Rational Theists and Rational Atheists of the World, Unite!

[hatsoff]

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

What exactly are you calling “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.

As I mentioned before, I understand not wanting to talk to him on account of his rudeness, but he is largely if not entirely correct in his criticism of your argument.

 

[Oreoracle]

Since I can instantiate anything with a “for all” statement, nothing stops me from instantiating “p” and “~p”.

The thing that throws me off about instantiation (in general), I think, is that variables are being switched without explanation. For all I know, “x” could be a shoe, and “p” could be a rubber duck. If that’s the case, then the proposition “no x are the case” does not imply anything about p. Unless someone mentions what “p” means, or how it relates to x, the transition doesn’t make sense. But it really doesn’t matter at this point, because I see what you mean.

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).

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

Alright, it looks like we agree on this matter. I’m glad that you are able to state what you mean directly, unlike some posters here. It makes discussions go more smoothly.

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

Maybe I was going in Quine’s direction, but as I said, I don’t know what his direction is.

 

[warpspeedpetey]

the last time i took symbolic logic, the only computers on campus took floppies. can anyone tell me how your putting operators and statements in your posts?

 

[Syntax]

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. [huh??]

Wrong:

(1) “There exists” is not even a statement in logic. It is merely an expression for the operator “Ex”
(2) Statements are not “instantiated,” they are merely uttered. Only properties are instantiated by objects, and those instantiations of properties by objects are what propositions and statements are about.

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), **[which 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/-].

This your problem. You are inventing meanings to suit your own purposes. But no one has to take you seriously. “Real” is just identical in meaning to “existent.”

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.

First, you are treating “the real” as if it were a predicate. Why? Does it have a different meaning than “to exist”? You need to argue for this assumption. All respectable logicians will disagree with your proposed ambiguity between “real” and “existent.”

Second, “~(Ax) Rx” does not mean “not all x’s are real.” It means “it is not the case all x’s are real.” It is **logically equivalent **to saying “there exists an x such that x is not real.”

~(Ax) Rx <=> (Ex) ~Rx

So if “real” means “exist” then you are stating another contradiction.

The second statement would be processed “Ex, ~Rx”, and then instantiated “~Rp”.

What does “processed” mean in logic?

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.

First, “q” is not a variable; it’s a constant. Only “x” “y” “z” are variables.
Second, if “real” means “existent” then this is a contradiction because your names “p” and “q” are presupposing the objects designated by those names exist. So how you can have a non-real, but existent thing is beyond me.

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

“Ax” can range over anything you want: objects, properties, propositions, sentences. But those things, whaterver they are, have to exist. For a statement using “Ax” to be true, false, or mean anything at all, it must range over really existent objects.

 

[Syntax]

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

Explain.

It does not bother me that you don’t seem to know what you are talking about.

If you think I am incorrect anywhere, then put your money where your mouth is and show me.

What bothers me is the attitude you have taken. If this is just my perception, then I apologize.

As someone who has a deep appreciation for clarity and logic, I will not let you say nonsense to other people on here. You are making very serious logical errors and proposing as if they were correct to other people. If you like to live within error, that’s your own choice. But don’t publicly paste your errors if you don’t expect correction from me or anyone else.

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.

Ok, so you choose to be ignorant. But I will continue to correct your errors for other people who are reading these posts.

 

[Syntax]

The thing that throws me off about instantiation (in general), I think, is that variables are being switched without explanation.

Oreo, Astro is making very serious logical errors. If maintaing clarity and logical rigor is one of your goals on your path to learning, then ignore his mumbo-jumbo. He is mis-using technical logical vocabulary to demonstrate a self-contradictory conclusion which he says is not self-contradictory.

 

[hatsoff]

Oreo, Astro is making very serious logical errors. If maintaing clarity and logical rigor is one of your goals on your path to learning, then ignore his mumbo-jumbo.

Seconded…

But I must remind you that you would be better received if you were more polite. Just because he’s inexperienced doesn’t mean he deserves to be mercilessly berated.

 

[Syntax]

Seconded…

But I must remind you that you would be better received if you were more polite. Just because he’s inexperienced doesn’t mean he deserves to be mercilessly berated.

