If Laws of logic are true or hold in all contexts, how can there be more one law? Do the two versions of De Mogan's laws differ? If so. how? Does the law of excluded middle differ from the law of non contradiction and from either version of De Morgans laws? Enoch

Notice that the same question arises in math, where the laws also hold no matter what. Arithmetic contains commutative laws of addition and of multiplication, associative laws of addition and multiplication, a distributive law of multiplication over addition, etc. Are those laws different? Their representations on the page certainly look different. I take it that you're asking, at bottom, how truths that hold in all possible worlds could count as distinct truths. The answer depends on how propositions are to be individuated , and here philosophers give various answers. On some theories, there's only one proposition that's true in all possible worlds, although there are indefinitely many sentences (some logical, some mathematical, some metaphysical) that express this single proposition. Other theories give a more fine-grained way of individuating propositions that allows for the existence of multiple propositions that are true in all possible worlds. You'll find more...

In predicate logic can we have valid arguments if we make an existential claim in our premises and not in the conclusion? In other words can we simply rename the existential quantifer to a "particular" quantifer or something of the sort? Does this particular quantifer always have to carry existential import?

If I understand your first question, the answer is no (unless the existential premise is superfluous). By an "existential claim," I take it you mean an existential generalization such as "There exists an x such that F x ," rather than a claim of the form "F a ," which implies an existential generalization. But you might wish to look into the rule of Existential Instantiation (or Existential Elimination in natural deduction systems); you'll find a brief summary of it here . I'm not sure I understand your second question. There are two ways of interpreting the universal and existential quantifiers: the objectual way and the substitutional way. I can't find a handy link to recommend, but if you search for discussions of those terms, you may find something relevant to your third question.

Me and my professor are disagreeing about the nature of logic. He claims that logic is prescribes norms for correct reasoning, and is thus normative. I claim that logic is governed by a few axioms (just like any in any other discipline, i.e. science) that one is asked to accept, and then follows deductively, free of any normative claims. My question is: which side is more sound? Thank you.

In this context, by "normative claims" I take it you mean claims that one ought to (or ought not to) do some particular thing. Can we get such claims out of principles of deductively valid inference? I think so. If you accept P, and you recognize that P implies Q, then there's a sense in which you ought to accept Q: you're logically and rationally committed to Q by propositions that you accept and recognize. If you accept Q, and you recognize that P implies Q, there's a sense in which you ought not to deduce P from those propositions alone: doing so would be fallacious. Now, you might say that the ought and ought not in those cases is only hypothetical: " If you want your deductive reasoning to be reliable, then you ought (or ought not)...." But I think the antecedent of that conditional (the "if" part) is easy to discharge. Plenty of people do want their deductive reasoning to be reliable, and so there's a sense in which such people really ought to use ...

Is it racist to use the word "niggardly," despite the word not being etymologically related to the notorious N-word?

It's not clear to me which of two questions you're asking: (a) Is it always racist to use the word "niggardly"? (b) Can it be racist to use the word "niggardly"? I'd answer "no" to (a). It's not racist, and it's accurate, to describe Ebenezer Scrooge (before his conversion) as a niggardly character. But suppose someone uses "niggardly," perhaps mistakenly thinking that it's related to the N-word, in order to express racial hatred. I think that counts as a racist use of "niggardly," so I'd answer "yes" to (b).

what is the difference between logical necessity and metaphysical necessity?

I think of logical necessity as (predictably enough) the necessity imposed by the laws of logic. So, for example, it's logically necessary that no proposition and its negation are both true, a necessity imposed by the law of noncontradiction. But one might regard logical necessity as broader than that, since one might say that it also includes conceptual necessities such as "Whatever is red is colored." Metaphysical necessity is a bit harder to nail down. Every proposition that's logically or conceptually necessary is also metaphysically necessary, but there may be metaphysical necessities that are neither logically nor conceptually necessary, such as "Whatever is water is H2O" or "Whatever is (elemental) gold has atomic number 79." Nothing in logic or in the concepts involved makes those propositions necessary, but many philosophers say that those propositions are nevertheless "true in every possible world," which is the root idea of metaphysical necessity. Even if some proposition P isn't...

