Possibility != Existence

Great Debates
1

It seems to me a useful principle of rational thought is that we should use as few terms as necessary. If two terms are so similar as to be identical, then they’re equivalent and one is redundant.

Libertarian argues that if it’s possible for a thing to be, it exists. He’s not suggesting that the possibility exists, but that the thing that is possible exists. He then makes a further distinction between actual things and merely possible things.

Therefore:
If something is possible, it exists.
If something is impossible, it doesn’t exist.

Now consider that Libertarian exists, and is actual. It seems rather odd to suggest that he must necessarily be alive, so we can determine that it’s possible that he could be dead, even if he isn’t (dead Lib isn’t actual). Therefore, living-Lib and dead-Lib both exist. We can make no distinctions between the two from logic alone. We can continue this with everything that it’s possible for Lib to be, and conclude that every possible him exists.

It seems to me that this makes the concepts of “existence” and “possibility” equivalent in every way. There’s no way something can exist but be impossible, be possible but not exist, be impossible but exist, or not exist and be possible.

Meanwhile, the concept of “actual” existence (as opposed to virtual) has all the properties of the general meaning of “existence”.

I conclude from this that Libertarian’s suggested definitions of possibility and existence are pointless. Accepting them changes nothing about what we can conclude or what we know; instead, it merely results in the renaming of concepts.

Therefore, I hold that we should reject the idea that a thing that is possible exists. We can speak of the possibility existing, but not of the thing. The standard meaning of “existence” should be used instead of the concept of actuality, which is equilvalent in every meaningful way.

2

I think you are misinterpreting him. His fondness of modal logic should explain the distinction he uses (unless things have radically shifted and I missed it) between possibility, actuality, and necessity.

One semantic interpretation of modalities is to treat them somewhat like the Many Worlds hypothesis first proposed (I believe) by Everett in quantum physics. That is, every possible world exists somewhere in… well, the set of all worlds that exist, really. That’s probably the best way to describe it.

When we want to discuss possibility, then, we discuss what consistent descriptions can be made of various events, people, things, universes, teakettles, et cetera. The actual world, the one we find ourselves in, is of course possible and we experience it. But our world is just one of many possible worlds. In fact something that is only possible here, that I bought a pack of Camels this morning instead of Salems, is actuality somewhere else.

That covers possibility and existence/actuality. Necessity is something that must be true/exist in all possible worlds. That, trivially[sup]†[/sup], includes this world, the actual world. If something necessarily is true/exists, it exists everywhere. One axiom of modal logic is that all theorems of it are necessary. The “process” is called “necessitation” and takes the form
A -> A
when A is a theorem (or another axiom), and indicates necessity.

The discussion of modal logic is not without its own traps, perils, semantic bickerings, and limitations (which set of axioms will we accept?). Stanford’s philosophy pages give a fantastic exposition on all the different axioms and arguments for and against them.

But I think you knew that… I swear you were in a discussion about this already when Libertarian pulled out the proof of necessary existence (as God).

This is not the case. If Lib’s existence is not necessary, but he clearly exists, then the statement
<>L
is true. In fact, what this “means” is that there exists a world in the set of possible worlds where Libertarian exists. Which we knew: we live in just such a world.

Not a chance, from where I’m standing. You only accept “exists” as in actuality, but I see a very practical use of considering possibility as viable as well. We can imagine things are not as we know them, and we can grant these considerations great weight, and eventually conclude that perhaps something is the case that we didn’t know previously, or conclude that something isn’t the case but now we know why (what conditions would have to be satisfied for such a thing to be the case). I would humbly suggest this encompasses all human endeavors.

†[sub]I say “trivially” because one of the axioms of modal logic is that the necessity of something implies actuality; that is:
A -> A[/sub]

3

** If I take your words at face value, you prove my point. Things that are possible == things that exist.

** What difference could it make? What if it weren’t actual elsewhere that you purchased Camels?

** Quibble: that includes part of this world, not necessarily all of it.

** How is this different from “possibility” and “existence”?

4

We also know that
<>~L
is true. Not-Libertarian must exist as well.

5

Possible== I may describe a consistent world where such a thing is actual.

Actual== The possible world in question is this world.

Possible but not Actual== The possible world in question is not this world.

Necessary==Pick a world. It is so.

Then it would be impossible. The necessity of its impossibility would be the case.
~<>A

We are not concerned with parts of worlds in the possible worlds semantics of modal logic. We are only concerned with states of affairs that are the case, states of affairs that could be the case, and states of affairs that are not the case; such states of affairs are the worlds (they are the whole of what is being considered). States of affairs that could be the case are given hypothetical treatment of actuality. This would be the equivalent, in a mathematical proof, of assuming a function exists with such-and-such properties already in order to proceed with deriving some shortcuts or applications or whatever theorems do. Such a function is possible: that does not mean it will ever be dealt with (or that we can create one). Disregarding possible world semantics lends one to different interpretations of possibility, but not really necessity (where we are mostly only concerned with the affect such a necessity has on actuality, which is that it implies it).

Again, pure deduction from the given axioms of modal logic are true in all states of affairs (which must be the case else we couldn’t use modal logic to describe them).

6

Yes. If ~L but <>L then <>~L, too. The relationship between necessity and possiblity runs thus (I proved it in another thread and can go find it if you like):

<-- > ~<>~
and
<> <–> ~~

Quite a nice symmetry. Given the definition of one in terms of the other, the other relationship can be derived in a few steps. It seems largely arbitrary which we choose to define first because of necessitation, both will always be true.

