Rational Theists and Rational Atheists of the World, Unite!

[TheAtheist]

That’s probably the most honest thing I’ve heard all day. I salute you. :yup:

:tips his hat:

There always be more Sophists than Philosophers, of this Plato’s followers were correct. Perhaps because the Sophists have more fun.

Or to the Catholic contingent watching:

For every 1 Thomas Aquinas that may exist today, there’s about 1,000,000 Peter Abelards.

The trick for me will always be: How to find good old Tom in the the sea of Abelards?

 

[warpspeedpetey]

What exactly does it mean for something to have an “essence” of existence?

en.wikipedia.org/wiki/Essence

In philosophy, essence is the attribute or set of attributes that make an object or substance what it fundamentally is, and which it has by necessity, and without which it loses its identity.

Again, “x exists” simply means that there is some object which conforms to the definition of x. In that way, existence is a relationship between an object and its definition. Defining something as being existent is meaningless. For example, I could define “The Magical Martian Pinball Machine” as a pinball machine that exists on Mars. Could we then conclude that a pinball machine exists on Mars? The idea is ludicrous. Defining the Martian Pinball Machine as being necessary gives us the same result. Why should it be any different for your god of choice?

we arent saying that x exists, we are saying that G-d is existence, so to speak. thats what it means for G-d to be the being whose essence is existence.

existence is necessary in all possible worlds, ergo, G-d as the being whose essence is existence, is therefore, necessary.

You assert this confidently, but you haven’t offered any rationale to support it.

we have had this conversation before. “there is no such thing as nothing” remember?

though astro gave a good demonstration above.

“no-thing exists” is a logical contradiction, if there is “no-thing” there is no existence.

Why must anything exist?

because then there would be nothing, a logical contradiction.

 

[Astrochemist]

The proof presented has nothing to do with Quine’s two dogmas.

Well, I think we should all agree on what we mean by “x exists” first. Presumably, “x exists” (in the context of the physical universe) means “there is some physical object that satisfies the definition of x.” For example, when we say “a bachelor exists” we mean that there is some physical object that satisfies the definition of “bachelor”; that is, there is at least one unmarried man in the physical world.

If we can agree on that, then I don’t see the logical issue here. There’s no reason to suspect that it is impossible for there to be no objects to satisfy definitions. I suppose you could cite conservation laws of science and claim that matter and energy must always exist in some form, but that’s not a logical issue in itself. Also, that isn’t saying that the existence of matter/energy is necessary.

 

[Oreoracle]

we arent saying that x exists, we are saying that G-d is existence, so to speak. thats what it means for G-d to be the being whose essence is existence.

But this just amounts to saying that God exists as existence. The phrase has no meaning–it tells us nothing about him.

existence is necessary in all possible worlds, ergo, G-d as the being whose essence is existence, is therefore, necessary.

You have not demonstrated this.

we have had this conversation before. “there is no such thing as nothing” remember?

Again, you’re playing word games here. “Nothing exists” just means “there is no such thing as anything.” It’s merely used to indicate universal absence. It’s no different than saying, “No socks exist” except it applies to every object. There’s nothing contradictory about it unless you interpret it as an objectification of nothingness, which would be an inaccurate interpretation. We’re negating all things, not positing a “no-thing.”

If it still bothers you, I could instead say, “It is possible that something does not exist”; that is to say, there is one possible world in which things do not exist. With the word games aside, how do you refute this? I suppose you might protest my deeming universal absence a “world” but that’s only a term we use for clarification.

though astro gave a good demonstration above.

“X is not the case” does not translate to “x is not-x,” despite Astro’s contention. Symbolically: ~X does not imply that X–>~X or that X=~X. If that were true, we wouldn’t be allowed to negate anything!

 

[Astrochemist]

“X is not the case” does not translate to “x is not-x,” despite Astro’s contention. Symbolically: ~X does not imply that X–>~X or that X=~X. If that were true, we wouldn’t be allowed to negate anything!

This is clearly not what I have demonstrated. You do not seem to understand my “contention”, nor my proof.

 

[Astrochemist]

Let me show my proof a little more robustly. This should (for those who understand symbolic logic) get rid of all arguments on both sides.

http://physics.ohio-state.edu/~pbrimmer/logic.JPG

I take (1) to be the statement “nothing exists” interpreted using the definition in quantification/first-order prepositional logic of “exists”.

