# Tag Info

### Can a function have a set as its value?

A function f: A --> B maps each element of the set A to an element of the set B. Example: Take A the set of natural numbers and B the powerset of A, i.e. elements of B are the subsets of A. For ...
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### Can a function have a set as its value?

In set theory, a “function” is actually a binary relation fulfilling certain properties. A “binary relation” is any subset of the Cartesian product of two sets. The Cartesian product of two sets is ...
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### Did David Deutsch really disprove the Simulation Hypothesis?

To be honest, I couldn't exactly follow your construction. But I can say that Deutsch is definitely not using an impossible scenario. He is actually adapting the Cantor Diagonalisation Argument which ...
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### How does the concept of the 'virtual' (Deleuze) relate to 'counterfactuals' (Lewis)?

In a sense, Deleuze's virtual and Lewis's possible worlds compete to provide the "right" conception of the possible. The descriptions are indeed similar but this is deceptive, Deleuze and ...
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### If we imagine a world that functions without causality, how absurd could it be?

If the world were without causality then it need not change in any way. It might fortuitously behave exactly as it does now. This is certainly a logical possibility. If the world were without ...
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### Does Tegmark's Mathematical Universe hypothesis allow existence of alternative mathematics?

Pigliucci gives an interesting review of the Mathematical Universe based on personal conversations with Tegmark. Apparently, Tegmark does admit plurality of mathematical structures, at least ...
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### Is the notion of “possible” vacuous?

You already said it yourself in your first sentence: We use the term possible to often refer to events that don’t violate a certain model of reality and impossible to refer to events that do. Note ...
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### Can a function have a set as its value?

tl;dr: Almost always, a function has an (implicit or explicit) intended output type; and sometimes that’s sets, but if it’s anything else, then the function’s values must be those things, not sets. A ...

### Why does it matter if we live in "the best of all possible worlds"?

I believe in good and evil but reject the argument, so will address this part as requested: how is it possible to criticize above argument and deny that we live in the best possible world? The ...
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### Did David Deutsch really disprove the Simulation Hypothesis?

Deutsch is restating some well known results in the theory of computation discovered by Godel and Turing. The result explains that not all functions can be calculated by a computer. This is not a ...
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### Why can we not reduce necessity to analyticity?

The OP is very close to Quine's considered view of necessity, as e.g. in Pursuit of Truth: "In respect of utility there is less to be said for necessity than for the propositional attitudes. The ...
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### Is essentialism compatible with naturalism?

Essentialism is compatible with naturalism, Aristotle, the father of essentialism, is typically named as a precursor of naturalism (and even empiricism), and today we have scientific essentialism ...
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### Computer vs brain in many-worlds interpretation of QM

But classical computers rely on quantum processes too, which underlie the function of semiconductors. You can't just say 'wooo quantum things are weird the brain is weird, therefore they are the same,...
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### If something is Possible is it therefore Necessary?

"Possible", "necessary" and "real" are the three modes of existence in ontologies with possible worlds. One of the main possible-worlds models has been introduced by ...
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David Lewis (IEP), a great contemporary philosophical mind, had empirical beliefs and certainly, like most professional contemporary philosophers, had a naturalized epistemology. But was he an ...
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### How can we test whether other possible worlds exist?

There are a number of SEP articles about this and similar questions: "Possible Objects." "The Possibilism-Actualism Debate." "Possible Worlds." "Impossible Worlds.&...
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### How can we test whether other possible worlds exist?

Most talk of possible worlds in philosophy uses that term in the sense of hypothetical worlds, or imaginary worlds, which are just supposed contexts for a particular idea. If you are a practically-...
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### Is there an idea of non-spatial reality in philosophy?

Whereas philosophy was once closely associated with nature this is less so in the modern era; for example, Newton thought of himself as a natural philosopher and not as a mathematician or physicist ...
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### Ontological status of Axiom of Choice

How one answers such questions obviously depends on ones philosophical views. A realist in truth-value such as Quine or Putnam, will argue that AC has an objective truth value independent of the ...
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### If we imagine a world that functions without causality, how absurd could it be?

The question needs a better definition of terms. What exactly is it that you mean? If you mean a complete disconnect between events so that there is no chain of causality, then the answer is simple: ...
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### Is there any way to represented nested modalities in alethic modal logic?

In S4 modal logic, nested modalities of the same type collapse, so □□A ↔ □A and ◇◇A ↔ ◇A. In S5 modal logic, all nested modalities collapse to the rightmost one, so □◇A ↔ ◇A, and ◇□A ↔ □A. If you want ...
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### Does semantic externalism imply modal realism?

This question seems to have been resurrected; I trust no-one minds if I answer it. If a philosopher accepts semantic externalism and accepts that possible worlds are the correct form of semantics ...
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### How could we get a world where only impossible things happen?

A very interesting question. I think that you are not committed to the existence of both the worlds, because you are looking at the impossible world (IW) from the perspective of the possible one (PW). ...
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### Can possible-but-non-actual objects have accidental properties?

In positive free logics, non-existent objects can satisfy (atomic) predicates, so it can come out as true that Pegasus has wings. But in negative free logics, non-existent objects cannot satisfy (...
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### Can many worlds interpretation have universes with different laws?

Couldn't MWI predict universes with different fundamental laws of physics (as a level-4 multiverse hypothesis would do, like string theory)? No. To understand why, you need to really grok what MWI ...
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### The intensionality of modal logic

Lets say that intensional roughly means something along the lines of Frege's sense/reference. In particular, we have that the sense of a proposition is intensional, it varies across possible worlds. ...
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The answer depends upon what you mean by the words believed, possible worlds and real. If you believe that somewhere, in different universes presumably, there are countless worlds that exist in the ...
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### Can one determine the meaning and truth value of counterfactual statements without invoking the existence of possible worlds?

There are a few things that can be said in answer to this question. As has been pointed out in the comments, one does not need to believe that possible worlds have real existence in order to make use ...
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### How be so sure that implications are bivalent? (An attempt to resolve paradoxes of material implication)

The logic you describe is not many-valued unless you allow for values other than true and false. The fact that you are using many worlds (usually called possible worlds) is pretty standard, but the ...
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