7

Okay. So what’s the difference between this conceptualization of “actuality” and the general conceptualization of “possibility”?

8

I’m sorry Vorlon but I have to go out of town. I will return on Wednesday at the latest. Lib should be in shortly to give another exposition. :slight_smile:

9

Oops. I meant “existence” instead of “possibility”.

If something is actual, doesn’t this mean the same thing as the old sense of existence? If something exists (new sense), isn’t this the same as saying it’s possible (old sense)?

10

But thassa thing: We can’t say that it is so until we have examined all other worlds, can we? Hell, we can’t even say that other worlds exist to prove the necessary existence of existence.

11

I’d like to hear that straight from the horse’s mouth; my understanding (in italic because I very quickly lost the plot in Lib’s God logic thread) is that Lib was saying that if something is possible and necessary then it must exist.

12

There are three axioms added to system 3 to form the system 5 propositional calculus:

The K Axiom — (p -> q) -> (p -> q)

The T Axiom — p -> p

and the 5 Axiom — <>p -> <>p

and one rule:

The Derived Rule of Necessitation — a metatheorem stating that anything derivable from necessary truths is a necessary truth. Formally, it is

T |- p -> T |- p (where |- means “within the set”)

There is no axiom or rule that states “<>p -> p”. However, there is an axiom in S3 that states “p -> <>p”.

13

Lib, was that responsive to Mangetout’s question? Or the OP?

I hope that you will note that most of the posts before yours went into a great deal of explanation in simple English before moving into symbolic logic.

I do not find your post to be useful to your argument.

You may well be correct, but how are people to judge?

A person that knows the subject well may simply dismiss it as
amateurish nonsense. A novice may dismiss it as pretentious nonsense.

You are posting on a board where the language is English. If you can’t state your argument in English, don’t bother.

The introduction of well defined words and symbols are useful shortcuts in some circumstances. The mere use of those words and symbols does not take the place of rational debate.

14

The post was a response to Mange. I have not read the OP. The T Axiom, shown above, states that if something is necessary, then it is actual.

15

Lib’s ontological argument for God has steps approximately equal to the following:

  1. The definition of God requires that if God exists, its existence is necessary.
  2. God is possible.
  3. God therefore exists in a possible world.
  4. Therefore, God exists in every world.
  5. Therefore, God exists in this world.

Step #2 is where his argument fails (it presumes something which I don’t think we can take for granted). However, step #3 also contains a massive gratuitous assumption: that if we consider something to be possible, it can be said to exist.

Someone once said that probability is an artifact of our ignorance. We have no way of knowing whether or not our world is truly deterministic or not (although I suspect that it is by nature deterministic, I have yet to find a geniune proof), and no experimental method could ever determine whether it is or not.

Saying that a possible event exists is an abuse of language. The ontological proof exploits an aspect of a particular system of symbolic logic that allows a possibility to be discussed as an actuality.

Possibility != existence. Claiming otherwise does not introduce any new meaning into the languge, but only allows us to creatively misinterpret proofs.

16

I have no problem with possible events existing, as long as their opposites have equal existence. A mere novice I am, but nowhere in Lib’s proofs do I see the possibility of eg. God not existing accounted for.

I have already promised him I will mug up on this “Necessary Existence” malarkey, but I still hold that equating “Necessary Existence” with “Supreme Being” smells rather fishy, as though one has just typed “Necessary Existence” into a thesaurus and cherry-picked the output. It still seems that God=Everything is part of the first step, and I am as likely to assert this as to enjoy having my wallet stolen.

17

Yes.

No, exist and actual are still very close. The only problem with “exist” now is that it must be qualified as to what kind of existence it is; is it possible existence, is it actual existence?

Consider, for example, the ever-popular mention of different geometries. In Euclidean space, we would ask: is it possible for the interior angles of a triangle to add to anything other than 180°? And the answer would be: Yes, it is possible (given these axioms instead), no it isn’t actual (I can prove all triangles here in Euclidean space must have etc), and hence it isn’t necessary. Is that any clearer?

Maybe. That depends on what you mean by “other worlds” and “examine”. We don’t have to go there, because we aren’t (necessarily) talking about entire universes or planets or anything… we’re just talking about a condition where such-and-such things are the case. The rest of the variables, or even their existence, is outside the scope of the proof.

I have nothing more to say on the modal ontological argument that I haven’t said in about four other threads. :stuck_out_tongue:

18

The big problem with the Ontological Argument is it is proof by definition. Recasting it in modal logic does not change this fundamental flaw.

19

Sentient wrote:

That would be a substantive denial of a positive ontological proposition. Necessity is logically possible, and therefore without contradiction. You cannot even posit necessity existing contingently, much less not existing at all.

Urban Ranger wrote:

As a matter of fact, recasting it in modal logic would reveal any such flaw. But when modalized, G is not an axiomatic premise, but the penultimate inference. Therefore what you say makes no sense, and is probably why no one else, including Spinoza, Suber, Hartshorne, or even Kierkegaard have ever made any such claim.

20

You mean recasting it in modal logic changes its nature? That’s interesting. That is not a pure transitional mapping operation then.

Considering that modal logic is based on K, which is attributed to Saul Kripke, I would be very surprised that Spinoza or Kierkegaard made any such claims. :rolleyes: