Set of Contingent Beings Need Not Be Contingent: Please Disprove

[ethereality]

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.

 

[Wesrock]

The argument from contingency assumes from the start the possibility of an eternal universe. It does not assume a beginning as a starting assumption. That part of your argument is a strawman.

Contingent just means the answer is Yes to the question of “Is it possible for ____ not to exist?” Are you proposing thay there is any matter or energy to which the answer is no?

 

[tweedlealice]

Salutations
You are in deep scientific debate. I should have marked my Bible where I found 2 interesting verses to secure the belief that God exists and creation occurred.
But, on another thought, The Romans wrote about Jesus, the rebel. Josephus wrote of Jesus. Some of his writings aren’t accurate but his comments on Jesus and description of the city of Jerusalem and temple are considered accurate.
Scientificslly.there is the new theory of Intelligent design. A Big Bang can only bring chaos.In the diagram of the big bang in National Geographic started w a bright light. curious.
The church says THAT GOD WAS CREATED NOT HOW GOD CREATED.
There is a thread that scientifically discusses, that which you are discussing.
It discusses the great singularity in the laws of physics.
I just feel you cannot have order out of a bang. Extraterstial beings and our being a cloned experiment would make more sense.
They have duplicated the God principle. They created a large machine that formulates the atom. It is Sweden, I think. I thought it would be pro God. The fact they found it is anti God!? Perchance they need to create a genome.
One day, God will come back and save his suffering church in Syria. The blood of the martyrs built the first church. This genocide where the blood of the believers
Soaks the sands of the mideast should start a revival.
Come, Lord ,Jesus, Come save your church. Bring our minds to clarity to understand the science behind your creation. We wish, as you do, to have all souls go to heaven.in Christ’s love
Tweedlealice

 

[DrTaffy]

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.

This comes down to graph theory - specifically directed graphs, easily visualised as a series of ‘things’ or nodes connected by arrows implying that one is contingent on the other. So if B is ‘contingent’ on A, we represent that as A->B.

Graph theory shows trivially that it is possible to have such a graph where all the nodes (such as A or B) have arrows leading to them (i.e. are contingent) if the graph either has cycles (A->B->C->A) or is infinite (consider a series of nodes numbered with positive and negative integers, where …-2]->-1]->[0]->+1]->+2]…)

At the same time, the whole set would have no arrows leading to it from ‘outside’, so would not itself be ‘contingent’.

But, IIRC, if you can reject both cycles and infinite sets, so you have a finite directed acyclic graph, then there must be at least one node with no arrows leading to it. So something that is ‘not contingent’.

A trickier issue is nailing down and all agreeing on what we mean by ‘contingent’ and ‘thing’, what is actually represented by the arrows and nodes (A->B).

 

[JuanFlorencio]

This comes down to graph theory - specifically directed graphs, easily visualised as a series of ‘things’ or nodes connected by arrows implying that one is contingent on the other. So if B is ‘contingent’ on A, we represent that as A->B.

Graph theory shows trivially that it is possible to have such a graph where all the nodes (such as A or B) have arrows leading to them (i.e. are contingent) if the graph either has cycles (A->B->C->A) or is infinite (consider a series of nodes numbered with positive and negative integers, where …-2]->-1]->[0]->+1]->+2]…)

At the same time, the whole set would have no arrows leading to it from ‘outside’, so would not itself be ‘contingent’.

But, IIRC, if you can reject both cycles and infinite sets, so you have a finite directed acyclic graph, then there must be at least one node with no arrows leading to it. So something that is ‘not contingent’.

A trickier issue is nailing down and all agreeing on what we mean by ‘contingent’ and ‘thing’, what is actually represented by the arrows and nodes (A->B).

The same Graph theory would show trivially that a system of “n” bodies in a gravitational field, each one of them independently attracted by a big massive body, can be kept immobilized in the field provided we attach them to each other in the following way: A->B->C->…->n->A, where A->B indicates that B is attached to A, which prevents it from “falling” onto the massive body.

The whole set would have no arrows leading to it from ‘outside’, so would not itself be attached to anything else. Still, it would not be moved by the massive body, and it would not matter how massive it could be.

 

[DrTaffy]

The same Graph theory would show trivially that a system of “n” bodies in a gravitational field, each one of them independently attracted by a big massive body, can be kept immobilized in the field provided we attach them to each other in the following way: A->B->C->…->n->A, where A->B indicates that B is attached to A, which prevents it from “falling” onto the massive body.

