The Ontological Arguments

[adamlsp]

There is more than one infintie set, countable and uncountable, but only one empty set. I see that.

 

[Hitetlen]

adamlsp:

Zero is defined as the empty set. Zero is a concept much like infinity correct? Zero and infinity are intimately tied together.

Yes and no. If you think about zero as the limit of the function of 1/x (or any similar function) then yes, zero is infinitesimally small, while “infinity” is infinitely large (this is part of the branch of calculus). However, if you only consider the whole numbers (…-2, -1, 0, 1, 2,…) then zero is just like any other number (Though the division with zero is undefined).

adamlsp:

Is infinity a set?

Yes, and as you point out in your next post, there are infinitely many of those sets.

adamlsp:

The empty set is a set with no members and because of this is unique.

True.

adamlsp:

There are a lot of things that have no members and this is because they are not sets.

Of course they are. The definition of a set is simply an abstract collection with zero or more elements in it. It is used everywhere, from pure mathematics, to object oriented programming to database design, ad infinitum.

adamlsp:

How can there be a unique set with no members, we can’t just hypothesize this into existence.

Not physical existence. But physical existence was never mentioned, we are only talking about hypothetical and abstract existence.

adamlsp:

I’m not decisively objecting I just wanted to raise these questions. There are those who doubt set theory despite is significant contribution to mathematics.

What does the word “doubt” mean here? Set theory certainly raises lots of interesting problems, and if one is uncautious and starts to talk about the “set of sets” or the “set of all sets”, then some real thorny probelms will emerge. But we don’t go there, not in this discussion. Here we just talk about the simple, everyday sets, with zero or more members in them.

adamlsp:

Also saying anything about the empty set is vacuous right?

No, it is not right. We can say that the empty set contains no members. It may be trivial, but not false.

“All things are true of the empty set,” as the saying goes. So to say nothingness, the content of the empty set, implies something will always be true right?

Why would it imply anything? It implies the lack of members, that is all.

adamlsp:

All tigers that are in loaves of bread are capable of speech. This is vacuous.

That is a syntactically correct sentence, but it refers to no actual tigers. One should not confuse “syntactically” correct linguistic constructs with sentences that actually say something about the real world or a mental abstraction.

adamlsp:

So to say anything of the empty set is also. Though it is true, it is useless.

Not at all. The only thing we can say about the empty set, that it contains no members. That is not useless at all.

adamlsp:

So we could say the contents of the empty world show that a necessarilly existent being exists. Is this right so far?

It simply does not follow, actually the opposite does.

Remember, we do not need to assume that a hypothetical “world” could be actualized. Maybe it can, maybe it cannot. The only requirement is that it should not rely on a logical contradiciton. That is all, and the empty world fulfills that criterion. Since the empty world contains no members, it does not contain any hypothetical beings either.

 

[Krebsbach]

Mornin guys,

Stever said:
What about nature, or matter, or the smallest parts of matter. I have a feeling people might say the smallest parts of matter (whatever they truly are) necessarily exist because without them there would be no existence. They may change form for eternity, but their existence is necessary for eternity.
~Steve~ (I got a new screen name)

Adam said:
You could say that the universe necessarily exists but then you’d be equating the universe with God. Pantheism is a whole different matter. Only if you equated the universe with God in some sense of the word would this hold. Otherwise you cannot say matter needs to exists. Also all matter is made of energy so you might want to shoot for energy necessarily exists instead. The reason you could belive the universe does not need to exist is because it could have been different, things didn’t have to exist the way they do now. If you believe they did have to exist the way they do now then that goes into fate and destiny. Also a whole different topic.

Adam

Me: The created universe, even in its fundamental elements (time, space, superstrings, whatever) doesn’t necessarily have to exist. I

 

[Krebsbach]

Originally Posted by Krebsbach
Those who object really are maintaining that there is no such thing as necessary existence. All existnece is contingent, they say. Why must that be true?

John said:
the problem is, in order to motivate such an argument, it would have to be shown that the concept of a necessary being is impossible - i.e. self-contradictory. and there’s no obvious way to do such a thing.

Adam said:

… Why do you think necessary existence is possible?

Me: Let’s look at the logical possibilities:

1. All existence is necessary.
2. Some existence is necessary.
3. No existence is necessary.

1 is obviously false, so really the argument is between 2 and 3. 3 is really going out on a limb, making a dogmatic, absolute statement. Like saying “No proposition is necessary true.” 3 must be self-contradictory.

