God Delusion is Delusional

[Spock]

Don’t worry, I read the rest and I am not ignoring it Now, that’s fair enough. However, given your view of abstract objects (or propositions, or whatever), and that all abstract objects are the qualitatively the same (you say they are all contingent) then it follows that just as Beethoven created Symphony 9 ex nihilo, minds created *the truth value *of 2+2=4 ex nihilo.

Well, let’s get down to the details. Most people think that mathematical propositions are absolute, or “necessary”, if you prefer. Nothing could be further from the truth. Mathematical propositions are contingent on two things: 1) a mind that can formulate them, and 2) the axiomatic system those minds happen to choose. We can have two propositions (for example): 1 + 1 = 2 and 1 + 1 = 1. They seem to be contradictory, don’t they? It is “impossible” that they both can be true. Yet, they are, depending on the axiomatic system chosen. If you choose a Boolean logic, then 1 + 1 = 1, if you choose the “regular” arithmetics, then 1 + 1 = 2. I am not playing word-games here either.

The axioms we happen to choose are totally, completely arbitrary, but not all of them will be equally useful. However, usefulness is not a question here. In all the axiomatic systems we make “truths” by accepting or creating some axioms. Whatever we choose to be axiomatically “true”, will be “true” by definition. Axiomatic systems may reflect reality, or they may not, but that is not the point here.

I think you missed the point. I didn’t say it wasn’t a proposition because it’s in a different language or because I don’t understand it. I said it’s not a proposition because it’s not capable of having a truth-maker. It’s not a truthbearer.

And who will decide if a proposition is true or not? And more importantly, how will that decison be made? If a proposition is part of an axiomatic system, it is true, if it can be reduced to the axioms - by definition. If a proposition is about reality, then the proposition is true if it correctly reflects the state of affairs. And that can only be decided empirically.

 

[Spock]

(1) There is a possible world W where there are no contingent beings.

You cannot “assume” that. In order to find out if a “being” is necessary or not, you must examine all the possible worlds, and prove that that being is present in all of them. Only then will you have a “necessary” being.

I want to emphasize one thing here. The word “contingent” is this scenario does not mean that its is “dependent” on something else. It simply means that the “contingent being” is not present in all the possible worlds. Also, it seems that the cruical question I posited has never been addressed: is there a lower limit of entities in a “metaphysically (or logically) possible” world?

 

[awatkins69]

Well, let’s get down to the details. Most people think that mathematical propositions are absolute, or “necessary”, if you prefer. Nothing could be further from the truth. Mathematical propositions are contingent on two things: 1) a mind that can formulate them, and 2) the axiomatic system those minds happen to choose. We can have two propositions (for example): 1 + 1 = 2 and 1 + 1 = 1. They seem to be contradictory, don’t they? It is “impossible” that they both can be true. Yet, they are, depending on the axiomatic system chosen. If you choose a Boolean logic, then 1 + 1 = 1, if you choose the “regular” arithmetics, then 1 + 1 = 2. I am not playing word-games here either.

That’s a nice try, but you *are *playing word games. We can affirm “1+1=1” when the symbol ‘+’ does not signify the same operation as the ‘+’ in “1+1=2”. They aren’t even remotely contradictory. The ‘+’ in Boolean logic’s “1+1=1” is completely different from “1+1=2” in mathematical terms. ‘+’ is a **disjunction **in Boolean logic. It’s not even the same operation. I’m sorry but this is not going to pass.

The axioms we happen to choose are totally, completely arbitrary, but not all of them will be equally useful. However, usefulness is not a question here. In all the axiomatic systems we make “truths” by accepting or creating some axioms. Whatever we choose to be axiomatically “true”, will be “true” by definition. Axiomatic systems may reflect reality, or they may not, but that is not the point here.

No. We choose them because they reflect reality. There is such a thing as a true logic and a true mathematical system. We “make” truths? We make it true that “something cannot both be and not-be in the same respect”? No. Something is not true because it is consistent within a formal system. It’s true because it has some corresponding external and objective truthmaker.

And who will decide if a proposition is true or not? And more importantly, how will that decison be made? If a proposition is part of an axiomatic system, it is true, if it can be reduced to the axioms - by definition.

I’d say it’s “consistent” not “true”. Or does consistency always entail truth? Is that always (necessarily) true?

If a proposition is about reality, then the proposition is true if it correctly reflects the state of affairs. And that can only be decided empirically.

This is a very good definition of truth, and I like it. Now, I don’t want to draw too sharp a line between empirical (a posteriori) and non-empirical (a priori) knowledge. But I think a priori knowledge is possible.

But this is interesting here. We can have it be the case that “2+2=4”, yet “2+2=4” is neither true nor false? I do like that we’re still denying (4) of the syllogism, like I predicted.