The whole set would have no arrows leading to it from ‘outside’, so would not itself be attached to anything else. Still, it would not be moved by the massive body, and it would not matter how massive it could be.

:ehh:
You presuppose that attaching B to A prevents B from moving, as opposed to, for example, restricting them to moving together. So yes, ridiculous mechanism leads to ridiculous result.

I did say quite explicitly that:

A trickier issue is nailing down and all agreeing on what we mean by ‘contingent’ and ‘thing’, what is actually represented by the arrows and nodes (A->B).

That is what you apparently do here. Define the relationship in a ridiculous way to make the conclusion look ridiculous.

Do you deny that if A is contingent on B which is contingent on C which is contingent on A, and none of them are contingent on anything else, that you then have a set [A,B,C] of contingent things, but the set itself is not contingent on anything else?

 

[JuanFlorencio]

:ehh:
You presuppose that attaching B to A prevents B from moving, as opposed to, for example, restricting them to moving together. So yes, ridiculous mechanism leads to ridiculous result.

I did say quite explicitly that:

That is what you apparently do here. Define the relationship in a ridiculous way to make the conclusion look ridiculous.

Do you deny that if A is contingent on B which is contingent on C which is contingent on A, and none of them are contingent on anything else, that you then have a set [A,B,C] of contingent things, but the set itself is not contingent on anything else?

I deny that such set exists.

Every day I hang my back pack on a nail on the wall, which prevents it from falling down. Do you deny that if B prevents A from falling, and C prevents B from falling , and A prevents C from falling, and if nothing else is needed to prevent the whole set from falling, then the whole set will not fall down?

 

[DrTaffy]

:ehh: Do you deny

that if A is contingent on B which is contingent on C which is contingent on A, and none of them are contingent on anything else, that you then have a set [A,B,C] of contingent things, but the set itself is not contingent on anything else?
I deny that such set exists.

Then you are demonstrably, objectively wrong. It exists, is well defined, and proves what it claims to prove.

Every day I hang my back pack on a nail on the wall, which prevents it from falling down. Do you deny that if B prevents A from falling, and C prevents B from falling , and A prevents C from falling, and if nothing else is needed to prevent the whole set from falling, then the whole set will not fall down?

Nope. I say that A preventing B from falling and B preventing A from falling is a silly mechanism with no realistic parallel. Exactly like pulling yourself up by your own bootstraps. Which has no bearing on the logically demonstrable graph theory proposition which I referred to.

Although what you say is technically true: if B prevents A from falling, and C prevents B from falling , and A prevents C from falling, and if nothing else is needed to prevent the whole set from falling, then the whole set will not fall down.

Techically true, but a silly mechanism.

What I said to start with. Go back and read it carefully.

 

[fisherman_carl]

You should check out William Lane Craig’s arguments for the universe having a beginning and for God’s existence.

Let’s assume for a moment that energy always existed. What causes energy to convert into matter? What causes matter to convert to energy? Is it not some outside force or event? For instance a change in temperature causes ice to turn into water. But ice does not change on its own volition into water. It has no will to decide or ability to change from one property to another. Instead, it simply has the potential to change into ice. And that potential can only be realized in actuality if the outside temperature changes.

Similarly energy or matter can not be converted from one form or another without something outside acting on it. Thus, you have to have an existing universe acting in order for energy to be able to change. With nothing except say ‘energy’ in existence what could cause a change in this energy? If energy was sitting there for infinity what would cause a change to occur which resulted in our universe?

If the conditions that created the universe were simply unconscious forces at work like say energy then why is the universe not infinite? For example, if you had ice for an infinite amount of time would you all of sudden some finite time ago get water? You would not get water unless something changed like the temperature rose above freezing. However, if the conditions were always present to make water , then you would not have water forming a finite time ago, but it would have always been water and not ice. Similarly if the natural conditions for the beginning of the universe were always present then you would not have the universe begin some finite time ago, but the universe would have always existed. But, if it always existed then why haven’t the stars burned out by now? Since it has had infinite amount of time to exhaust their fuel.

However, if the agent that caused the universe was not unconscious but a mind that can choose to create a universe then that would explain the universe coming into existence a finite time ago.

