Bede Rundle has an interesting book out called “Why there is something rather than nothing”

Rundle argues for the view that there cannot be nothing, either at some point in the past, or at some point in the future. Rundle is not alone in making this sort of claim but he does give some arguments for it rather than merely asserting it as obvious and the conclusion is tentatively held. This is because it is based on the considerations of arguments that might in principle be mistaken.

These arguments that nothing and we are talking about absolute nothing here cannot be conceived of stem from Kantian considerations about the conditions of possibility for conceiving objects or events involving space/time. We can readily conceive of particular objects going out of existence, like marbles in a box, but it is more difficult if not impossible to conceive of the setting for all the objects to go out of existence. We may imagine all the planets to go out of existence but when we do this we tend to imagine empty space rather than absolute nothingness.

Rundle thinks that our attempting to conceive of total non-existence always leaves us “with something, if only a setting from which we envisage everything having departed, a void which we confront and find empty…”

Once this is granted the argument assumes that what we cannot conceive of delimits what is genuinely possible and so nothing is not genuinely possible because it is inconceivable.

Then he claims that the question “Why is there something rather than nothing?” assumes a false possibility i.e., that nothing is possible.

Hence Rundle explains why there is something rather than nothing instead. Something was more likely than nothing. There is a link to him on conversation discussing his work below

http://www.closertotruth.com/video-profile/Why-is-There-Something-Rather-than-Nothing-Bede-Rundle-/368

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1. States of affairs are conceivable

2. States of affairs posit empirical facts

3. States of affairs can be true or false

4. ‘The present day King of France is bald’ is a state of affairs but not an empirical fact

:. 5. States of affairs are not themselves empirical facts

6. ‘The negation of everything’ is a state of affairs (but not an empirical fact)

7. ‘The negation of everything’ excludes all empirical facts but not states of affairs

8. ‘The negation of everything’ would be inconceivable iff it excluded states of affairs (and empirical facts)

:.9. ‘The negation of everything’ is not inconceivable

‘The negation of everything’ = ∀x, Ǝy ¬(x=y)

Well, quite, I think Rundle is probably confusing what we can imagine with what is intelligible. I admit that I cannot IMAGINE the non-existence of everything; but I don’t see how any very strong argument can be based on human imaginative capacities. The question is, as the previous commentator more or less implied, whether it is meaningful to say ‘For all f, there is no x such that fx’. And this certainly does seem intelligible. At least, I understand what it means. If it could be shown to lead to a contradiction, then the matter would be different, but then the deduction must be set out.

I wonder if Rundle has not unconsciously been influenced by the following (fallacious) argument: if I think of anything, or conceive of anything, then there must be something I think or conceive. Thought must be thought of SOMETHING. Therefore, it is impossible to conceive of what is not. This argument goes back to Parmenides of Elea:

“…that it is not and that it is needful that it not be, that I declare to you is an altogether indiscernible track: for you could not know what is not – that cannot be done – nor indicate it…What is there to be said and thought must needs be: for it is there for being, but nothing is not. I bid you ponder that, for this is the first way of enquiry from which I hold you back, but then from that on which mortals wander knowing nothing, two-headed; for helplessness guides the wandering thought in their breasts, and they are carried along, deaf and blind at once, dazed, undiscriminating hordes…”

At the risk of being classed with the “undiscriminating hordes” I think it clear that we can think of “what is not”. Russell’s theory of descriptions really sorts out this tangle. If I say “the golden mountain does not exist” I am not ascribing the property of non-existence to an object called ‘the golden mountain’. Rather, I am saying ‘there is no value of x for which “x is golden and mountainous” is true’.

“‘The negation of everything’ = ∀x, Ǝy ¬(x=y)”

What a funny thing to say, TC. Far from being equivalent to “the negation of everything”, ∀x, Ǝy ¬(x=y) asserts that for every x, there is at least one item (y) which is not the same as x. This is a true proposition so long as there are at least two things in the universe.

If you construe ‘for some’ as ‘there exists’ (not uncontroverted, but not uncommon either),

∀x, Ǝy ¬(x=y) reads ‘It is not the case that anything exists.’ Note that x=y falls within the scope of the negation sign. So it is not the case that anything is equivalent to something existing.

If you only want to assert that there is at least one item (y) which is not the same as x,

∀x, Ǝy ¬(x=y) will not do, because it will be false whenever x is equivalent to something.

