Suppose Thalia makes a case for premise one: that moral standards really do presuppose the existence of a divine lawgiver. At that point, Agatha has a choice: give up belief in objective moral standards, or take up theism. Depending on how convinced she is that there really are moral standards, she might well decide that she should opt for theism. Notice that from Agatha's point of view, there's no need for proof that there are objective moral standards. She already believes that. What she'd need to be convinced of is that premise 1 is true. And although I'm personally skeptical of premise 1), I do think there's more to be said here than meets the eye ...

I'm trying to wrap my mind around the Reformed Epistemology idea of the proof of God, but I am a total novice at this and I can't figure it out. As far as I can tell by the article "Without Evidence or Argument" by Kelly James Clark, the proof is 1) We should believe that God exists only with sufficient proof that God exists 2) We cannot get sufficient proof that God exists, because every argument would have to be justified by another argument infinitely Therefore, we do not need proof that God exists. I am completely baffled by this, and I'm pretty sure I'm reading it all wrong. I could really use a hand. Am I even understanding the premises at all?

Reformed epistemologists, as I understand them, are saying that we could know that God exists even if we were utterly unable to give a proof. That's because on their view, knowing something isn't a matter of being able to give reasons for believing it. Knowing something is a matter of being connected to it in the right sort of way. A little too simply, suppose there really is a God, and that the reason I believe God exists is because God reliably causes me to believe it. (And if God's causings wouldn't be reliable, then which ones would?) Reformed epistemologists would say that in that case, I know that God exists. This isn't a proof that God exists, and it isn't an argument to convince you that you should believe in God. It's a special case of a general view about knowledge: that we know things when they're true and our beliefs about them are caused in the right sort of way. And notice that this sort of view has some advantages. If there really is a computer in front of me, and if my belief...

When did the definitions of induction and deduction change from reasoning from the universal to the particular (deduction) and particular to universal (induction), to this non-distinction of the strength of support the premises give to the conclusion? When did it happen and who did it?

I did it, last Tuesday. But actually, I'm a bit puzzled. The distinction between deduction and induction never was a distinction between universal-to-particular and particular-to-universal. Consider: All dogs are mammals; all mammals are animals. So all dogs are animals. We haven't gone from universal to particular, but surely the reasoning is deductive. Or better: If Max is in Cincinnati, then so is Jennifer. But Max is in Cincinnati. So Jennifer is there too. A perfectly good deduction, but not a case of reasoning from universal to particular. On the induction side, suppose that every egg I've eaten has given me hearburn. I'm about to eat an egg. So I infer that this particular egg will (probably) give me heartburn. This is inductive reasoning, but it doesn't go from particular to universal. In a correct deductive argument, the conclusion follows from the premises. Put roughly, it's impossible for the premises to be true and the conclusion simultaneously false, but whether premises or...

For what I've seen until now, logical laws are always assumed to be necessarily true (in the "all possible worlds" sense), but is it possible that this necessity is weaker? Is it possible that our logical capabilities are adaptations to physical regularities of the actual world and are still evolving, together with our minds? If our logical capabilities are tracking our evolution, then the Necessity of Logic laws could be only Physical, instead of Metaphysical, and there could be possible worlds where the Physics would constrain Logic differently. This (I think) would also have implications regarding the Ontological commitment of Logic: instead of assuming that there is none, it would be possible, even likely, that the physical existents of the World would appear in our logical theories. Has anyone put forward sustained arguments for/against this?

People have talked about this. One oft-cited paper is Hilary Putnam's 1968 paper "Is Logic Empirical?" (Reprinted in his Mathematics, Matter and Method as "The Logic of Quantum Mechanics.") Putnam's arguments were of a "web of belief" sort: our beliefs form a web with some more central than others, but all are revisable. Quantum mechanics, Putnam thought, has given us the same sorts of reasons to revise our logical opinions as relativity gave us to revise our geometrical opinions. A large literature (to which I made some contributions) followed in the wake of Putnam's paper. The issues here resist easy summary. In an unpublished talk, Saul Kripke offered some trenchant criticisms of Putnam's approach. My own view is that many of Kripke's criticisms can be met, but the upshot is not exactly that logic is empirical in the way Putnam believed. Rather, it could be, for all Kripke has shown, that there are logical relations found in some worlds that may be absent in others. If that's right, it...

How does one _prove_ that an informal fallacy is a fallacy (instead of just waving a Latin name?)

But two qualifications to William's comments. First, not all arguments are susceptible to truth-table analysis. (For example: every horse is an animal. Therefore, every horse's head is an animal's head.) Second, there are plenty of good arguments (inductive arguments, for short) whose premises don't strictly imply their conclusions, but that make their conclusions probable given the premises. At least sometimes, informal fallacies aspire to inductive rather than deductive goodness, and so showing that the conclusion doesn't strictly follow from the premises is beside the point. Peter's point still applies however: we can show that such arguments are bad by showing that they have the same form as arguments that are patently bad. Here's a patently bad argument: most pets are mammals. Kiki is a mammal, and so (probably) Kiki is a pet. Any argument with this form is bad, even though the aim isn't to show that the conclusion strictly follow from the premises.

is it logically impossible for there to be an infinite regress? A lot of people make an argument and then if it leads to an infinite regress, the argument is taken to be faulty. Something like the first cause argument where the conclusion that an infinite regress occurred is to be avoided. Why is this the case? I don't see how we couldn't have an infinite regress.

There's more than one issue here, I think. It is logically possible -- near as I can tell -- for there to be an infinite regresses of causes. Someone might find it unsatisfying that A is caused by B, which is caused by C, which is caused by D... with no end. BUt there's no contradiction or incoherence here, various proponents of various First Cause arguments notwithstanding. But sometimes what's at issue is justification. If I justify my belief that A by appeal to B, and justify my belief that C, then if B and C are equally as much in need of justification as A, then I've made no progress. And if I can show that something inherent in the style of justification I've adopted is bound to generate this sort of regress of justification, then the approach I've adopted isn't going to work. The problem isn't whether or not there could be an infinite regress. The probem is that the notion of justification doesn't allow for something to be justified by way of an infinite regress, if each step in the regress...

If I am correct, the opposite of 'A' is not 'B', 'C', 'D', etc., but rather, the opposite of 'A' is 'not-A.' Likewise, the opposite of 'Green' is not 'Blue', 'Orange', etc., but rather, the opposite of 'Green' is 'not-Green.' And the opposite of 'Dog,' is not 'Cat' or 'Whale,' but rather, the opposite of 'Dog' is 'not-Dog.' And so on. However, each letter 'B' through 'Z' is not 'A' (after all, it seems, 'B' is not 'A', 'C' is not 'A'. and so on). Does that mean that 'not-A' is, or can be, or includes 'B' through 'Z'? Thus, does that mean that the opposite of 'A' is or can be 'B', 'C', etc.? Logically, I suppose, letters can stand for anything -- so perhaps 'A' is or can be equal to, say, 'B' and, therefore, 'not-A' would be equal to 'not-B,' so the opposite of 'A' might be 'not-B'. But what about objects that are not logical symbols? Cats and whales or not dogs. So, if the opposite of 'dog' is 'not-dog', and if cats and whales are not dogs, then are cats and whales the opposite of dogs? Am I missing...

The idea of an "opposite" isn't really well-defined. What you're calling the opposite (e.g., "not-dog" as the opposite of "dog") is what a logician might call the contradictory . But even though "opposite"' doesn't have a precise meaning, it's clear from the way that people use the term that it doesn't just mean the contradictory. If we want to figure out what a term means, we're well-advised to attend to how competent speakers use it. Ask any competent speaker for the opposite of "white" and she'll say "black." Ask any competent speaker for the opposite of "tall" and he'll say "short." But what can we gather from this? First, that a term and its opposite can't both apply to the same thing. Opposites are contraries . A bit more precisely, if the term "Y" is the opposite of a term "X," then "a is an X" and "a is a Y" can't both be true. However, in typical cases of opposites, they could both be false. (My pen is neither white nor black, for instance.) Still, that isn't enough. After all, ...

Consider the argument: I am more than six feet tall. Therefore, I am over five feet tall. Is this a sound argument? Is it circular? Tautologous?

Let me muddy the waters in hopes that Peter will say more. According to at least some philosophers, it is simply impossible that something should contain water without containing H 2 O. If they are right, then given the notion of validity presupposed by Peter's (1), this is a valid argument: The plastic jug in my refrigerator contains water. Therefore, the plastic jug in my refrigerator contains H 2 O. But this doesn't strike most of us as a valid argument, and it doesn't help to invoke standard notions of meaning, since "water" and "H 2 O" aren't connected by meaning . One reply would be to invoke a notion of validity of the following sort: an argument is valid if there is no argument with the same logical form whose premises are true and whose conclusion is false. On that account, the little argument about water isn't valid. Needless to say, this raises tricky questions about the notion of "logical form," but it lets us honor the intuition that the water/H 2 O...

Following along from http://www.askphilosophers.org/question/2039: "Does the law of bivalence demand that a proposition IS either true or false today? What if the truth or falsity of this proposition is a correspondence to a future event that has yet to occur?" What's problematical about saying "yes, it's either true or false, but I don't happen to know which"? Is that substantively different from saying the same thing about an open problem in science or mathematics, to which the answer is presumably knowable but happens not yet to be known? The questioner seems to be demanding both that there be an answer, which may be a reasonable thing to want, and to be able to know what the answer is, which isn't necessarily reasonable. Is it reasonable always to expect somebody (other than deity) to know the answer to a question?

The issue about so-called "future contingent" propositions isn't just about whether we're in a position to know whether they're true, but whether there are any facts for them to pick out. And that issue arises from a tempting but controversial metaphysical picture: reality as it were "unfolds" in time. Reality consists at least of what's so now, and perhaps as well of what's already taken place, but on this picture there simply are no definite facts about future events. This may seem odd at first, but a couple of examples might make it seem less so. Suppose you think that people make choices that are free in the sense of being not just uncoerced but undetermined. Mary is a juror in the penalty phase of a trial. Tomorrow she will decide whether to vote that the defendant should be executed. If you think that there is nothing that fixes her decision before it's made, you might wonder what it would mean for there to be a correct answer to the question "What will she decide?" before she actually decides...

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