So that leaves us with 2.

And isn’t it Plantinga’s argument that as soon as we entertain that it is possible for a necessary being to exist, it must be exist?

kordially,

karl

 

[john_doran]

Hitetlen:

Easy as a breeze. In order to illistrate it, I will give you a perfectly valid sentence - in Hungarian - and see what does it mean to you: “Sok hulyeseget beszelnek ossze ezek az istenesek”. Does it mean anything to you? Why not? Because there is no independent meaning to anything. The meaning of a sentence depends on the accepting mind: if the mind does not have the necessary information to decipher the meaning, then the sentence is meaningless - for that mind.

you miss the point: that sentence is synonymous with another in english and another in german and…

what is it to say that all of those different sentences mean the same thing? what is a “meaning”, and how can many sentence tokens have one of them?

Hitetlen:

Also very easy: it is the result of mutual agreement: the word “rain” is something we have been exposed to since childhood. I recall a nice little cartoon (from the British Punch magazine) which depicts a gentleman eating a thin soup is a restaurant and the waiter behind him looking out the window. The caption runs: “It looks like rain”. A beautiful example of a pun: where a sentence intentionally has two rather divergent meanings.

right: one sentence has more than one “meaning”. it can have more than one “meaning” that is completely unrelated to the sentence itself. how?

and you failed to address how marks of pen on a page can express the same thing as neurons firing in your head can express the same thing as soundwaves issued by your larynx.

basically, all of your examples admit that there is something to “meaning” that is distinct from the sentence/brain-state/sounds used to express it. what is that distinct thing?

Hitetlen:

Ah, unsupported mythology raises its ugly head again.

oh, it’s supported - you just happen not to think the support is very good. just like i don’t think your support for your own beliefs is very good…

 

[john_doran]

Hitetlen:

It is just as logical to imagine an completely empty world as it is logical to accept the notion of an empty set, which is a very useful mathematical concept. Since it is totally empty, there is nothing in it, therefore there can be no “maximally great” being in it either - therefore the idea of a “necessarily existing being” has been refuted.

no, it’s not: either that empty world is a world, and it is something, or it is nothing at all, not even a world.

 

[adamlsp]

john doran:

no, it’s not: either that empty world is a world, and it is something, or it is nothing at all, not even a world.

The empty world is something but what is contains is nothing. A bag with no marbles basicly. If you doubt that this is possible can you give your argument?

Adam

 

[adamlsp]

Hitetlen:

Yes and no. If you think about zero as the limit of the function of 1/x (or any similar function) then yes, zero is infinitesimally small, while “infinity” is infinitely large (this is part of the branch of calculus). However, if you only consider the whole numbers (…-2, -1, 0, 1, 2,…) then zero is just like any other number (Though the division with zero is undefined).

Yes, and as you point out in your next post, there are infinitely many of those sets.

True.

Of course they are. The definition of a set is simply an abstract collection with zero or more elements in it. It is used everywhere, from pure mathematics, to object oriented programming to database design, ad infinitum.

Not physical existence. But physical existence was never mentioned, we are only talking about hypothetical and abstract existence.

What does the word “doubt” mean here? Set theory certainly raises lots of interesting problems, and if one is uncautious and starts to talk about the “set of sets” or the “set of all sets”, then some real thorny probelms will emerge. But we don’t go there, not in this discussion. Here we just talk about the simple, everyday sets, with zero or more members in them.

No, it is not right. We can say that the empty set contains no members. It may be trivial, but not false.

Why would it imply anything? It implies the lack of members, that is all.

That is a syntactically correct sentence, but it refers to no actual tigers. One should not confuse “syntactically” correct linguistic constructs with sentences that actually say something about the real world or a mental abstraction.

Not at all. The only thing we can say about the empty set, that it contains no members. That is not useless at all.

It simply does not follow, actually the opposite does.

Remember, we do not need to assume that a hypothetical “world” could be actualized. Maybe it can, maybe it cannot. The only requirement is that it should not rely on a logical contradiciton. That is all, and the empty world fulfills that criterion. Since the empty world contains no members, it does not contain any hypothetical beings either.

I think in the last 2/3 of your response you completely missed what I said. I’m assuming you know what vacuous means. (I’m not being rude, I’m just going slow so as to eliminate confusion) All elephants inside loaves of breads are pink. That statement is vacuous. So if I said the members of the empty set prove the existence of God. It would be true but useless. Like wise you could say the members of the empty set disprove the existence of God and this would be true. All is true of the members of the empty set. This idea is used in logic frequently. That from a false is you derive a truth the entire statement is truth. Also I did not mean physical existence because clearly there are other types of existence that surpass physics. Our thoughts I mean. And as a side note, do you believein free will? Is an easy question, define free will how you like and answer, instead of getting all dodgy.

Adam

 

[john_doran]

adamlsp:

The empty world is something but what is contains is nothing. A bag with no marbles basicly. If you doubt that this is possible can you give your argument?

Adam

1. what is the “world” that is containing nothing?
2. there is no such thing as an empty world because there are necessary beings, like sets and propositions and numbers and…

 

[Vietnatalians]

Krebsbach:

Me: Let’s look at the logical possibilities:

1. All existence is necessary.
2. Some existence is necessary.
3. No existence is necessary.

1 is obviously false, so really the argument is between 2 and 3. 3 is really going out on a limb, making a dogmatic, absolute statement. Like saying “No proposition is necessary true.” 3 must be self-contradictory.

So that leaves us with 2.

And isn’t it Plantinga’s argument that as soon as we entertain that it is possible for a necessary being to exist, it must be exist?

kordially,

karl

So in this philosophy could that necessary existence be nature? Or energy? Or something completely non-intelligent?

~Steve~

 

[john_doran]

Vietnatalians:

So in this philosophy could that necessary existence be nature? Or energy? Or something completely non-intelligent?

~Steve~

nothing that exists necessarily can be physical, because not every possible world contains physical objects.

necessary beings can certainly be non-intelligent: the proposition “some necessary beings are non-intelligent” is itself non-intelligent.

 

[adamlsp]

1) what is the “world” that is containing nothing?

1. there is no such thing as an empty world because there are necessary beings, like sets and propositions and numbers and…

Yes, and the empty world has none of these. The empty world itself is a set, a number. Empty is defined as zero.

 

[john_doran]

adamlsp:

Yes, and the empty world has none of these. The empty world itself is a set, a number. Empty is defined as zero.

A) but it can’t lack any necessary beings: that’s what it means to be necessary - existing in every possible world. thus, a world without them is impossible.

B) a world isn’t a set - it’s a world. a set is a set.

 

[adamlsp]

Oh and Hitetlen, God is not some spiritual ethergy that fills the universe. I know you don’t belive in God, but that is not the definition of omnipresence. You were right to question it and I think I dismissed it rather quickly. God is a nonphysical entity so it would be rather odd for him to take up space or to be bound by time. Just like the set is not its contents, likewise God could be like the set, which necessarily exists in order to hold its contents, even if those contents are nothing. And also the empty set is a subset of all other sets correct? Meaning its contents are not not present in all other sets. Just replace sets with worlds for the world version. And you never really addressed the “if a tree falls in the forest” thing. Do you think the existence of sound depends on our hearing it?

Adam

 

[adamlsp]

john doran:

A) but it can’t lack any necessary beings: that’s what it means to be necessary - existing in every possible world. thus, a world without them is impossible.

B) a world isn’t a set - it’s a world. a set is a set.

Clarify why these things are necessary and why a set cannot act as a world. Is the analogy between them illconceived? If so, why? 0 is defined as the empty set. That is what I meant in my last post.

 

[john_doran]

adamlsp:

Clarify why these things are necessary and why a set cannot act as a world. Is the analogy between them illconceived? If so, why? 0 is defined as the empty set. That is what I meant in my last post.

well, for example, the proposition “1+1=2” is necessarily true, which means that there is no world in which it fails to obtain. but for it to be true requires that there be numbers and numerical relations that make it true. which means that there are at least two things that exist necessarily: numbers and propositions.

if you like set theory, then the fact that there are numbers in every world means that there are sets in every world.

i’m not sure how to be clearer about the difference between sets and worlds. i mean, a set can’t be a person, either. or a cup of tea. they’re just not the same thing. i suppose, on the more technical side, you might demonstrate that a set and a possible world have different properties, and thus fail the basic test of identity. but that hardly seems necessary.