Duly noted–

I am merciless, yes, and I ought to be. We may have different philosophical opinions about this or that, which is perfectly ok, but we shouldn’t be taking logical errors lightly at all simply because logic is the foundation for making sense of anything. These errors are the source of so much heinous nonsense proposed on these forums that comes from both theists and atheists alike. The entire rest of the discussion subsequently becomes meaningless and no one gets anywhere if a logical fallacy rests at the dicussion’s foundation. So I am not a fan of letting errors slide just to spare someone’s feelings from being hurt. The discussion must be arrested in its tracks before it should be allowed to continue.

 

[SugarMagnolia]

Rationality and hope possess the potential to bring Atheists and Theists together to better our world. The New Atheists – Dawkins, Dennett, Harris, Hitchens, and company – miss something simple yet profound in their polemical attacks on Theists: the mystery of existence itself. We must start with this basic fact – the fact of existence. That there is an is. That there is a world, a universe at all. That there is something rather than nothing. Existence is a great, awesome, wondrous mystery.

In the face of this mystery, Atheists remain as stunned and speechless, as flabbergasted and inarticulate as Theists. From within the confines, within the perspective of our universe, solving this mystery is probably not even possible. All we can do is reach for answers, always seemingly just beyond our grasp.

And the Atheistic answers to this mystery are no more rational than the religious ones. Is it any more rational to assert that existence arose out of nothing or that existence has always existed than to assert that a divine intelligence – outside of time and space – created it? Science, in the end, cannot disprove the Theistic conjecture nor prove one of the Atheistic ones. We ought not therefore conclude that it is by definition irrational to confront this mystery and cast one’s lot with Theism. Theism and Atheism are equally reasonable beliefs.

Atheists and theists do not need to agree on metaphysical questions. The rational thing for both atheists and theists to do is to put aside their metaphysical disagreements and work to together to improve life on earth for all of us.

 

[TheAtheist]

Seconded…

But I must remind you that you would be better received if you were more polite. Just because he’s inexperienced doesn’t mean he deserves to be mercilessly berated.

Politeness is not one of the hallmarks of these forums.

It comes down to the fact of different personality types interacting on the forum, some are scholars, others questioners, and others are for lack of a better word “Debate-addicts.”

 

[TheAtheist]

Atheists and theists do not need to agree on metaphysical questions. The rational thing for both atheists and theists to do is to put aside their metaphysical disagreements and work to together to improve life on earth for all of us.

Lo’ and behold, how utterly irrational humanity really is.

 

[Syntax]

I’m not quite sure about that… If the domain for x is treated as a -]set of sentences/-] [don’t you mean the domain of all or some objects? Or are you talking about the domain of all or some maximally consistent true propositions? Those are different things], 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.

 

[hatsoff]

don’t you mean the domain of all or some objects? Or are you talking about the domain of all or some maximally consistent true propositions? Those are different things

No. I’m referring to what wikipedia calls the domain of discourse. It is the context of quantifiers.

If every member of the domain of discourse, let’s call it D, is a wff, and a is a member of D, then a is a wff. If follows, I should think, that (∃x)x is a wff, since for each x in D, x is a wff.

 

[Syntax]

No. I’m referring to what wikipedia calls the domain of discourse. It is the context of quantifiers.

If every member of the domain of discourse, let’s call it D, is a wff, and a is a member of D, then a is a wff. If follows, I should think, that (∃x)x is a wff, since for each x in D, x is a wff.

This is isn’t correct. I don’t see how “(Ex)x” itself is a wff, because it doesn’t say anything. So it doesn’t have any propositional content because it is not interpreted–it is not truth-valuable. “x” needs a predicate, and 1st-order logic will tell you this is a necessary condition for being a wff. My own symbolic logic book says exactly this: “An atomic wff is any n-ary predicate folowed by n terms, where terms can contain either variables or individual constants.” The key word is “predicate” here. So “(Ex)x” is not even a sentence. Again, it doesn’t **say **anything.

Sorry, I hate to say it, but your own criticism of my post is incorrect.

 

[hatsoff]

I can clearly see that, but I don’t see how “(Ex)x” itself is a wff, because it doesn’t say anything. So it doesn’t have any propositional content because it is not interpreted–it is not truth-valuable. “x” needs a predicate.

Yup, I see what you mean now. Thanks for the correction.