(2) is clearly equivalent to (1). (3) is simply (2) repeated. I perform an instantiation on (2) using the statement “p” and get (4). I then perform an instantiation on (3) using “~p” and get (5). (6) is (5) reduced by double negation. We take (4) and (6) to get (7) by conjunction.

By simple truth-values, this can also be shown. If all ~x’s are the case, then their conjunction will be a statement where the only possible truth value is “false”, and so is by definition a self-contradiction.

---

The above is all I am saying. I think that, if nothing existed, there would be no logic, and so this wouldn’t matter. I also know that, if we take a different understanding of “existence”, say “in reality”, we can simply state this (R being “exists in reality”):

http://physics.ohio-state.edu/~pbrimmer/logic2.JPG

And there is no self-contradiction with this statement.

My assertion is true, almost trivially so, is clearly independent of Quine’s framework, and does not in itself interfere with or support any theistic or atheistic philosophy.

 

[Think_About_It]

My assertion is true, almost trivially so, is clearly independent of Quine’s framework, and does not in itself interfere with or support any theistic or atheistic philosophy.

That seems to be intuitive enough, though I’m not up on the symbols of expression. Thanks for sharing

 

[Astrochemist]

That seems to be intuitive enough, though I’m not up on the symbols of expression. Thanks for sharing

Happily.

The most important message to take away is that it has nothing to do with the theistic assertion that “something must exist”.

We don’t get that from logic. We get that from opening our eyes.

 

[Oreoracle]

(2) is clearly equivalent to (1). (3) is simply (2) repeated. I perform an instantiation on (2) using the statement “p” and get (4). I then perform an instantiation on (3) using “~p” and get (5). (6) is (5) reduced by double negation. We take (4) and (6) to get (7) by conjunction.

Admittedly, I only know a little about first-order logic. Why is it that you can use P on one premise and ~P on another? Isn’t that begging the question? I mean, if you substitute p for x and ~p for x then of course you’ll end up with a contadiction; that holds true for any argument.

The above is all I am saying. I think that, if nothing existed, there would be no logic, and so this wouldn’t matter.

The argument was about the physical world, not concepts. Logic is based on inference rules, not physical objects. I concede that tautologies, for example, would exist even if nothingness was the case. But again, we weren’t talking about concepts.

My assertion is true, almost trivially so, is clearly independent of Quine’s framework, and does not in itself interfere with or support any theistic or atheistic philosophy.

I’m not familiar with Quine, and so I don’t base my arguments on his authority.

 

[hatsoff]

Nothing exists: “For all x, there does not exist an x”.

This is not a well-formed formula.

 

[Syntax]

Speaking from purely logical standards, that a contradiction arises from the statement “nothing exists” does not require that something exists.

Yes it i does so require it. In logic we translate

“nothing exists”

as

“it is not the case that something exists in the domain of (Ex).”

Since “something exists” is true, and “it is not the case that everything exists” is false, “nothing exists” is likewise false.

The burden of proof is on you to logically demonstrate “nothing exists” is true. If you can’t, then you’re talking nonsense.

It simply requires that, for people to understand anything about the world, something must exist, and this is self-evident (after all, if -]nothing existed /-] **[if it were not the case that everthing existed] **what would be doing the understanding?).

This is stupid. You forget: In symbolic logic we treat “existence” **neither **as a subject **nor **as a predicate. So why are you treating “nothing” this way? You are drawing conclusions from your sloppy use of language. But none of this makes any logical sense. Here’e a challenge: demonstrate to me that “nothing exists” is true.

Is it possible that “nothing is real”, without producing a contradiction? Yes.

We don’t have to treat it as a contradiction. But we can show that it is absurd. For instance:

“Everything exists” is true.
Therefore, “nothing exists” is false.

Is it possible that “nothing exists”, without producing a contradiction? If you are talking about the -]logical function of “exists/-]” then yes, there is a logical contradiction.

Clarify what you mean here. (Ex) is an operator that binds all existent entities in some domain; it is neither a subject nor a predicate. So stop treating ~(Ex) as if it were a subject, because it is not.

Nothing exists: -]“For all x, there does not exist an x”. /-][This is not a well-formed univerally quantified statement] This can be devolved to: -] -]“For all x, x (identity)” /-]and “there does not exist an x such that x.” /-]The second statement can be-] reduced to “for all x, not x.” /-] **[Huh???] **These, combined, form a logical contradiction: -]“for all x, x and not x”/-].