 

[adamlsp]

john doran:

well, for example, the proposition “1+1=2” is necessarily true, which means that there is no world in which it fails to obtain. but for it to be true requires that there be numbers and numerical relations that make it true. which means that there are at least two things that exist necessarily: numbers and propositions.

if you like set theory, then the fact that there are numbers in every world means that there are sets in every world.

i’m not sure how to be clearer about the difference between sets and worlds. i mean, a set can’t be a person, either. or a cup of tea. they’re just not the same thing. i suppose, on the more technical side, you might demonstrate that a set and a possible world have different properties, and thus fail the basic test of identity. but that hardly seems necessary.

OK I like your last paragraph but I think the first is flawed. Logic is not necessary actually. It is only necessary in our world and our idea of other worlds but there are worlds called impossible worlds. I know the name implies they don’t exist but actually mathematicians and logicians hold they do. This is a pretty useful concept in explaining worlds where certain laws of logic do not hold or where contadictions are true or both. So math does not necessarily hold in every world. There are articles on the interenet if you wish. **Impossible worlds **is the key word. This may or may not be applicable to the empty world, if there is such a thing. Maybe this world exists but the laws of logic do not hold there. If Hitetlen is still going to run with his set theory. Then this would be true since everything is true of the empty world, including contadictions. If I made some fatal flaw in logic please point it out.

Adam

 

[john_doran]

adamlsp:

OK I like your last paragraph but I think the first is flawed. Logic is not necessary actually. It is only necessary in our world and our idea of other worlds but there are worlds called impossible worlds. I know the name implies they don’t exist but actually mathematicians and logicians hold they do. This is a pretty useful concept in explaining worlds where certain laws of logic do not hold or where contadictions are true or both. So math does not necessarily hold in every world. There are articles on the interenet if you wish. **Impossible worlds **is the key word. This may or may not be applicable to the empty world, if there is such a thing. Maybe this world exists but the laws of logic do not hold there. If Hitetlen is still going to run with his set theory. Then this would be true since everything is true of the empty world, including contadictions. If I made some fatal flaw in logic please point it out.

Adam

logic and math are necessarily true. it literally makes no sense to suggest that there is some possible world where, for example, A&~A. i mean, one of the basic features of modal logic is that “possibility” is tied to broadly ***logical ***possibility.

i’m not sure what thinkers you have in mind when you say that there are people who maintain these views, but i’d be interested to read what they say.

and i would say that they’re wrong, but i can’t say any more than that until i have reasoning with which to find fault.

 

[adamlsp]

john doran:

logic and math are necessarily true. it literally makes no sense to suggest that there is some possible world where, for example, A&~A. i mean, one of the basic features of modal logic is that “possibility” is tied to broadly ***logical ***possibility.

i’m not sure what thinkers you have in mind when you say that there are people who maintain these views, but i’d be interested to read what they say.

and i would say that they’re wrong, but i can’t say any more than that until i have reasoning with which to find fault.

Kripke, Saul. 1965. Semantical analysis of modal logic, II: non-normal modal propositional calculi. In J.W. Addison, L. Henkin, and A. Tarski, eds., The Theory of Models. Amsterdam: North Holland.

Priest, Graham (ed.). 1997. Notre Dame Journal of Formal Logic 38, no. 4. (Special issue on impossible worlds.) Table of contents

Priest, Graham. 2001. An Introduction to Non-Classical Logic. Cambridge: Cambridge University Press.

Kripke is the foremost authority on logic and Priest is rather intelligent I’ve heard but I’ve never read him.

Adam

 

[john_doran]

adamlsp:

Kripke, Saul. 1965. Semantical analysis of modal logic, II: non-normal modal propositional calculi. In J.W. Addison, L. Henkin, and A. Tarski, eds., The Theory of Models. Amsterdam: North Holland.

Priest, Graham (ed.). 1997. Notre Dame Journal of Formal Logic 38, no. 4. (Special issue on impossible worlds.) Table of contents

Priest, Graham. 2001. An Introduction to Non-Classical Logic. Cambridge: Cambridge University Press.

Kripke is the foremost authority on logic and Priest is rather intelligent I’ve heard but I’ve never read him.

Adam

those are just varieties of paraconsistent logics, which involve manipulation of operators, functions, and variables - they are not necessarily ontologically relevant. that is to say, you’d need a further philosophical theory to relate the logic to an ontology. and that’s the part that i would say cannot be done, simply because it’s absurd (i.e. the project cannot coherently even be described).