Set of Contingent Beings Need Not Be Contingent: Please Disprove

[Gorgias]

Then you need to reread what I wrote. Actually, start by reading the topic of the thread: “Set of Contingent Beings Need Not Be Contingent”

I have. And I get what you’re saying. And I disagree. Now that we’ve cleared that up…

I never said that it did. What I did say, and have proven, is that even if we grant the (unsupported) assertion that every member of ‘the universe’ is ‘contingent’, that does not per se prove that ‘the universe’ itself is contingent.

Yet, that’s exactly the opposite of what the argument from contingency asserts. It does not attempt to say, “this comb is contingent… and this person is contingent… and this planet is contingent… therefore the universe is contingent” – which is what you’re attempting to argue here, it seems. The argument from contingency does not assert that for every member u (something that exists in the universe) in U (the universe), u is contingent and therefore U is likewise contingent. As you’ve shown, that’s pretty easy to obfuscate with math.

Rather, the argument from contingency only deals in U itself: it claims that the universe itself (without considering its members) is contingent – since, after all, it does not necessarily exist. Could we conceive of the universe not existing? Of course. Perhaps you might show that it necessarily exists?

Therefore, the argument from contingency continues, if the universe itself (not its members, mind you – the universe itself!) is contingent, then it needs something to explain its existence. If that ‘something’ is itself contingent, then we peel another layer and ask what explains the existence of that ‘something’; if that ‘something’ is necessary, then we’ve reached our goal. This argument, however, asserts that the ultimate cause must be something necessary, and names it ‘God’.

An assumption that is not proven. Even the term ‘contingent’ is ambiguous. Does it meant that it can exist without depending on another entity? Or that it must exist? Or that it cannot exist in a different form to that we see? Or do these imply each other?

Fair questions. The problem here, I think, is the confusion you’re having, is in the failure to distinguish between ‘contingency’ (i.e., a thing that is not necessary – in other words, a thing that could have not existed), and ‘contingency upon s.t.’ (e.g., I am contingent upon my parents). Both speak to similar situations… but it’s strict contingency, in the philosophical sense, that we’re talking about here: we’re talking about things that necessarily exist.

(OP seems to be suggesting, without explicitly saying it, that something that has no temporal ‘beginning’ is necessary. That doesn’t seem to hold up. Once we’re done helping you understand what ‘contingent’ means, perhaps we can take up that argument… )

It is an interesting subject, but discussing it constructively requires you to not deliberately misrepresent what I have said.

I don’t think I’ve done that. Yet, your arguments don’t work here, since they try to deconstruct the argument from contingency backwards – that is, they ‘deliberately misrepresent’ the argument. If you take the argument at what it says, then you’ll see that the ‘set theory’ approach is irrelevant.

 

[JuanFlorencio]

Nope. It is the premise that is wrong. A valid argument, given a false axiom, can still reach a false conclusion.

Certainly! There is a difference between logical validity and truth. To demonstrate the truth of a given proposition our argument must be valid. I have examined the form of your argument, and -as you can see above- it is invalid (or incorrect, as you wish).

The argument I gave is a very well known, proven, rigorously demonstrated, effectively indisputable one. Graph theory is a very mature field.

I would like to see that demonstration, Taffy.

It is your assertion that the backpack can be supported by the wall and the wall can be supported by the backpack that is erroneous - and an error that is in any case covered by the condition of whether or not the ‘graph’ may include cycles.

Sorry, but in the nicest way possible, graph theory is demonstrably, objectively rigorous and you are demonstrably, objectively wrong here.

Well, besides the formal invalidity of your argument, it can be said of course that your assertion that A is contingent on B (and on nothing else) and B is contingent on A (and on nothing else) is erroneous.

 

[inocente]

I would like to see a refutation of this rebuttal to Copleston: A set of contingent beings is not necessarily contingent, and God’s existence is not required to explain such a set.

Recently “Catholic Answers Live” brought my attention to this debate between Copleston and Russell. To be clear, Russell has no good response, fails to make this objection, and a stalemate occurs because of his stubbornness.

Copleston defines the universe as the aggregate of all things, but that would seem to exclude space, unless space is redefined as a thing, which raises Russell’s general question of what is meant by a thing.

Russell asks what is meant by a thing existing, I think in the sense that existence isn’t a property of a thing - a thing must necessarily exist or else it would be nothing. So in that sense all things necessarily exist, since if they didn’t, they wouldn’t be things.

Then there’s the point about cause and effect, whether it is ever real, whether it even has meaning then applied to the universe (everything) rather than individual things.

I think Russell is concerned only with the logical validity of the argument, since scientific explanations are subject to change. But on your point about matter and energy: It’s hypothesized that the sum total of all the energy in the universe, including the energy bound-up in matter is exactly zero, since otherwise there’s nowhere the energy could have come from (whether the universe is eternal or created).

I am reminded of Bertrand Russell denying cause and effect due to the observation that they cannot be simultaneous. One follows after the other, and so how can one be the cause, since by the time the effect starts the cause has ceased to exist? He makes the point that you can (or must) instead conceive of reality as a sequence of ‘brute force’ snapshots: “Every time the air has been this temperature, water has frozen,” and not postulate the existence of ‘cause’ and ‘effect’. I suppose this denies the principle of sufficient reason, that literally everything “just happens” without explanation. Hence our science is a useful fiction: We’ve invented laws and a lawgiver as shorthand convenience to live with it.

Re the comment about water freezing, yes, a physical law is defined as “a theoretical statement inferred from particular facts, applicable to a defined group or class of phenomena, and expressible by the statement that a particular phenomenon always occurs if certain conditions be present” - en.wikipedia.org/wiki/Physical_law

 

[catholic1seeks]

I would like to see a refutation of this rebuttal to Copleston: A set of contingent beings is not necessarily contingent, and God’s existence is not required to explain such a set.

Recently “Catholic Answers Live” brought my attention to this debate between Copleston and Russell. To be clear, Russell has no good response, fails to make this objection, and a stalemate occurs because of his stubbornness.

Nonetheless, it is a good opportunity to discuss the argument from contingency, because this is perhaps my central problem with it: It assumes that everything in the universe is contingent in a non-cyclical way. Coincidentally, Fr. Robert Spitzer fails egregiously to prove this point in his terrible not-worth-reading book New Proofs … by tripping over (misapplying) his own definitions. (As I recall, he reworks the problem in terms of ‘conditioned realities’ and ‘conditions’, and then mistakes the two.)

My argument is that we know matter is converted into energy, and energy is converted into matter. If a set – the universe – contains these two things, it appears that one of the two necessarily will exist for all time: We have never seen both matter and energy cease to exist. It appears the principle of sufficient reason ends here with matter and energy just as the theist would say it ends with God: Just as God “contains the reason for His own existence”, we can equivalently say that the universe “contains the reason for its own existence” by virtue of having matter and energy.

This raises the question of the Second Law of Thermodynamics, i.e. that entropy has been seen to always increase as objects decrease in energy, and of the history of the universe, as we extrapolate the expansion of galaxies backwards to the Big Bang: Wouldn’t the universe be cold and still now if it had always existed? Doesn’t the expansion of the universe show that the universe had a beginning? The answer is agnosticism. We simply do not know, and it is an unjustified assumption of the theist to declare that there was nothing before the Big Bang, and it is an unjustified assumption to declare that our mathematical modeling of our observations which we call the Second Law of Thermodynamics must apply everywhere for all time. (Apparently it is also a misconstruing of the Borde-Guth-Vilenkin theory to declare that it proves our universe is finite, because it also rests on a set of assumptions we’re not sure are true for our universe.)

Hence the argument from contingency, as presented by Copleston (and Catholic Answers), fails to prove God’s existence because it rests on the unjustified assumption that the universe itself is contingent.

The universe is the set of all contingent things.

If it said that this means the set, or the universe itself, is not necessarily contingent, then…

Does that mean the entire set, the entire collection of contingent things (the universe) minus ONE item – say, a star, or one hydrogen atom, or a chunk of rock – would then make the that collection (minus the one item) contingent?

I’m a bit confused on what this atheist’s argument is saying. For if we admit the universe contains contingent things, and the universe is simply the collection of contingent things, then how does it not follow the entire set is contingent? An apple is contingent. Now grab the whole basket of apples - that’s contingent. Now collect the entire supply from the supermarket. That’s contingent. Now add on all cities, the entire earth, everything in our solar system. Still contingent items. Now keep collecting until you reach ALL items in the universe.

What makes having every item together no longer contingent?