∀x, Ǝy x=¬y asserts that for every x, there is at least one item (y) which is not the same as x.

Note that, by contrast, ∀x, Ǝy x=¬y will not be false whenever x is equivalent to something

Hmm, I think we’re obviously using symbols to mean different things – we obviously had different logic tutors! For me, “¬” is a negation sign, so that it can only be put in front of propositions, not variables (“¬p” is true when p is false and false when p is true). Thus “x=¬y” is meaningless. “=” is the sign of identity, not equivalence. It makes sense to say of two propositions that they are equivalent (i.e. that they have the same truth-value), but it makes no sense to assert equivalence of two variables. “∀x” means “for all x”. “Ǝx” means “there exists an x such that”. I confess that I am unfamiliar with your use of these symbols.

Perhaps you could explain what you mean by the symbols ∀, Ǝ, = and ¬.

““¬” is a negation sign

“∀x” means “for all x”. “Ǝx” means “there exists an x such that”.”

I understand that, which I think is clear enough from what I have said.

I have either missed or forgotten that the negation sign cannot be put in front of variables and that “it makes no sense to assert equivalence of two variables.”

My motive for presenting that formula was not to ‘pimp up’ my remarks but to make my thinking clear. If I have got that wrong then it is something for me to look at.

Could one not construe ‘x=¬y’ as ‘x≠y’?

∀x, Ǝy ¬(x=y) does not seem to be the same as ∀x, Ǝy x≠y

I concur on the meaning of the universal and existential quantifier. What do you mean by a “negation sign”? The reason why the negation sign cannot be put in front of variables is that is applies to propositions, and has its own truth-conditions. “¬p” is true when p is false, and false when p is true. “x” is not a proposition and is thus neither true or false, hence I don’t see what “¬x” could mean.

You can say that “a=b”, but this is to assert identity, not “equivalence”. “Equivalence” is used in two ways according to whether we are referring to “material” or “formal” equivalence. For “material” equivalence, p≡q (“≡” being the sign of material equivalence) iff p and q have the same truth-value. For “formal” equivalence, p is equivalent to q if each formally entails the other. Both these concepts apply to propositions. Hence again I don’t see what x≡y could stand for, since “x” and “y” are not propositions and don’t have a truth-value (and, not being propositions, don’t formally “entail” anything). Perhaps you were just using “equivalence” to mean “identity”. Probably.

I still claim that ∀x Ǝy ¬(x=y) asserts the existence of at least two things in the universe.

We are agreed that “∀x” means “for all x” and “Ǝy” means “there exists a y such that”. “¬(x=y)” means “it is false that x=y” or “it is not the case that x=y” or “x is not identical with y”. So the whole propositions reads: “For all x, there is a y such that x is not identical with y” or “For every x, there is a y such that x is not identical with y”. In a universe consisting of just two items, “a” and “b”, this proposition is true. For in such a universe, “x” has two possible values, “a” and “b”. If x is “a” then there exists an entity that is not identical with “a”, namely “b”, and if x is “b” then there exists an entity which is not identical with “b”, namely “a”. Hence, for every possible value of x, there is an entity y such that y is not identical with x.

“∀x, Ǝy ¬(x=y) does not seem to be the same as ∀x, Ǝy x≠y”

If that’s the case, then you are clearly using ¬(x=y) (“it is false that x=y”, or “it is false that x is identical with y”) to mean something different to x≠y (“x is not identical with y”). To me “it is false that x is identical with y” is formally equivalent to “x is not identical with y”, but if for you this is not the case, then maybe you construe “¬(x=y)” and “x≠y” to mean different things, in which case I would be interested in your definitions of “¬(x=y)” and “x≠y”.

“Could one not construe ‘x=¬y’ as ‘x≠y’?”.

Well, for me “x=¬y” means nothing, but if you are taking it as meaning the same as “x≠y” (“x and y are not identical”, or “x is not identical with y”) then at least now I know what you mean! In which case, “∀x, Ǝy ¬(x=y)” means “∀x Ǝy x≠y” (“For every x, there is a y such that x and y are not identical”). I’m not sure how this helps you. This still seems to me to be true in any universe where there are at least two objects.

Okay, I understand your points about negation, propositions, identity and equivalence.

A couple of questions, for clarification:

1. Do variables not behave differently when bound by quantifiers, such that it does make sense to say that some x = y, no x = y, etc.? Or should one always use propositions (some P are Q, no P are Q) or predicates and variables (for some x, Fx, for no x, Fx)?

2. I still feel that ∀x Ǝy ¬(x=y) says ‘For all x, for some y, it is not the case that x=y’, which is the same as ‘It is not the case that any x is y’ and ‘No x is y’. This is different from saying that “For all x, there is a y such that x is not identical with y”. You disagree, but I assume you appreciate the difference I am trying to convey. How would you adequately render this difference formally?

“To me “it is false that x is identical with y” is formally equivalent to “x is not identical with y”, but if for you this is not the case, then maybe you construe “¬(x=y)” and “x≠y” to mean different things, in which case I would be interested in your definitions of “¬(x=y)” and “x≠y”.”

My understanding of “¬(x=y)” and “x≠y” is they are equivalent in that form but not when bound by the quantifiers in ∀x, Ǝy ¬(x=y) and ∀x, Ǝy x≠y.

This is because ∀x, Ǝy ¬(x=y) is false whenever x=y, whereas ∀x, Ǝy x≠y is not false whenever x=y.

1) ∀x, Ǝy ¬(x=y) seems to assert that ‘No x is identical to some y’

2) ∀x, Ǝy x≠y seems to assert that ‘Any x is not identical to some y’

(1) is false whenever x=y because it denies that any x=y

(2) is not false whenever x=y because it claims that there are only some y that are not identical to any x. It does not exclude the possibility that some y might still be identical with any x.

Re. (2): Perhaps this does result from my confused use of variables, but I am thinking of the square of opposition, where Some x are P and Some x are not P are subcontraries. They cannot both be false, but they can both be true.

“1) ∀x, Ǝy ¬(x=y) seems to assert that ‘No x is identical to some y’”

The proposition “No x is identical to some y” seems very odd. It says that there is some one entity (y) such that nothing is identical with that entity, not even itself (since ∀x is all x, including y if, as the proposition asserts, there is some y). It seems to me that such a proposition must always be false in any universe, and can never be true. It is not true in a universe consisting of nothing, since it asserts that something – y – exists. That is indicated by the existential quanitifer Ǝ.

If I were asserting that “nothing exists” I would say: ∀f ¬Ǝx fx (“For every predicate, f, there is nothing satisfying that predicate”, or “nothing can be asserted as characterising anything”). That, I think, is the nearest one can get in formal logic to “Nothing exists”.

But you know what? It’s far too absurd to debate logic at 1 in the morning. Especially as we both agree with the IMPORTANT point that it is a perfectly intelligible proposition that nothing exists!

Okay

“If I were asserting that “nothing exists” I would say: ∀f ¬Ǝx fx (“For every predicate, f, there is nothing satisfying that predicate”, or “nothing can be asserted as characterising anything”). That, I think, is the nearest one can get in formal logic to “Nothing exists”.”

That makes perfect sense.

I also understand ∀x, Ǝy ¬(x=y) and ∀x, Ǝy x≠y to be propositions, but perhaps that is a mistake?

To me, both are propositions. Indeed, they seem to me the same proposition, namely “for every x, there is some y such that y is not identical with x”; but, you see, for me this means that there are at least two things, so that for each of them there is something (the other thing) which isn’t identical with it.

Agreed, although I didn’t really want to fail at rendering intelligible what I claimed to be intelligible. I also managed to squeeze some free logic tuition out of it!

Cheers John 😛

““1) ∀x, Ǝy ¬(x=y) seems to assert that ‘No x is identical to some y’”

The proposition “No x is identical to some y” seems very odd. It says that there is some one entity (y) such that nothing is identical with that entity, not even itself (since ∀x is all x, including y if, as the proposition asserts, there is some y). It seems to me that such a proposition must always be false in any universe, and can never be true. It is not true in a universe consisting of nothing, since it asserts that something – y – exists. That is indicated by the existential quanitifer Ǝ.”

Looks like I had better reread that Chisholm paper on Meinong…

My head hurts.

Meinong had some weird views. He agreed with Parmenides that you can’t think of something unless that something is there to be thought, so that even non-existent entities have some sort of being. Hence, even the golden mountain IS in some sense. To reject this, in his view, was to display “a prejudice in favour of the actual”. Funny guy…