This is total nonsense! Have you ever worked with the logical quantification at all in your life? None of this makes any sense.

(1) “For all x, there does not exist an x” does not mean anything at all. It’s not even a logically well-formed formula. Besides, It’s a contradiction right from the start anyway since you are essentially saying

“everything that exists does not exist.”

(2) “For all x, x (identity)” doesn’t make any lick of sense either.

(3) “For all x, x and not x” is not a logically well-formed formula either.

Clearly, you don’t have a clue what you’re talking about.

 

[Astrochemist]

Syntax,

I find your commentary disrespectful.

Beyond that, there is nothing of substance that I with to comment on, with your critique. It’s not worth my time.

 

[warpspeedpetey]

But this just amounts to saying that God exists as existence. The phrase has no meaning–it tells us nothing about him.

G-d is existence. what more do you think it should tell us about him?

maybe this will help. newadvent.org/cathen/06612a.htm

You have not demonstrated this.

its self evident, if a possible world does not exist, then its not a possible world.

Again, you’re playing word games here. “Nothing exists” just means “there is no such thing as anything.” It’s merely used to indicate universal absence. It’s no different than saying, “No socks exist” except it applies to every object. There’s nothing contradictory about it unless you interpret it as an objectification of nothingness, which would be an inaccurate interpretation. We’re negating all things, not positing a “no-thing.”

if we say ‘existence’ only applies to ‘things’, then no-thing, means no existence

or

if we say that ‘existence’ is a ‘thing’ in itself, then no-thing still means no existence

either way its a logical contradiction. A=notA

if you want to call it only a property, then we have to ask “a property of what?” because properties only apply too ‘things’.

If it still bothers you, I could instead say, “It is possible that something does not exist”; that is to say, there is one possible world in which things do not exist. With the word games aside, how do you refute this? I suppose you might protest my deeming universal absence a “world” but that’s only a term we use for clarification.

id say that the null set isnt a possible world for the reasons outlined above.

existence is necessary for a world to be possible in the first place.

 

[Syntax]

Let me show my proof a little more robustly. This should (for those who understand symbolic logic) get rid of all arguments on both sides.

http://physics.ohio-state.edu/~pbrimmer/logic.JPG

These are NOT “proofs.” They are not even statements. There is nothing logically well-formed about them.

I take (1) to be the -]statement/-] “nothing exists” interpreted using the definition in quantification/first-order prepositional logic of “exists”.

(Ex) just means “there exists an x such that…”
~(Ex) just means “it’s not the case there exists an x such that…”

Neither “~(Ex)” nor “(Ex)~” means, “nothing exists.”

Nor does “~x” have any meaning independent of being being bound by a universal or existentially quantifying operator. So we need a quantifier before we can talking about a range of variables. For instance,

~(Ex) Rx means “it’s not the case there exists an x such that x is red.”

(Ex) ~Rx means “there exists an x such that x is not red.”

(Ex) Rx means “there exists an x such that x is red.”

There is no reference to “nothing exists”–only the “~” symbol as a truth function for negation.

-](2) is clearly equivalent to (1). (3) is simply (2) repeated. I perform an instantiation on (2) using the statement “p” and get (4). I then perform an instantiation on (3) using “~p” and get (5). (6) is (5) reduced by double negation. We take (4) and (6) to get (7) by conjunction/-].

-]By simple truth-values, this can also be shown. If all ~x’s are the case, then their conjunction will be a statement where the only possible truth value is “false”, and so is by definition a self-contradiction/-].

 

[Syntax]

Syntax,

I find your commentary disrespectful.

Beyond that, there is nothing of substance that I with to comment on, with your critique. It’s not worth my time.

It is perfectly legitimate to criticize both your conclusions and your formulation of the problem. You DON’T know what you’re talking about. So what’s wrong with speaking the truth?

 

[hatsoff]

Syntax,

I find your commentary disrespectful.

Beyond that, there is nothing of substance that I with to comment on, with your critique. It’s not worth my time.

I agree that he was out of line with his disrespect, but he is quite correct that your supposed contradiction is actually just a series of incoherent strings. It’s an understandable mistake for the inexperienced—in fact, I didn’t catch it until he pointed it out, thus revealing my own inexperience. But (x)(¬∃x) is an ill-formed formula. You would have to change it to something like (x∈D)(¬(x∈D)), where D is a set of individual constants. Unfortunately, such a statement implies D = ∅ is a necessary condition, which means you’re not really saying anything at all. A better approach would be to define a predicate P such that we read Px as “x has no existence in reality,” or something like that. In either case, though, no contradictions arise.