 

[awatkins69]

You cannot “assume” that. In order to find out if a “being” is necessary or not, you must examine all the possible worlds, and prove that that being is present in all of them. Only then will you have a “necessary” being.

I don’t understand why you need to examine all possible worlds to know there is a possible world where no contingent being exists. That’s all we need right now. The argument is formally valid, so you have to deny some premise. Just saying that you think we must “examine all possible worlds” does not change the validity of the argument. If it is valid, you must deny some premise. What premise does your objection here contradict?

Anyways, take a possible world W with just one contingent being. Suppose the being is annihilated. We agreed that it is impossible that the state of affairs “no being is instantiated” ever obtains. That means there must exist either a necessary being or a contingent being. But no contingent being exists. Therefore, modus tollendo ponens, a necessary being exists in W. Therefore, by S5, a necessary being exists. This is not very hard stuff.

If a necessary being exists, something is necessary.

I want to emphasize one thing here. The word “contingent” is this scenario does not mean that its is “dependent” on something else. It simply means that the “contingent being” is not present in all the possible worlds. Also, it seems that the cruical question I posited has never been addressed: is there a lower limit of entities in a “metaphysically (or logically) possible” world?

You’re quite right in saying “contingent” doesn’t mean “dependent”. There is a lower limit. There is at least one entity in each possible world. We agreed that it is impossible that no being is instantiated. Now, interestingly enough, this implies that necessarily there is at least one entity in each possible world. You’ve just given us a necessary truth.

 

[awatkins69]

Sorry. I wanted to edit my post some more, so here it is:

You cannot “assume” that. In order to find out if a “being” is necessary or not, you must examine all the possible worlds, and prove that that being is present in all of them. Only then will you have a “necessary” being.

I don’t understand why you need to examine all possible worlds to know there is a possible world where no contingent being exists. That’s all we need right now. The argument is formally valid, so you have to deny some premise. Just saying that you think we must “examine all possible worlds” does not change the validity of the argument. If it is valid, you must deny some premise. What premise does your objection here contradict?

Anyways, take a possible world W with just one contingent being. Suppose the being is annihilated. We agreed that it is impossible that the state of affairs “no being is instantiated” ever obtains. That means there must exist either a necessary being or a contingent being. But no contingent being exists. Therefore, modus tollendo ponens, a necessary being exists in W. Therefore, by S5, a necessary being exists. This is not very hard stuff. What it seems you’re denying is the hidden premise, the S5 axiom, which is a very basic modal axiom. Is that correct? If that’s the case, then we still have the preliminary conclusion, “a necessary being exists in W” and we will work with that.

And of course, if a necessary being exists, something is necessary.

I want to emphasize one thing here. The word “contingent” is this scenario does not mean that its is “dependent” on something else. It simply means that the “contingent being” is not present in all the possible worlds. Also, it seems that the cruical question I posited has never been addressed: is there a lower limit of entities in a “metaphysically (or logically) possible” world?

You’re quite right in saying “contingent” doesn’t mean “dependent”. There is a lower limit. There is at least one entity in each possible world. We agreed that it is impossible that no being is instantiated. Now, interestingly enough, this implies that “there is at least one entity” is a true state of affairs in all possible worlds. The phrase “all possible worlds” is just another way of saying “necessarily”. You’ve just given us a necessary truth.

 

[Spock]

That’s a nice try, but you *are *playing word games. We can affirm “1+1=1” when the symbol ‘+’ does not signify the same operation as the ‘+’ in “1+1=2”. They aren’t even remotely contradictory. The ‘+’ in Boolean logic’s “1+1=1” is completely different from “1+1=2” in mathematical terms. ‘+’ is a **disjunction **in Boolean logic. It’s not even the same operation. I’m sorry but this is not going to pass.

Ok, let’s choose a different example then. In Euclidean geometry the fifth postulate says that we can have exactly one parallel line drawn through an external point. In Riemann geomerty we can have none. In the Gauss-Bolyai-Lobatchevsky geometry we have infinitely many. We talk about the same concept here - a parallel line. All 3 propositions are true, based upon the surface we choose.

No. We choose them because they reflect reality.

We do not choose them for that purpose. We choose axioms because they are fun to play with, and if they happen to reflect reality, all the better.

Here is another conondrum: take a circle and a line intersecting it. Also take the inscribed equilateral triangle into that circle. What is the probability that the cross-section of this line will be longer than the side of the triangle? Is it: 1/2 or 1/3 or 1/4? Guess what: all three are true, depending on how we select that intersecting line.

