7

Let Γ be the class of all impossible sentences, i.e., Γ = {φ : ¬◊φ}. Someone claiming that nothing it impossible is simply claiming that Γ = ∅. That commits them to the thesis that no formula is necessarily false, not that "the impossible is impossible" (whatever that means). The thesis is obviously false (i.e. Γ ...


7

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 Lewis, in part reflecting their respective traditions (continental and analytic), are far apart on the possible because they are far apart on the real. Lewis's &...


7

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 causality but none the less followed probabilistic laws - exhibited probabilistic regularities - then we could easily get by counting on such regularities if their ...


7

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 hypothetically, but his plurality is much reduced compared to what even "one-truth" mathematical platonists admit. First, "Tegmark replied that perhaps only Gödel-...


6

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 is a well known technique in Pure Mathematics. He is demonstrating that for any infinitely long list of scenarios, there is some scenario (which is a possible ...


5

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 argument hinges on the existence of 'good' that suppresses evil to the greatest extent. However, even if we accept for the sake of argument that there are other ...


5

It seems to me that your question is ill-posed. With that I mean that the question is not well defined: take for example the classic problem "If a tree falls but no one is there, does it make any sound?" The problem with this is the unclear definition of "sound", so if one does not define it better, the question is ill-posed. Back to your problem. ...


5

Each possibility, from what range of possibilities? By the very nature of the notion of something which holds "in a world", it does not make obvious sense that something which holds of a world can be a property of the collection of all worlds. To make a (rough) analogy: it is not clear that if one country does not (politically speaking) formally recognise ...


5

Another option using a Possible Worlds account is to interpret "possible" and "impossible" slightly differently, making use of alternative Modal Logics for the box and diamond operators. These can still be worked into discussions about possible worlds, but the semantics of how these worlds are related to one another becomes a little more ...


4

Yes, there is the framework which is known as two dimensional semantics, a concept first developed by Robert Stalnaker in the 1970s. The related two modal dimensions are not modal in the same sense. According to a common interpretation (following the terminology of Saul Kripke in Naming and Necessity), one modal dimension is considered "metaphysical", ...


4

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 expression does serve a purpose in daily discourse, but of a shallow sort. We modify a sentence with the adverb 'necessarily' when it is a sentence presumed ...


4

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 founded by Kripke and Putnam. Essentialism is simply the claim that objects have some properties "of necessity" while others are "accidental". ...


4

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, woooo'. "the brain is likely to have different patterns of electrical activity in each of the branching worlds." Why? You are assuming brains are ...


3

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 for modal statements, is she then forced to commit to a belief in modal realism? No, at least not the extreme modal realism of the sort Lewis endorses. Here's ...


3

Step two of the cited argument from Sider is a step that relies upon a certain link between conceivability and possibility. It could have been split into two steps and phrased thusly: "2a) Gunky objects are conceivable 2b) (therefore) Gunky objects are possible". Possible worlds seems to play a merely heuristic role here. There is, however, a more general ...


3

Sure. In certain modal logics, the concepts of necessity and possibility are taken as quantifications over those worlds that are accessible to a world, which allows us to say things like "necessarily, P, but not necessarily necessarily P". If we have a semantics in which there is a value assigned to a given world (let's say the number of cute fuzzy bunnies ...


3

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 language, mind, or mathematician reflecting on the question. On the other hand, a non-realist in truth-value will argue that AC is independent of set theory and ...


3

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 though these are the names we retrospectively use to describe him. This break was occurred in the early part of the 20C. It was quite common then for scientists ...


3

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: The world would not "be" in any sense that we could apply. Consciousness requires causality, otherwise no thoughts would arrive from any inputs to the system. ...


3

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). 1+1=3 trigger the principle of explosion if our logic works, but it doesn't if logic is different as it should be in the IW. From the point of view of the ...


3

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 criticism of the simulation argument. Deutsch's criticism of the simulation argument can be found on pp. 11-12 of It from Qubit. A universal computer only requires ...


3

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 is. You seem to be under the impression that MWI posits that each time there's a quantum event of a certain type, the universe actually splits into two or more ...


2

Possibility and necessity in St. Thomas's sense cannot be understood without Aristotle's doctrine of matter and form (hylemorphism). Possibility (or necessity) in the modern philosophical sense (the Humean sense) is more about whether we can conceive another world in which something can be (or must be). Regarding how "All the objects collectively have a ...


2

Yes, according to Lewis. In Lewis' modal realism, to say that some statement R(x) is possible dictates that a possible world exists in which R(x) is not only possible but actually true. This stance is called alethic modality (intimately related to epistemic modality in philosophy of language). Note that Lewis does not claim that for each statement R, a ...


2

The arity of a relation R is the number of its "argument places". Thus, the relation "less than" is a binary relation: it has arity 2. We usually write: x < y, but we can write it "more formally" as: <(x,y). An extensional relation of arity n on D is a subset of D^n (i.e. D x D x ... x D: the set of all n-uples). The set of all extensional relations ...


2

Your questions assumes a lot. The contemporary conception of possible worlds stem from the work of David Lewis. On his account, Modal Realism, worlds are defined as concrete maximal mereological sums, all of which parts are spatio-temporally related. If you don't like Modal Realism (and no one really does), then, if you still want to employ possible worlds ...


2

Eli Bashwinger has a point, and there does indeed seem to be something wrong with the quotation. I think the article makes an implicit distinction along these lines: a presumably modal notion of consistency applies to a set of uninterpreted sentences, whereas a non-modal notion of consistency would apply to a set of interpreted sentences; where a sentence ...


2

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 to be able to say that it is possible for something to be impossible, i.e. ◇□ ¬A, without this collapsing to □¬A, you need to use a modal logic weaker than S5.


2

Something logically possible is something that is not logically impossible, and logical impossibility need not be defined circularly. Much of our modern ways of thinking about modal logic can be traced back to Leibnizian thought, and Leibniz associated impossibility with contradiction. For him, contradictions were impossible combinations such that, for any ...


2

The problem is that you have defined in 1) that there is good and evil and in 2) you have defined the characteristics of each, but you have not specified that either of these things are the case in all possible worlds. If you do, then such a situation as you describe in 3) exists in all possible worlds, so your conclusion at 4) is wrong, we do not live in ...


Only top voted, non community-wiki answers of a minimum length are eligible