 

[catholic1seeks]

edwardfeser.blogspot.com/2010/12/hume-cosmological-arguments-and-fallacy.html?m=1

This blog post relates to the issue

 

[DrTaffy]

I have. And I get what you’re saying. And I disagree.

Fine.

Then you are objectively, demonstrably wrong. Feel free to gloat about that.

Now that we’ve cleared that up…

Indeed…

DrTaffy;13814604:

What I did

say, and have proven, is that even if we grant the (unsupported) assertion that every member of ‘the universe’ is ‘contingent’, that does not per se prove that ‘the universe’ itself is contingent.

Yet, that’s exactly the opposite of what the argument from contingency asserts.

OK - logic 101: if an argument starts by asserting the opposite of a statement proven to be true, what is the validity of that argument?

Could we conceive of the universe not existing? Of course. Perhaps you might show that it necessarily exists?

Can you show that God necessarily exists? If so, why bother with the ‘argument from contingency’ if you already have proof that God exists?

I do have empirical proof that the universe exists - look around you and, why, slap me silly and call me Jemima, there it is!

Therefore, the argument from contingency continues, if the universe itself (not its members, mind you – the universe itself!) is contingent, then it needs something to explain its existence. If that ‘something’ is itself contingent, then we peel another layer and ask what explains the existence of that ‘something’; if that ‘something’ is necessary, then we’ve reached our goal. This argument, however, asserts that the ultimate cause must be something necessary, and names it ‘God’.

In other words, it makes utterly unfounded assertions. Wonderful!

Fair questions.

Not questions, points. Which you utterly ignore.

The problem here, I think, is the confusion you’re having, is in the failure to distinguish between ‘contingency’ (i.e., a thing that is not necessary – in other words, a thing that could have not existed), and ‘contingency upon s.t.’ (e.g., I am contingent upon my parents).

In other words, you refuse to acknowledge the validity of any other definition of ‘contingent’ than yours, and mock me for doing so.

OK, fine. I have your intellectual position placed.

Once we’re done helping you understand what ‘contingent’ means, perhaps we can take up that argument… )

Or you could learn to discuss issues in an adult manner. Whatever.

I don’t think I’ve done that.

Again, objectively demonstrably false.

Yet, your arguments don’t work here, since they try to deconstruct the argument from contingency backwards

Nope. They address the topic of the thread. Need a “Set of Contingent Beings” Itself be ‘Contingent’?

– that is, they ‘deliberately misrepresent’ the argument.

Again, nope.:nope:

If you take the argument at what it says, then you’ll see that the ‘set theory’ approach is irrelevant.

It is relevant to the thread. Possibly not to your red herring, but so what?

 

[DrTaffy]

I have examined the form of your argument, and -as you can see above- it is invalid (or incorrect, as you wish).

Neither. Don’t take my word for it - you are attempting to contradict a well known, formally and rigorously proven mathematical truth.

I would like to see that demonstration, Taffy.

Which one? You kinda have already, probably, but to pick the three most obvious contenders:
Assertion 1: a cyclic set of ‘contingent’ entities need not itself be contingent
Proof: consider the set [A->B->C->A]
Each element is contingent, but the set is not. QED

Assertion 2: an infinite set of ‘contingent’ entities need not itself be contingent
Proof: consider an infinite set of nodes, each labelled with an integer (positive or negative) where node N is ‘contingent’ on (N-1)
So …-3]->-2]->-1]->[0]->[1]->[2]->[3]…
Again, each element is contingent, but the set is not. QED

Assertion 3: in a finite acyclic directed graph there must be at least one node with no arrows leading to it
Proof: start with any point and work your way back against the direction of the arrows. Either:

a) you eventually come to a dead end, meaning a node with no arrows leading to it. QED
b) You never come to dead end. meaning either an infinite set or at least one cycle, either of which violates the stated premise of a finite acyclic directed graph​

Well, besides the formal invalidity of your argument, it can be said of course that your assertion that A is contingent on B (and on nothing else) and B is contingent on A (and on nothing else) is erroneous.

No it cannot. That is the premise. You have no grounding in formal logic, do you?

 

[JuanFlorencio]

No it cannot. That is the premise. You have no grounding in formal logic, do you?

I do. There are true premises and false premises. Yours is a false premise.

Neither. Don’t take my word for it - you are attempting to contradict a well known, formally and rigorously proven mathematical truth.

