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If it's possible for a cat to be alive and dead at the same time, or for a particle to be in two places at the same time, would that show there are at least some things about which one couldn't rely on "Either P or not P" as a sound step in reasoning?

Your question concerns the classical law of excluded middle (LEM): For any proposition P, either P or not P. Because logic is absolutely fundamental, ceasing to rely on LEM will have ramifications that are both widespread and deep. In classical logic, we can derive LEM from the law of noncontradiction (LNC), so to give up LEM is to give up LNC or the equally obvious laws that allow us to derive LEM from LNC. We should be very reluctant to do that. In my view, the alleged possibilities that you cite from physics are not enough to overcome that reluctance. First, they are possibilities only according to some, not all, interpretations of quantum mechanics. Second, even if we accept them as possibilities, rejecting LEM or LNC is more costly than (1) reconceiving "being dead" and "being alive" so that they name logically compatible conditions and (2) reconceiving "being here at time t " and "being elsewhere at time t " so that they name logically compatible conditions. It's less costly to mess with the...

Many astrophysicists speculate that everything came from nothing. How can something come from nothing? The above speculation would break the law of conservation. Either something has always been here or what we call something is actually made of nothing (nonmaterial.) Please give me your prospective. Thank you, Awareness1963

My perspective: Even if matter hasn't always existed, something or other has always existed (which is compatible with the claim that our Big Bang occurred finitely long ago). For the perspective of someone much better-informed about this issue than I am, see this link .
For the record, I'm far from happy with Krauss's way of putting things, which is why in my response I linked not to Krauss's book but to Albert's (scathing) review of it, the same review later linked to by Professor Stairs.

Assuming that the multiverse account of the universe is true -- and every possible reality is being simultaneously played out in an infinite number of parallel universes -- am I logically forced into accepting a nihilistic outlook on life? Or is it still possible to accept the truth of the multiverse account and still rationally believe that the pursuit of life goals is both meaningful and valuable, despite the fact that every possible outcome -- or potential reality -- is unfolding somewhere in another parallel universe?

I don't think that the multiverse account implies that it's irrational to pursue life goals or irrational to believe that pursuing life goals is meaningful or valuable. For even if the multiverse theory is true, I take it that you yourself are confined to one universe, our universe. The beings very similar to you who inhabit other universes are at best "counterparts" of you, which leaves open the question "What will you do with your life?" It may be well and good if one of your counterparts works hard to achieve wisdom, promote justice, or whatever, in some other universe. But his/her hard work isn't yours and doesn't occur in your universe. We need your shoulder to the wheel here!

The big bang theory says that time began with the big bang. Is that correct? Then does that mean that those who describe the big bang theory as an idea that something comes from nothing are incorrect? If time began with the big bang doesn't that mean there never was a time when there was nothing?

I can't resist responding to one thing that Prof. Stairs says in his excellent reply: "If there's no such [necessary] being, then it might be that there's no explanation for why contingent things exist." I used to think that myself. But as I thought more about the question "Why do any contingent things exist?" I concluded that the question has a very simple answer -- indeed, many simple answers -- if it's a well-posed question in the first place, and those answers have nothing to do with any necessary being. I try to explain why in this paper .

Is length an intrinsic property or is it something which is only relative to other lengths? Is an inch an inch? Or is it simply a relation between other (length) phenomena?

Interesting questions. As I understand it, special relativity in physics says that having a particular length isn't intrinsic to an object, because observers in various "inertial frames of reference" can measure different values for the length of an object without any of them being mistaken: the length of an object is always relative to an inertial frame, and no inertial frame is objectively more correct than any other. As for units of length such as an inch, I'm inclined to say that they're always relative to some physical standard, whether the standard is a single physical object such as a platinum bar or, instead, some physical phenomenon like the path traveled by light in a given period of time (with units of time also being physically defined). In a universe containing no physical standard that defines an inch, nothing has any length in inches even if things have lengths in (say) centimeters when a physical standard exists for the centimeter. I hesitate a bit in holding this position,...

Is Kant's project of reconciling freedom with an apparently deterministic nature still relevant given how Quantum mechanics does not (as I understand it) see nature as a deterministic totality?

In my opinion, it's no harder to reconcile freedom (free choice, responsible action) with determinism than to reconcile it with indeterminism. On the contrary, it may be easier; see, for example, this SEP entry . According to compatibilists, we can act freely even if determinism should turn out to be true and hence even if the indeterministic interpretation of quantum mechanics should turn out to be false. But no one thinks that the truth of indeterminism (whether quantum indeterminism or some other kind) by itself would suffice to give us freedom. The debate is about whether indeterminism is necessary for freedom. In my view, incompatibilists bear the burden of showing that it is and have failed to discharge that burden.