 

[Syntax]

Let me show my proof a little more robustly. This should (for those who understand symbolic logic) get rid of all arguments on both sides.

http://physics.ohio-state.edu/~pbrimmer/logic.JPG

This isn’t a “proof.” The first three are not even logical statments. Nor are they well-formued formula to even qualify as being **propositional **at all.

I take (1) to be the -]statement/-] “nothing exists” interpreted using the definition in quantification/first-order prepositional logic of “exists”.

(Ex) just means “there exists an x such that…”
~(Ex) just means “it’s not the case there exists an x such that…”

Neither “~(Ex)” nor “(Ex)~” means, “nothing exists.”

Nor does “~x” have any meaning independent of being being bound by a universal or existentially quantifying operator. So we need a quantifier before we can talking about a range of variables. For instance,

~(Ex) Rx means “it’s not the case there exists an x such that x is red.”

(Ex) ~Rx means “there exists an x such that x is not red.”

(Ex) Rx means “there exists an x such that x is red.”

There is no reference to “nothing exists”–only the “~” symbol as a truth function for negation.

-](2) is clearly equivalent to (1). (3) is simply (2) repeated. I perform an instantiation on (2) using the statement “p” and get (4). I then perform an instantiation on (3) using “~p” and get (5). (6) is (5) reduced by double negation. We take (4) and (6) to get (7) by conjunction/-].

-]By simple truth-values, this can also be shown. If all ~x’s are the case, then their conjunction will be a statement where the only possible truth value is “false”, and so is by definition a self-contradiction/-].

 

[Astrochemist]

Admittedly, I only know a little about first-order logic. Why is it that you can use P on one premise and ~P on another? Isn’t that begging the question? I mean, if you substitute p for x and ~p for x then of course you’ll end up with a contadiction; that holds true for any argument.

Since I can instantiate anything with a “for all” statement, nothing stops me from instantiating “p” and “~p”. Syntax, for all his bluster (and some errors), actually gets it right. The very first statement I have made (there does not exist an x such that x) is self-contradictory. This, however, is simply one possible interpretation for the statement “nothing exists”. I prefer statements like “it is possible that nothing is real, or that nothing would be real.”

Another example involves the statement “there exists”. When one instantiates any statement in logic, one cannot instantiate any “there exists” statement afterwards with the same constant.

For example, using (Rx) to mean “x is real”, you can say “Ex, Rx” (“there exists an x such that x is real”) and “~Ax, Rx” (“not all x’s are real”). Both of these are perfectly possible, without producing a self-contradiction. The second statement would be processed “Ex, ~Rx”, and then instantiated “~Rp”. Once that one’s instantiated, another variable must be chosen for the first statement “Ex, Rx”, so we get “Rq”. Combining these two we get “Rq & ~Rp” which is not a contradiction.

However, “Ax” is everything “for all x”, and so this would include all statements, including “p” and “~p”.

The argument was about the physical world, not concepts.

I agree. It is possible that the physical world would never have existed. It is possible that nothing at all would exist (and thus there would be no mind to worry about whether it made sense).

Logic is based on inference rules, not physical objects. I concede that tautologies, for example, would exist even if nothingness was the case.

That’s my only point. There it is, trivial as it is.

I’m not familiar with Quine, and so I don’t base my arguments on his authority.

I thought that might be the direction you were going with the bachelors and unmarried men. My apologies if it was not.

 

[Astrochemist]

This isn’t a “proof.” …

You see the statements as nonsense. I’d suggest considering almost any representation of the “set axiom”.

It does not bother me that you don’t seem to know what you are talking about. What bothers me is the attitude you have taken. If this is just my perception, then I apologize.

Nevertheless, it’s not to my spiritual health, nor to anyone’s edification, that I continue to communicate with you. You are now on my “ignored” list.

 

[hatsoff]

The first three are not even logical statments. Nor are they well-formued formula to even qualify as being **propositional **at all.

I’m not quite sure about that… If the domain for x is treated as a set of sentences, and we fix his notation, then (∃x)x is a wff, which means ¬((∃x)x) is also a wff. Of course, this requires that the domain is empty, but I don’t see why this would pose a problem.