You just have to write it down here. Or say where you saw it. That is all you have to do. Not much.

Which one? You kinda have already, probably, but to pick the three most obvious contenders:
Assertion 1: a cyclic set of ‘contingent’ entities need not itself be contingent
Proof: consider the set [A->B->C->A]
Each element is contingent, but the set is not. QED

Assertion 2: an infinite set of ‘contingent’ entities need not itself be contingent
Proof: consider an infinite set of nodes, each labelled with an integer (positive or negative) where node N is ‘contingent’ on (N-1)
So …-3]->-2]->-1]->[0]->[1]->[2]->[3]…
Again, each element is contingent, but the set is not. QED

Assertion 3: in a finite acyclic directed graph there must be at least one node with no arrows leading to it
Proof: start with any point and work your way back against the direction of the arrows. Either:

a) you eventually come to a dead end, meaning a node with no arrows leading to it. QED
b) You never come to dead end. meaning either an infinite set or at least one cycle, either of which violates the stated premise of a finite acyclic directed graph​

In your first proposal you are asking me to consider the set {A, B, C}, and you conceive your defined contingency relation between its elements represented by [A->B->C->A]. This is a set of relations that we can express this way: {A->B, B->C, C->A}. Of course we can write the same thing using propositions:

A is contingent on B
B is contingent on C
C is contingent on A

Then you conclude that the set {A, B, C} is not contingent on anything else; it simply is or exists. In other words, you are concluding the existence of the set based on the relations you have conceived between its elements.

“A is contingent on B” could be expressed as “the existence of A implies the existence of B” or simply as “A implies B” or “If A then B”. Same thing with the other relations. So, we could represent your graph as follows:

If A then B
If B then C
If C then A

Those are your premises. You conclusion can be expressed as

A and B and C exist; or simply “A and B and C”.

Your argument would be

If A then B
If B then C
If C then A

Therefore,

A and B and C

However, given a set of rules of inference, from your premises you could only conclude other conditionals, like

If A then C
If B then A

And

If A then A

But you cannot conclude

A
nor
B
nor
C,
nor
A and B and C.

This is clear for someone who knows the basics of logic. Another way of looking at it is by forming the proposition:

(If A then B) and (If B then C) and (If C then A) and (A and B and C)

If your argument is valid, then this proposition should be a tautology. Well, it is not.

 

[JuanFlorencio]

I would like to see a refutation of this rebuttal to Copleston: A set of contingent beings is not necessarily contingent, and God’s existence is not required to explain such a set.

Recently “Catholic Answers Live” brought my attention to this debate between Copleston and Russell. To be clear, Russell has no good response, fails to make this objection, and a stalemate occurs because of his stubbornness.

Nonetheless, it is a good opportunity to discuss the argument from contingency, because this is perhaps my central problem with it: It assumes that everything in the universe is contingent in a non-cyclical way. Coincidentally, Fr. Robert Spitzer fails egregiously to prove this point in his terrible not-worth-reading book New Proofs … by tripping over (misapplying) his own definitions. (As I recall, he reworks the problem in terms of ‘conditioned realities’ and ‘conditions’, and then mistakes the two.)

My argument is that we know matter is converted into energy, and energy is converted into matter. If a set – the universe – contains these two things, it appears that one of the two necessarily will exist for all time: We have never seen both matter and energy cease to exist. It appears the principle of sufficient reason ends here with matter and energy just as the theist would say it ends with God: Just as God “contains the reason for His own existence”, we can equivalently say that the universe “contains the reason for its own existence” by virtue of having matter and energy.

This raises the question of the Second Law of Thermodynamics, i.e. that entropy has been seen to always increase as objects decrease in energy, and of the history of the universe, as we extrapolate the expansion of galaxies backwards to the Big Bang: Wouldn’t the universe be cold and still now if it had always existed? Doesn’t the expansion of the universe show that the universe had a beginning? The answer is agnosticism. We simply do not know, and it is an unjustified assumption of the theist to declare that there was nothing before the Big Bang, and it is an unjustified assumption to declare that our mathematical modeling of our observations which we call the Second Law of Thermodynamics must apply everywhere for all time. (Apparently it is also a misconstruing of the Borde-Guth-Vilenkin theory to declare that it proves our universe is finite, because it also rests on a set of assumptions we’re not sure are true for our universe.)