Here is yet another one: in number theory (which deals with the integers) we have a beautiful theorem, called the Great Prime Number theorem. It says that every composite number can be constructed as the multiplication of prime numbers, and this factorization is unique (if we disregard the order the factors). This theorem is proven. For example 6 = 2 * 3. Is this an “absolute” or “necessary” truth? Guess what, it is not. If we happen to choose a generalized concept of integers, then this theorem does not hold any more. If we say that an integer is the form of “a + b * sqrt(-5)”, where both “a” and “b” are integers, then we have another consistent system, and the “usual” integers are a subset of this system, when we choose “b = 0”. In this system 6 = 2 * 3 or 6 = (1 + sqrt(-5)) * (1 - sqrt(-5)) - two distinct factorizations.

The reason I bring up these examples to show that mathematics does not deal with absolute or “necessary” truths, it deals with contingent truths.

There is such a thing as a true logic and a true mathematical system.

No, there is not. There are many of each, and some are more useful than others.

We “make” truths? We make it true that “something cannot both be and not-be in the same respect”? No. Something is not true because it is consistent within a formal system.

If something is the corollary of the axioms, it is called “true”. By definition.

It’s true because it has some corresponding external and objective truthmaker.

Another “oh brother” moment. Presumably you refer to God. Or do you?

I’d say it’s “consistent” not “true”. Or does consistency always entail truth? Is that always (necessarily) true?

It is true in that particular axiomatic system. But axiomatic systems are abstractions, made up (arbitrarily) by some thinking minds. They do not exist as independent ontological entites.

This is a very good definition of truth, and I like it. Now, I don’t want to draw too sharp a line between empirical (a posteriori) and non-empirical (a priori) knowledge. But I think a priori knowledge is possible.

An example, please?

But this is interesting here. We can have it be the case that “2+2=4”, yet “2+2=4” is neither true nor false?

A proposition cannot be true or false if it does not exist. Going back a few hundred thousand years, the primitive people who existed then had absolutely no concept of numbers, except “one”, “two” and “many”. For them the concept of “four” simply did not exist. A more recent example is the huge problem which was created around the number zero and the negative numbers. People could not conceptualize “zero” apples (for example). For them it made perfect sense to talk about one apple, or two apples, even one hundred apples. They could even conceptualize a half apple. But “zero” apples or minus one apple simply did not make sense to them. It was a long process to arrive at the stage when people could understand these concepts.

 

[IsThisCeral]

Read the full book stupid.

I don’t just pick up the bible read one random section and if I read one where God condones Rape and Murder then I just stop reading and call it BS.

Try not to make yourself look stupid next time.

 

[Spock]

I don’t understand why you need to examine all possible worlds to know there is a possible world where no contingent being exists.

What you say is imprecise. In any world there can be contingent entities. The question is: “is there an entity, which appears across all the possible worlds”? That is the definition of “necessary” existence.

That’s all we need right now. The argument is formally valid, so you have to deny some premise. Just saying that you think we must “examine all possible worlds” does not change the validity of the argument. If it is valid, you must deny some premise. What premise does your objection here contradict?

Ouch. Here is a valid argument:

1. All elephants can play the piano.
2. Jumbo is an elephant.
3. Therefore Jumbo can play the piano.

A formally valid argument. Which does not make it a “sound” argument. I am saying that your syllogism is formally valid and yet unsound, for the very same reason this presented syllogism is unsound. Both rest on an invalid premise, in this “all elephants can play the piano”, in yours “there is a necessary being”.

Anyways, take a possible world W with just one contingent being. Suppose the being is annihilated. We agreed that it is impossible that the state of affairs “no being is instantiated” ever obtains.

Now we may get somewhere! What your line of reasoning shows that the single entity in that particular world must be there in order for that world to exist. But that is far cry from proving that the same entity is also present in all the other possible worlds. And that is what we are talking about.

In a very good sense the words “necessary” and “contingent” existence are very unfortunate choices. Necessary does not mean that it “must” be there, and “contingent” does not mean that it is dependent on something else. “Necessary” simply means that an alleged entity is part of every possible world. “Contingent” means that the entity is part of some possible worlds, but missing from others. The choice of “necessary” and “contingent” is unfortunate, since they carry overtones.

Staying with your example: let that entity be a quark of a specific “flavor”. According to our current understanding, quarks are the “final” building blocks or matter, and they come in several “flavors”, all distinct from each other. Now let’s select another world, which contains one entity only, namely a quark of a different flavor. There is nothing in “common” within these two worlds. Therefore there is no “entity” which would appear in all the possible worlds, and thus: there is no necessary existence". This is a constructive proof.

That means there must exist either a necessary being or a contingent being. But no contingent being exists. Therefore, modus tollendo ponens, a necessary being exists in W. Therefore, by S5, a necessary being exists. This is not very hard stuff. What it seems you’re denying is the hidden premise, the S5 axiom, which is a very basic modal axiom. Is that correct?

I most certainly deny S5. It is a vacuous concept. In the example above I proved that there is no entity that would appear in all possible worlds, therefore the postulated “necessary existence” is exactly like a “married bachelor”, a valid string of letters, which refers to nothing.

If that’s the case, then we still have the preliminary conclusion, “a necessary being exists in W” and we will work with that.

And here the nebulous “necessary” raises its ugly head again, and that is why I object its use. From the fact that in your example that one entity “must” exist, in order for that world to exist, it does not follow that the same entity also “must” exist in other possible worlds. The different meanings of “necessary” make these conversations so difficult. I don’t think that you intentionally use it in different connotations, but I do think that you are inadvertantly influenced by the different meanings.

You’re quite right in saying “contingent” doesn’t mean “dependent”. There is a lower limit. There is at least one entity in each possible world. We agreed that it is impossible that no being is instantiated. Now, interestingly enough, this implies that “there is at least one entity” is a true state of affairs in all possible worlds. The phrase “all possible worlds” is just another way of saying “necessarily”. You’ve just given us a necessary truth.

Partially agree. Your final conclusion is: “in every possible world there is something”. And please pardon me, but this is met by a resounding DUH! “Something” is not an entity, it is a concept. And concepts do not exist if there are no minds which can conceptualize. We can make propositions about the state of affairs in those worlds, but our propositions do not exist in those worlds, they exist here.

 

[awatkins69]

Hi Spock. Sorry I can’t reply to your other argument, but we can only do so much here. I’d note though, that I don’t think you understand what I mean by “truthmaker”. Another quick note: even given that some truths which are considered “necessary” are just parts of formal systems (though I do think some systems, like Euclidean geometry, are falsifiable, and indeed have been falsified), it doesn’t follow that they are contingent. They are necessarily true given the rules. Moreover, metaphysically necessary truths like “something cannot both be and not-be at the same time and in the same respect” could never fall to the same criticism. This proposition describes something about the way reality is, not about the rules of our formal game.

Ouch. Here is a valid argument:

1. All elephants can play the piano.
2. Jumbo is an elephant.
3. Therefore Jumbo can play the piano.

A formally valid argument. Which does not make it a “sound” argument. I am saying that your syllogism is formally valid and yet unsound, for the very same reason this presented syllogism is unsound. Both rest on an invalid premise, in this “all elephants can play the piano”, in yours “there is a necessary being”.

I know the difference between validity and soundness. You still did not point to a premise of mine which you contradict. Where in my argument is there a premise, “there is a necessary being”? That’s my conclusion, (5). Premises are propositions which are used as “connectors” in a logical syllogism. Conclusions on the other hand are just what we get from the reasoning.

Now we may get somewhere! What your line of reasoning shows that the single entity in that particular world must be there in order for that world to exist. But that is far cry from proving that the same entity is also present in all the other possible worlds. And that is what we are talking about.

Yes, we are now getting somewhere. This is good. If I understand you correctly, I was entertaining this idea myself while I was watching a movie. What you are saying is for it to be a possible world, it must have some entity. In all possible worlds, that entity is contingent, correct? Thus, there is no contradiction between our saying “everything is contingent, nothing is necessary” and “in all possible worlds something exists” (although I take the term “in all possible worlds” to be equivalent to “necessarily”; more on that below).

Consider this. Take the sum total of all contingencies C. Is it possible for C to have an external cause? External causes are logically possible in general. So it is a perfectly reasonable inference to say possibly C has an external cause. But that means the cause cannot be contingent, or else it would simply be a part of the set. And if it is not contingent, then…

Staying with your example: let that entity be a quark of a specific “flavor”. According to our current understanding, quarks are the “final” building blocks or matter, and they come in several “flavors”, all distinct from each other. Now let’s select another world, which contains one entity only, namely a quark of a different flavor. There is nothing in “common” within these two worlds. Therefore there is no “entity” which would appear in all the possible worlds, and thus: there is no necessary existence". This is a constructive proof.

To call these worlds possible I think this is just to beg the question my friend. As you describe these worlds, I say they are **impossible **worlds, because they do not contain our necessary being. Any world in which a necessary being does not exist is not a possible world. For, as was shown above, a necessary being exists in the possible world in which C is externally caused. By definition what is necessary does not differ from world to world. Therefore, etc.

I most certainly deny S5. It is a vacuous concept. In the example above I proved that there is no entity that would appear in all possible worlds, therefore the postulated “necessary existence” is exactly like a “married bachelor”, a valid string of letters, which refers to nothing.

At least I know where you stand on your modal logic. However, it’s really not a very controversial idea amongst modal theorists. As I have shown, in your argument those are not possible worlds.

The different meanings of “necessary” make these conversations so difficult. I don’t think that you intentionally use it in different connotations, but I do think that you are inadvertantly influenced by the different meanings.

Well, I try to only use “necessary” to mean “in all possible worlds”, as you say. And “contingent” to mean “true in some possible worlds, false in other.” The problem is, since I see an identity between the terms “in all possible worlds” and “necessary” or “necessarily”, then we have to say something is necessary in places you don’t really want to, such as “in all possible worlds something (variable) exists”. If the term “in all possible worlds” is identical to “necessarily” we say “necessarily something exists”.

Of course, this is just word play and I won’t get into it too much.

 

[awatkins69]

One more question for clarification. Is it a contingent fact that there are contingent beings?

 

[Spock]

Hi Spock. Sorry I can’t reply to your other argument, but we can only do so much here. I’d note though, that I don’t think you understand what I mean by “truthmaker”.

Well, I went to your link and still do not have the foggiest idea what it is all about. Not surprisingly, since some philosophers strive to create a brand new terminology, and many of them are totally esoteric.

Yes, we are now getting somewhere. This is good. If I understand you correctly, I was entertaining this idea myself while I was watching a movie. What you are saying is for it to be a possible world, it must have some entity. In all possible worlds, that entity is contingent, correct?

No, I am not saying that. I most certainly did not say that it is the same entity. On the very contrary, I said that it is not the same entity. The definition of a possible world is a state of affairs, which is different from our existing one. No more, no less. Our world is clearly “possible”, since it exists. By observing our world, we can conclude that it might be different. Where there is a pine-tree, it might contain an oak-tree, or no tree at all. Where there is no tree, there might be a tree. In theory, a world might not even contain anything (a null-world) and it would still satisfy the definition of a “possible world”. If you wish to introduce a different definition we shall have to start afresh, provided that we can agree on a proposed new definition. Though I see no reason for that. (One remark. I agreed that we shall restrict our conversation to non-empty worlds. I did that to make the conversation easier. As far as I am concerned, a null-world is a possible world, since it conforms to the definition of “possible worlds”. But this is just a remark, I do not want to make things more complicated by going into details.)

Consider this. Take the sum total of all contingencies C. Is it possible for C to have an external cause? External causes are logically possible in general. So it is a perfectly reasonable inference to say possibly C has an external cause. But that means the cause cannot be contingent, or else it would simply be a part of the set. And if it is not contingent, then…

You are treading on thin ice here. First of all, it is not obvious at all that causation can even be defined for an arbitrary set. And even if it can be defined, you are playing with a varaint of the Russell-paradox. The “set of all sets” type of proposition leads to logical problems. We can say that the “set of all sets of anything” is nonsensical and frequently self-contradictory.

To call these worlds possible I think this is just to beg the question my friend. As you describe these worlds, I say they are **impossible **worlds, because they do not contain our necessary being. Any world in which a necessary being does not exist is not a possible world.

I hope that you are just trying to pull my leg here. Those possible worlds I described follow the definition of possible worlds. Now you wish to add a new twist to it, and say that a possible world is not “possible”, if it does not contain a “necessary” entity? Come on. You cannot just redefine the concept of “possible world”, just because the original definition refutes your hypothesis.

For, as was shown above, a necessary being exists in the possible world in which C is externally caused. By definition what is necessary does not differ from world to world. Therefore, etc.

And here you deviate from the “necessary” existence, too. It makes no sense that something is “necessary”, if it exists in one possible world. And I don’t think that you can even show the validity of your assumption - for reasons stated above.

Well, I try to only use “necessary” to mean “in all possible worlds”, as you say. And “contingent” to mean “true in some possible worlds, false in other.” The problem is, since I see an identity between the terms “in all possible worlds” and “necessary” or “necessarily”, then we have to say something is necessary in places you don’t really want to, such as “in all possible worlds something (variable) exists”. If the term “in all possible worlds” is identical to “necessarily” we say “necessarily something exists”.

The main problem with “something exists in all possible worlds” (or something exists necessarily) is the fact that it is not necessarily the same something. In other words: the proposition that “something (undefined) exists in all the possible worlds” has no informational value, it is too vague to mean anything.

Is it a contingent fact that there are contingent beings?

Since this is a proposition, it is contingent upon someone who can make that proposition.

 

[awatkins69]

Hi Spock. These posts are getting awful long. It wouldn’t even let me post it because of length. I’m going to split it up.

Well, I went to your link and still do not have the foggiest idea what it is all about. Not surprisingly, since some philosophers strive to create a brand new terminology, and many of them are totally esoteric.

It’s not just some new esoteric thing. It’s one of the main theories of truth in modern philosophy. There are entire books and peer-reviewed journals dedicated to stuff like it. However, I can’t blame you. Ofttimes Wikipedia is bad. SEP’s entry is better. This isn’t all directly pertinent, so I won’t go on about truthmaking. But if you’re interested in learning more for yourself you can check it out here.

 

[awatkins69]

No, I am not saying that. I most certainly did not say that it is the same entity. On the very contrary, I said that it is not the same entity. The definition of a possible world is a state of affairs, which is different from our existing one. No more, no less. Our world is clearly “possible”, since it exists. By observing our world, we can conclude that it might be different. Where there is a pine-tree, it might contain an oak-tree, or no tree at all. Where there is no tree, there might be a tree. In theory, a world might not even contain anything (a null-world) and it would still satisfy the definition of a “possible world”. If you wish to introduce a different definition we shall have to start afresh, provided that we can agree on a proposed new definition. Though I see no reason for that. (One remark. I agreed that we shall restrict our conversation to non-empty worlds. I did that to make the conversation easier. As far as I am concerned, a null-world is a possible world, since it conforms to the definition of “possible worlds”. But this is just a remark, I do not want to make things more complicated by going into details.)

Sorry. I guess I wasn’t clear enough, and that’s my fault. I don’t mean you say it is the same entity. I mean that, according to you, in every possible world something exists. But “something” doesn’t mean some definite entity. Since you say nothing is necessary, then it can only be contingent entities. So the better way to put it is, for you, in each possible worlds there is at least one individual contingent entity. But it’s not necessarily the same entity in all possible worlds.

I don’t understand something to be a possible world just in case I can conceive it. I can conceive of a world with nothing (I guess), but that doesn’t make it possible. I can conceive of a necessary being, and a non-world. But one must be possible, and the other impossible. In case you didn’t know, there is such a thing as an impossible world. This is what a null-world is. We agreed to this earlier.

To make everything crystal clear, I’m going to define our modal terms now.
X is…
Impossible iff “there is no possible world where X obtains”
Possible iff “there is at least one possible world where X obtains”
Contingent iff “there are some possible worlds where X obtains and some possible worlds where X does not obtain”
Necessary iff “X obtains in all possible worlds”

You are treading on thin ice here. First of all, it is not obvious at all that causation can even be defined for an arbitrary set. And even if it can be defined, you are playing with a varaint of the Russell-paradox. The “set of all sets” type of proposition leads to logical problems. We can say that the “set of all sets of anything” is nonsensical and frequently self-contradictory.

Okay. So you’re saying the sum total of all contingencies is not possibly externally caused? And why? You think we don’t know what ‘external cause’ means here? However you define causation (“actualization”, “constant conjunction of events”, “necessitation”, whatever) the concept can be applied. I don’t see anything logically impossible about it. And you have a problem with the idea of “the sum total of all contingencies”? Be clear and explain what the problem is, and why it makes it impossible that C is externally caused.

Prima facie, I don’t find these “possible” objections compelling at all. I’d like you to really focus in here. The rest we should pick up on later.

I hope that you are just trying to pull my leg here. Those possible worlds I described follow the definition of possible worlds. Now you wish to add a new twist to it, and say that a possible world is not “possible”, if it does not contain a “necessary” entity? Come on. You cannot just redefine the concept of “possible world”, just because the original definition refutes your hypothesis.

I think you don’t understand what I was saying because that’s not what I was doing at all. That may be my fault. Okay. If X is necessary then X obtains in all possible worlds. That is equivalent to saying that if X is necessary then there is no possible world where X does not obtain. This is equivalent to saying if X is necessary then it is impossible that X not obtain. So I follow this general line of reasoning. X is necessary. In your scenarios S and S, X does not obtain. Therefore S and S are impossible.

And here you deviate from the “necessary” existence, too. It makes no sense that something is “necessary”, if it exists in one possible world. And I don’t think that you can even show the validity of your assumption - for reasons stated above.

It only deviates from the definition of “necessary” if I were to say that it exists in **only **one possible world. If something is necessary of course it exists in one possible world. It exists in all possible worlds!

 

[awatkins69]

The main problem with “something exists in all possible worlds” (or something exists necessarily) is the fact that it is not necessarily the same something. In other words: the proposition that “something (undefined) exists in all the possible worlds” has no informational value, it is too vague to mean anything.

I understand. That’s what I meant earlier in trying to understand your position. According to you, it is not necessarily the same something. I’m glad we have that clear.

The proposition you speak of has plenty of informational value however. If it is true, contrary to what you say, there is no possible world which is a non-world. That has significant ramifications, as we see.

Since this is a proposition, it is contingent upon someone who can make that proposition.

I hope you’re not equivocating here by taking “contingent” to mean “dependent”. We agreed earlier that the two are not equivalent. I think this is what you mean though. So, with terms defined above, once again, is it a contingent fact that there are contingent beings?

Earlier, I wanted to show that there is a possible world where no contingent being exists. So if it is a contingent fact that there are contingent beings, that means there are some worlds where there are contingent beings and some where there are not. Q.E.D.

The necessary being follows, given that something (undefined) exists in all possible worlds and that there is a possible world where no contingent being exists.

 

[awatkins69]

You are treading on thin ice here. First of all, it is not obvious at all that causation can even be defined for an arbitrary set.

Wait. Is this the “fallacy of the stolen concept” of Ayn Rand? lol

Well Spock, I’m going to have to run away from this one. Sorry if I don’t reply, because I have a lot of work on political philosophy to do this week. One of the better discussions I’ve had with an atheist though. Thanks. \//

 

[Spock]

Sorry. I guess I wasn’t clear enough, and that’s my fault. I don’t mean you say it is the same entity. I mean that, according to you, in every possible world something exists. But “something” doesn’t mean some definite entity. Since you say nothing is necessary, then it can only be contingent entities. So the better way to put it is, for you, in each possible worlds there is at least one individual contingent entity. But it’s not necessarily the same entity in all possible worlds.

So far we are in agreement.

I don’t understand something to be a possible world just in case I can conceive it. I can conceive of a world with nothing (I guess), but that doesn’t make it possible. I can conceive of a necessary being, and a non-world. But one must be possible, and the other impossible.

I fail to see the dichotomy. Let’s slow down for a second. We have our world, which is clearly possible. We can add to this world or subtract from this world some things (observe, I did not say “anything”) and arrive at a new possible world. Specifically, if we consider a simple causal chain, A → B-> C, then maybe we cannot remove “B” from this chain, since then C would be left “hanging”, so to speak. At least it seems so at first glance, but it must be scrutinized further.

Now we could argue that C still could be there, via a different causal chain, or simply stay there uncaused. After all “the law of causality” is merely the result of zillions of observations, so it is conceivable that there are uncaused events. As a matter of fact, if we happen to have libertarian free will, then our actions are free, in the sense that they are not determined (or caused) by external factors. They are obviously influenced, but not caused. We we have a good ground to argue that there can be uncaused events, so the A → ? C is still a possible world. However, I am not going to rely on this.

From this we can deduce that the “middle” of a causal chain cannot be removed (probably) and still have a possible world. However, the end of the causal chain can be removed with impunity. If we cut off a causal chain anywhere in the middle, and remove everything from that point onward, the resulting world will still be possible. Naturally, if we start from a possible world, we can always add new causal chains to it, or add uncaused events, as long as the new uncaused events do not form a logical contradiction with the rest.

Side (but not snide ) remark: this is what I had in mind when I was saying that there can be infinitely many possible worlds. The number of entities in a possible worlds is unspecified, and there is upper limit to it. It would be strange to say that there can be “N” entities in a world, but it cannot have “N + 1” entities.

To make everything crystal clear, I’m going to define our modal terms now.
X is…
Impossible iff “there is no possible world where X obtains”
Possible iff “there is at least one possible world where X obtains”
Contingent iff “there are some possible worlds where X obtains and some possible worlds where X does not obtain”
Necessary iff “X obtains in all possible worlds”

Perfectly clear and agreed. I substituted “exists” into “obtains”. (Some jargons rub me the wrong way. Sorry.)

Now, starting from this (current world) the question arises, and it is a valid question, “is there any entity (or even some entities!), which is (are) present in every possible world?”. In other word, is there a necessarily existing entity? I agree that this is a valid problem to investigate. As I also said the only way to affirm this hypothesis is to “review” all the possible worlds and see if there is any overlap among them. If there is, we have necessary entity (or entities!); if there is none, then the hypothesis of the necessary existence is null and void, and thus must be discarded. There is no shortcut here, by executing some word-games as S5 would do.

From the possibility that there is a specific entity, which appears in all the possible worlds it does not follow that there is actually such an entity - notwithstanding the assertion that “if something is possibly necessary, then it is necessary”. That is total bogus. It is word game, played upon the ambiguous use of “possible”.

The 6000 character limit bytes again. Will continue below.

 

[Spock]

Continued from above.

Okay. So you’re saying the sum total of all contingencies is not possibly externally caused? And why? You think we don’t know what ‘external cause’ means here? However you define causation (“actualization”, “constant conjunction of events”, “necessitation”, whatever) the concept can be applied. I don’t see anything logically impossible about it. And you have a problem with the idea of “the sum total of all contingencies”? Be clear and explain what the problem is, and why it makes it impossible that C is externally caused.

Prima facie, I don’t find these “possible” objections compelling at all. I’d like you to really focus in here. The rest we should pick up on later.

As you say, let’s concentrate on this problem. First, is the “set of all contingencies” a valid, coherent structure? It is not. I mentioned the Russell paradox, and this construct is just another example of it.

Let’s examine an identical concept. Let’s divide all the sets into two subsets: 1) those sets which do not contain themselves as a member, and 2) those sets, which contain themselves as members. (Remember a “set” is an arbitrary collection of anything!). Let’s call the sets of the first type “regular” sets, while the sets of the second type “irregular” sets. Now let’s collect all the regular sets into a “super-set”, and present the question: “is this super-set regular or not?”. The answer is a paradox: if it is a regular set, then it must be included, since we collected all the regular sets, therefore it contains itself as a member, therefore it is not a regular set, so it cannot be included. A clear equivalent of the “this sentence is false” type of self-contradiction.

Therefore the aggregate set of “all contingencies” is not a valid set. Just like we cannot posit the the aggregate of all “regular” sets, we cannot posit the “set of all contingencies” as a valid set. No matter how causation is defined, it cannot be applied to an undefinable set.

For those, who might find these “regular” and “irregular” sets confusing, I will give another example, called the “barber of the army”.

Let’s consider an army, where the job of all members is clearly defined. There is a rule in this army, which says that no one can wear any facial hair, everyone must always be clean-shaven. However, not all the soldiers shave themselves. There is a barber in the army, whose job is to shave all those soldiers who do not shave themselves. However, he is forbidden to shave anyone who does shave himself. So the question arises: what can he do about his own facial hair? If he starts to shave, he is one of those soldiers, who shave themselves, and so he cannot continue according to the rule. As soon as he asks another soldier to shave him, he is one of those solders who do not shave themselves, and so he must shave himself. A clear contradiction: the ruleset leads to a paradox. Exactly as in your stipulated “set of all contingencies”.

I think you don’t understand what I was saying because that’s not what I was doing at all. That may be my fault. Okay. If X is necessary then X obtains in all possible worlds. That is equivalent to saying that if X is necessary then there is no possible world where X does not obtain. This is equivalent to saying if X is necessary then it is impossible that X not obtain. So I follow this general line of reasoning. X is necessary. In your scenarios S and S, X does not obtain. Therefore S and S are impossible.

I think I did understand you perfectly. You put the cart in front of the horse. It is true, if there is a necessary entity, then it would be part of my stipulated worlds (S and S*). Since it is not included, all you can say that “ex hypotesi” they cannot be possible worlds. But that is not acceptable. You cannot start with positing your hypothesis and then use it as a supporting argument. That is a logical error. Until the hypothesis is established, you cannot use the hypothesis to differentiate between “possible and impossible” worlds!

Now, let’s get down to a constructive proof again. We have two possible staring points, either our current, existing world, or the suggested “mini-worlds”. I will explore both cases.

Let’s start with our existing world, which is obviously possible. Let’s remove objects which are at the end of some causal chain. The resulting world will always be a possible world, since the end of any causal chain can always be removed. At the end of this process we shall arrive at the mini-worlds, by removing everything except those quarks. Since the quarks are the final building blocks of matter, they cannot be at the “end point” of a causal chain. So the S and S* are possible worlds.

Let’s start with either one of the mini-worlds (S or S*), and keep adding entities and causal chains to it. At the end of this process we shall arrive at our existing world, if we do it judiciously. So starting from the mini-worlds we can build our world, and since successive additions will always yield a possible world, and at the end of the building process we arrive at our existing world, we prove that the starting point was a possible world as well. It is obvious that from an impossible world you cannot create a possible world by adding something to it.

 

[Spock]

Well Spock, I’m going to have to run away from this one. Sorry if I don’t reply, because I have a lot of work on political philosophy to do this week. One of the better discussions I’ve had with an atheist though. Thanks. \//

Take your time, and if you are so inclined, please return. I want to reciprocate your compliment, I also enjoy our exchange of ideas tremendously.

 

[Warrenton]

How about the delusion that an invisible, inexplicable superman in the sky whipped the universe together in a few days for no readily apparent reason?

Take out the God part, and you are left with the same delusion, only more delusional.

Why shoud the universe inexplicably exist?

Why should we trust our senses in such an inexplicable universe?

It’s a muddle.

 

[TarkanAttila]

Take out the God part, and you are left with the same delusion, only more delusional.

Why shoud the universe inexplicably exist?

Why should we trust our senses in such an inexplicable universe?

It’s a muddle.

This is a good point. Man does not make order out of the world. The world is ordered and man is able to perceive it.

If not Christianity, the evidence of the Universe should at least lead a man to Deism, not atheism. Atheism is pompous in assuming that man is the only (or highest) creator.