 

[Syntax]

Yup, I see what you mean now. Thanks for the correction.

No worries. It’s just that logic demands that we be very meticulous about our use of logical terminology because its rampant misuse is exactly how errors arise as in the case of Astro’s muddle-headed overly-excited misuse of symbolic logic. So I am not trying to be pedantic. I’d rather be talking about things other than the appropriate use of logical notation anyway.

 

[hatsoff]

No worries. Logic demands that we be very meticulous about our use of logical terminology because this is exactly how errors arise as in the case of Astro’s muddle-headed overly-excited misuse of symbolic logic. So I am not trying to be pedantic. In fact, I’d rather be talking about things other than the appropriate use of logical notation.

Oh, don’t worry, I completely understand. As the saying goes, close only counts in horseshoes, darts and grenades. As long as I’m using ill-formed formulas, I’m spouting utter nonsense. So I thank you for putting a stop to it!

EDIT: By the way, I’m currently in the middle of Stoll’s Set Theory and Logic. Hopefully by the end of it I will no longer make such grievous errors. I should have known better anyway, but apparently not. Oh well.

 

[Oreoracle]

Oreo, Astro is making very serious logical errors. If maintaing clarity and logical rigor is one of your goals on your path to learning, then ignore his mumbo-jumbo. He is mis-using technical logical vocabulary to demonstrate a self-contradictory conclusion which he says is not self-contradictory.

Yeah, I’m kind of fence-sitting at the moment. I have a friend who’s quite adept with logic (he has a degree in philosophy), so I might ask him about instantiation later. In any case, I need to know more about first-order logic before I side with anyone. However, I do agree with you that “x” can represent anything, so we need to know what x and p represent before they can be used in instantiation.

I do agree with one of Astro’s points, however, and he says it’s the gist of his argument: Certain tautologies will hold true no matter how empty the world is, and if those tautologies can be said to be existent, then some things must always exist. “X=X” will always exist, for example (that is, it will always be the case). Likewise, certain conditionals will always hold true, and so on. I think everyone here can agree on that much.

 

[Syntax]

Yeah, I’m kind of fence-sitting at the moment. I have a friend who’s quite adept with logic (he has a degree in philosophy), so I might ask him about instantiation later. In any case, I need to know more about first-order logic before I side with anyone. However, I do agree with you that “x” can represent anything, -]so we need to know what x and p represent before they can be used in instantiation./-]

Sorry to keep correcting. But x is a variable that ranges over a domain of discourse, and by itself it is unbound–so it needs either a universal quantifier (Ax) or an existential quantifier (Ex). ** But that is not problematic at all. **So we don’t “need to know” what x “refers” to, because it just “refers” to a SET of objects, not any particular objects like names do.

On the other hand, “John” “Washington DC” “a” “b” “c” are constants, or names–and these DO refer to particular objects.

Finally, the question of knowing whether or not an existential or universal statement is true or false, is not a question that logic deals with. So I wouldn’t worry about variables in logic not specifying any particular entity. However, (Ex) and (Ax) can be used rather easily to designate one and only one object if you want. It’s not hard. For instance, suppose we say in Russell’s famous formulation that “The King of France is not Bald.” It would look like this.

Ex(Kx & Ay(Ky → y=x)) & Bx].

I do agree with one of Astro’s points, however, and he says it’s the gist of his argument: Certain tautologies will hold true no matter how empty the world is.

That’s correct.

and if those tautologies can be said to be existent, then some things must always exist. “X=X” will always exist, for example (that is, it will always be the case). Likewise, certain conditionals will always hold true, and so on. I think everyone here can agree on that much.

Sure, no one disagrees here. Tautologies are propositions that are necessarily and trivially true.

Be careful though. Tautologies are not “things.” They are propositions. And it all depends on what you think exists. Do propositions exist? I say they do. But some people will differ. You just need to keep in mind that this is a question for metaphysics or *philosophy of language *to answer, not logic. It’s crucial that you understand that.

 

[twinc]

This is a textbook example of the fallacious argument from ignorance. Just because we don’t know of a thing in the physical world that could have caused the physical world to exist does not mean that such a thing doesn’t exist.

There is no problem except that created by pseudo philosopy and philosophers There just is not a physical world but only maya - btw God is no thing and everything comes from God or the void or from nothing - twinc