Hence the argument from contingency, as presented by Copleston (and Catholic Answers), fails to prove God’s existence because it rests on the unjustified assumption that the universe itself is contingent.

Our principles of conservation of mass and energy as well as our second law of thermodynamics and the knowledge about the conversion of mass and energy have been derived, directly or indirectly, from our experience. And our experience is restricted to a limited extension of the universe and to a limited period of time. If, as you suggest, we cannot be sure that the second law of thermodynamics applies everywhere and for all time, what is different in relation to our conservation principles? There seems to be no difference. Then, we could not say that if a set -the universe- contains matter and energy, one of the two necessarily will exist for all time. Therefore, we could not say that the universe has existed and will exist forever and if, “by chance”, this implied that it contains the reason for its own existence, we could not say it either.

 

[Gorgias]

Then you are objectively, demonstrably wrong. Feel free to gloat about that.

Again, objectively demonstrably false.

Fine. Then demonstrate it, not just claim it without proof.

OK - logic 101: if an argument starts by asserting the opposite of a statement proven to be true, what is the validity of that argument?

Logic 101: the ‘opposite’ of an argument is not the ‘converse’, ‘inverse’, or ‘contrapositive’ of an argument. In this case, I’m asserting that you’re arguing something that the argument from contingency doesn’t argue; and therefore, you can’t prove that the argument from contingency doesn’t hold by showing that your argument doesn’t hold. But, if you want to claim that you’ve disproven the contrapositive… then let me know where I can mail that Logic 101 textbook to you.

Can you show that God necessarily exists? If so, why bother with the ‘argument from contingency’ if you already have proof that God exists?

Non sequitur. If you don’t want to answer my question – or are unable to do so – just say so. It’s ok; we all know you don’t have an answer.

I do have empirical proof that the universe exists - look around you and, why, slap me silly and call me Jemima, there it is!

The question isn’t whether the universe exists… it’s whether the universe exists necessarily. If you’re having problems with that distinction… then I’m not the one who needs to re-examine his understanding of what this thread is asking…

In other words, you refuse to acknowledge the validity of any other definition of ‘contingent’ than yours, and mock me for doing so.

No, and no.

You ask for a definition, and I provided one. Did I mock you for asking the question? No… just pointed out that you seem to want to conflate two ways of using the word ‘contingent’, and then use that conflation to attempt to discredit arguments which use that term.

OK, fine. I have your intellectual position placed.

You’ve got me pegged, alright: I don’t mind teasing those who berate others and argue illogically.

Nope. They address the topic of the thread. Need a “Set of Contingent Beings” Itself be ‘Contingent’?

And I’ve addressed that question: it’s not the question that the argument from contingency addresses, and any attempt to frame up the argument as if that’s what it’s saying… is mistaken.

 

[JuanFlorencio]

Assertion 2: an infinite set of ‘contingent’ entities need not itself be contingent
Proof: consider an infinite set of nodes, each labelled with an integer (positive or negative) where node N is ‘contingent’ on (N-1)
So …-3]->-2]->-1]->[0]->[1]->[2]->[3]…
Again, each element is contingent, but the set is not. QED

I can conceive “many” nodes, but not an infinite. On the other hand, every time I conceive one of them, besides been contingent on the (N-1) node, it is contingent on me. I am its creator. And the always growing set is contingent on me too, no less than each one of its elements. And I am not part of the set.

 

[ethereality]

The universe is the set of all contingent things. …]

What makes having every item together no longer contingent?

You short-circuited the entire argument of this thread with your first statement here. The universe, by definition, is not “the set of all contingent things”. It is the set of all physical things. The argument in this thread is that there may exist a collection of physical things whose collection together necessarily exists. Again, if you have A and B and one of them will always exist when the other is absent, such as matter turning into energy which turns into matter, such that matter or energy will always exist, then the universe necessarily exists unless something else renders it finite.

I am growing tired of this thread, because there’s been a lot written but basically no progress (no refutation of what I wrote), and much misunderstanding.

 

[DrTaffy]

I do. There are true premises and false premises. Yours is a false premise.

No. Really really no.:banghead:

We have not defined A or B or even what is meant by B being ‘contingent’ on A beyond the implicit assertion that this relationship can be represented by A->B.

So unless you assert that it is impossible for anything labelled ‘B’ to be ‘contingent’ (whatever that may mean) on a thing labelled ‘A’ then it is meaningless to call the premise “let us assume that A->B” ‘false’!