The notion of something being a "fake" seems linguistically odd. Normally, if you have an adjective and a noun, the noun notes what the thing being talked about is, and the adjective describes some quality of the thing in question. A "fake plant", however, doesn't seem to fit that pattern at all, because a fake plant isn't a plant to begin with; the noun seems to be violating its intended function. Is "fake" something other than an adjective, then, perhaps analogous to "not a"? Or is a "fake plant" actually a "fakeplant", i.e. the fake is a part of the noun rather than an adjective, despite its apparent form? Doesn't the adjective "fake" somehow undermine the purpose of nouns?

I'm having trouble confirming it online at the moment, but I believe that linguists have a category for words such as fake , artificial , would-be , and the like: I think they're called "cancelling modifiers" or "cancelling adjectives." These words are well-known exceptions to the rule that, given an adjective A and a noun N, any AN is an N. I don't think they "undermine the purpose" of nouns or adjectives; instead, they perform a special and useful adjectival function in language. Anyway, you might search for information on the linguistics of cancelling modifiers or cancelling adjectives. I hope you find the clarification you're seeking.

Is logic "universal"? For example, when we say that X is logically impossible, we mean to say that in no possible world is X actually possible. But doesn't this mean that we have to prove that in all possible worlds logic actually applies? In other words, don't we have to demonstrate that no world can exist in which the laws of logic don't apply or in which some other logic applies? If logic is not "universal" in this sense, that it applies in all possible words, and we've not shown that it absolutely does apply in all worlds, how can we justify saying that what is logically impossible means the not possible in any possible world, including our actual world?

I don't understand the question, because I don't understand the phrase 'a world in which the laws of logic don't apply'. I don't think any sense can be attached to that phrase. Is a world in which the laws of logic don't apply also a world in which they do apply? If no, why not? If yes, is that same world also a world in which the laws of logic neither apply nor don't apply? If no, why not? It's as if the questioner had asked, "Don't we have to demonstrate that no world can exist in which @#$%^&*?"

Is it possible for there to be a world that logic does not apply? That is, can't a "married bachelor" actually exist in some world that there is no logic or that there is a different logic that applies? And if so, then isn't it the case that we merely assume the first principles of logic (noncontradiction, identity, excluded middle, etc...) because we observe them in our actual world, which is 1 of many possible worlds? And if it is mere assumption, then can't we be wrong about them when we say they can/should apply to other possible worlds?

I don't think this question can be answered. I think no one -- including the questioner -- understands the question being asked. In asking "Is it possible for there to be a world where logic doesn't apply?" is the questioner asking (a) "Is it possible for there to be a world where logic doesn't apply?" or (b) "Is it possible for there to be a world where logic does and doesn't apply?" or (c) "Is it possible for there to be a world where logic neither applies nor doesn't apply?" or (d) "Is it possible for there to be a world where logic does apply?" If logic doesn't apply in a world, then...then what? In a world where logic doesn't apply, does logic also apply? If not, why not? Unless logic applies in every world, how can we tell which, if any, of (a)-(d) is the question that the questioner is asking?

Are first principles or the axioms of logic (such as identity, non-contradiction) provable? If not, then isn't just an intuitive assumption that they are true? Is it possible for example, to prove that a 4-sided triangle or a married bachelor cannot exist? Or must we stop at the point where we say "No, it is a contradiction" and end there with only the assumption that contradictions are the "end point" of our needing to support their non-existence or impossibility?

In any "complete" logical system, such as standard first-order predicate logic with identity, you can prove any logical truth. So you can prove the law of identity and the law of noncontradiction in such systems, because those laws are logical truths in those systems. But I don't think that answers the question you're really asking: Can we prove (for example) the law of noncontradiction using premises and inferences that are even more basic , even more trustworthy than the law of noncontradiction itself? No, or at least I can't see how we could. In that sense, then, the law of noncontradiction is bedrock. Pragmatically, we can explain the law of noncontradiction in terms of related notions such as inconsistency and impossibility, but I don't think we thereby "support" the law of noncontradiction by invoking something more basic than it.

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