That is just trying to obstruct rational debate.

You just have to write it down here. Or say where you saw it. That is all you have to do. Not much.

I have done so.

In your first proposal you are asking me to consider the set {A, B, C}, and you conceive your defined contingency relation between its elements represented by [A->B->C->A]. This is a set of relations that we can express this way: {A->B, B->C, C->A}. Of course we can write the same thing using propositions:

…and yadda yadda yadda.

Nope. The proposition is that it is possible to form a graph with given characteristics.

The proof is a concrete example of such a graph.

QED. End of story. You lose. What is slippery about this concept??:ehh:

This is clear for someone who knows the basics of logic.

A set that apparently does not include you…

 

[DrTaffy]

I can conceive “many” nodes, but not an infinite.

:banghead:

A) Your inability to conceive of something is not a proof. I personally have no problem with conceiving of an infinite series, but do instinctively (but not rationally) reject a causal loop. This, again, is not a proof
B) All you are doing is rejecting (irrationally, as it happens, but that does not matter for this point) one of the conditions of an infinite and/or a cyclic graph. If it is neither, or if you reject the proposition that ‘contingency’ can be represented by a directed graph at all, then the argument does not hold.
But if that were the case, why are you trying to derail the conversation rather than simply saying so?:ehh:

 

[inocente]

You short-circuited the entire argument of this thread with your first statement here. The universe, by definition, is not “the set of all contingent things”. It is the set of all physical things. The argument in this thread is that there may exist a collection of physical things whose collection together necessarily exists. Again, if you have A and B and one of them will always exist when the other is absent, such as matter turning into energy which turns into matter, such that matter or energy will always exist, then the universe necessarily exists unless something else renders it finite.

I am growing tired of this thread, because there’s been a lot written but basically no progress (no refutation of what I wrote), and much misunderstanding.

Then I’ll refute it . You don’t have matter or energy, since energy can neither be created nor destroyed. The sum total energy since the universe began has always been constant, it’s only the amount bound up in matter which can vary.

There are good logical reasons for thinking that the sum total energy is and always has been exactly zero (see post #23). This is what cosmologists mean by a universe from nothing (not quite what philosophers or theologians mean).

 

[DrTaffy]

Fine. Then demonstrate it, not just claim it without proof.

I have done so. The topic of the thread is whether or not a “Set of Contingent Beings” need be ‘Contingent’

I have shown that it can, as long as:

• ‘contingency’ can be represented by a directed graph
• that graph is either cyclic or infinite

Obviously you could deny either condition, or address the argument itself, but you have not done so - instead you have attempted only to derail the thread.

Logic 101: the ‘opposite’ of an argument is not the ‘converse’, ‘inverse’, or ‘contrapositive’ of an argument.

It is not my fault if you use imprecise language. My point stands.

In this case, I’m asserting that you’re arguing something that the argument from contingency doesn’t argue;

The argument from contingency is not the topic of the thread. What I have proven is.

But, if you want to claim that you’ve disproven the contrapositive… then let me know where I can mail that Logic 101 textbook to you.

Keep it. You seem to need it more than I.

DrTaffy;13815639:

Can you show that God necessarily

exists? If so, why bother with the ‘argument from contingency’ if you already have proof that God exists?

Non sequitur.

Soo the answer is ‘no’. And you apparently do not know what non sequitur means. Peachy.

Lacking proof that ‘God’ is ‘necessary’ then asserting that any necessary thing implied by the argument from contingency must be ‘God’ remains an unsupported assertion. And as pointed out, if you could prove that ‘God’ were necessary, then there would be no need to appeal to the argument from contingency to prove his existence…

The question isn’t whether the universe exists… it’s whether the universe exists necessarily.

Natch - the question is in the title of the thread, and that is not it. If you are free to insert other questions, then so am I.

I can at least show that the universe exists. You apparently cannot show that God exists at all, let alone that he does so ‘necessarily’.

Did I mock you for asking the question?

Yes:

… then let me know where I can mail that Logic 101 textbook to you.

Once we’re done helping you understand what ‘contingent’ means, perhaps we can take up that argument…

You’ve got me pegged, alright: I don’t mind teasing those who berate others and argue illogically.

What is illogical about showing that it is possible to form a graph with given properties by giving a concrete example of such a graph?

But yes, you are ‘teasing’ as you would put it, not engaging in adult debate.

 

[o_mlly]

Propositional logic: Set of Contingent Beings Need Not Be Contingent.
Definitions:
Contingent – a thing whose existence is not explained within itself
Necessary – a thing whose existence is explained within itself
Contingent /Necessary – a thing whose existence is not explained within itself but can be Necessary to explain the existence of another contingent thing.
Argument:
Premise: Energy requires matter
Therefore, Energy is Contingent
The premise implies Matter is necessary
But Matter cannot explain its own existence
Therefore, Matter is Contingent/Necessary
Therefore, Matter and Energy are not Necessary things either independently or in union.

 

[JuanFlorencio]

:banghead:

A) Your inability to conceive of something is not a proof. I personally have no problem with conceiving of an infinite series, but do instinctively (but not rationally) reject a causal loop. This, again, is not a proof
B) All you are doing is rejecting (irrationally, as it happens, but that does not matter for this point) one of the conditions of an infinite and/or a cyclic graph. If it is neither, or if you reject the proposition that ‘contingency’ can be represented by a directed graph at all, then the argument does not hold.
But if that were the case, why are you trying to derail the conversation rather than simply saying so?:ehh:

I think this conversation is well within the scope of the original thread.

In general, I don’t see any problem with the graph representation of a contingency relation between two entities. The problem I see is that based on the fact that you can represent a cyclic graph you think you can interpret its relations as contingency relations without any problem. But there is a problem: you need to put at least one of the entities (either A or B or C) in order to have the others and, therefore, the full set; but the moment you do it, it is clear that such entity is contingent on you; and so, the full set is contingent on you. This can be seen if you evaluate the argument form:

• A
• If A then B
• If B then C
• If C then A

Therefore,

• A and B and C

(you could also state “B” or “C” instead of “A” as the first premise. The result will be a valid form)

I tend to instinctively reject the causal loop too, but this rejection has the above rational foundation as well.

A similar thing happens with the infinite sequence: you need to put at least one of its elements, and then you could generate the successors and the predecessors without ending. Therefore, the infinite set would be contingent on you.

 

[Gorgias]

I have done so. The topic of the thread is whether or not a “Set of Contingent Beings” need be ‘Contingent’

Re-read the OP then, Taffy:

I would like to see a refutation of this rebuttal to Copleston: A set of contingent beings is not necessarily contingent, and God’s existence is not required to explain such a set.

Nonetheless, it is a good opportunity to discuss the argument from contingency, because this is perhaps my central problem with it: It assumes that everything in the universe is contingent in a non-cyclical way.

The OP asks about a set of contingent beings only in the context of talking about the argument from contingency. In fact, he presumes that the argument from contingency deals with the things in creation, rather than the universe as a whole. That’s inaccurate. That’s why my comments are relevant and your responses kinda miss the boat.

Obviously you could deny either condition, or address the argument itself, but you have not done so - instead you have attempted only to derail the thread.

Nope; if I talked about the weather in Havana, I’d be derailing the thread. Rather, I’m pointing out that the OP’s assumptions don’t hold… and therefore, the thread’s premise is flawed.

The argument from contingency is not the topic of the thread.

It really is. It’s sad that you can’t see that.

What is illogical about showing that it is possible to form a graph with given properties by giving a concrete example of such a graph?

What’s illogical is that it doesn’t apply to the argument from contingency. You seem to have missed that.

 

[catholic1seeks]

You short-circuited the entire argument of this thread with your first statement here. The universe, by definition, is not “the set of all contingent things”. It is the set of all physical things. The argument in this thread is that there may exist a collection of physical things whose collection together necessarily exists. Again, if you have A and B and one of them will always exist when the other is absent, such as matter turning into energy which turns into matter, such that matter or energy will always exist, then the universe necessarily exists unless something else renders it finite.

I am growing tired of this thread, because there’s been a lot written but basically no progress (no refutation of what I wrote), and much misunderstanding.

I am sorry you have gotten tired of this thread, but this objection is not new. I am just now getting more familiar with contingency, cosmological arguments, etc., so anything I say you have probably come across.

A set of things whose collection together may entail the existence of said things; that is the collection may necessarily exist insofar as every item in the collection is explained. But that does nothing to explain why the collection exists, in the first place.