It seems to me there is no way around needing the existence of an immaterial divine mind to explain the creation of the universe.

 

[Gorgias]

Then you are demonstrably, objectively wrong. It exists, is well defined, and proves what it claims to prove.

Yet, this doesn’t prove what (I think) you think it proves.

The fact that such a system is able to be modeled, and therefore exists in theory, does not demonstrate that the universe is such a set.

The argument from contingency only presumes that the universe itself (as an entity) is contingent.

One of the strengths of the argument from contingency is that it doesn’t require the universe to have a beginning; in other words, whether the universe had a beginning or not, the argument from contingency still works.

ethereality asks whether, since matter and energy are mutually convertible, a universe of infinite chronological existence refutes the argument from contingency. It does not. The question still holds: even though the universe (may be) infinite in time, does that imply that it necessarily exists? The answer is still ‘no’ – the fact of the existence of matter and energy does not imply necessity. One still can assert that it’s not necessary that matter and/or energy exist.

 

[fisherman_carl]

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, …

Actually, it is a claim of science not theism that the expansion of the universe means a beginning.

"The universe began from a state of infinite density. . . . Space and time were created in that event and so was all the matter in the universe. It is not meaningful to ask what happened before the Big Bang; it is like asking what is north of the North Pole. Similarly, it is not sensible to ask where the Big Bang took place. The point-universe was not an object isolated in space; it was the entire universe, and so the answer can only be that the Big Bang happened everywhere. "

Richard J. Gott, et.al., “Will the Universe Expand Forever?” Scientific American (March 1976), p. 65.

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

Actually, this assumption is what science builds on. If this assumption were not true then we could not do science. What could cause the second law of Thermodynamics to change? This seems like special pleading for your cyclical theory. Why would it be more of an assumption to assume that the law of Thermodynamics does not change, for which we have plenty of examples, then to assume that it does in order to make cyclical theory a possibility, and for which we have no examples?

It is also an assumption that you are not a brain in a vat and all your experiences are generated by a mad scientist. Science assumes this not the case either.

I suggest you read reasonablefaith.org/the-existence-of-god-and-the-beginning-of-the-universe

We have never seen both matter and energy cease to exist.

Who is talking about ceasing to exist? A begging is where something comes into existence.

 

[fisherman_carl]

Yet, this doesn’t prove what (I think) you think it proves.

The fact that such a system is able to be modeled, and therefore exists in theory, does not demonstrate that the universe is such a set.

The argument from contingency only presumes that the universe itself (as an entity) is contingent.

One of the strengths of the argument from contingency is that it doesn’t require the universe to have a beginning; in other words, whether the universe had a beginning or not, the argument from contingency still works.

ethereality asks whether, since matter and energy are mutually convertible, a universe of infinite chronological existence refutes the argument from contingency. It does not. The question still holds: even though the universe (may be) infinite in time, does that imply that it necessarily exists? The answer is still ‘no’ – the fact of the existence of matter and energy does not imply necessity. One still can assert that it’s not necessary that matter and/or energy exist.

Yes. When you think about it the universe is composed of parts and systems that require an explanation for how those parts and systems came together. One could easily imagine a different arrangement of those parts and systems such that we would have a different universe. Thus, it’s possible to have a different universe then the one we have, making the universe as it is not metaphysically necessary. Even the underlying physics of the universe are particles and systems which could be different. There could be more or less atoms in the universe making the number of atoms in the universe not metaphysically necessary.

This also, I think, leads us to the divine simplicity of God who is not composed of parts requiring an explanation for how those parts came together.

 

[JuanFlorencio]

Then you are demonstrably, objectively wrong. It exists, is well defined, and proves what it claims to prove.

Nope. I say that A preventing B from falling and B preventing A from falling is a silly mechanism with no realistic parallel. Exactly like pulling yourself up by your own bootstraps. Which has no bearing on the logically demonstrable graph theory proposition which I referred to.

Taffy, if you think you have a demonstration (that I am wrong or that your representation using a graph is a true proposition), the best thing you can do for yourself (and for me too), is to present it. It would strengthen your position. Can you?

Of course the counter example I proposed is a “silly mechanism”, if you want! It is as silly as your own graph representation of the question. I have no doubt, on the other hand, that everybody can realize that the representation by means of a graph does not add any “demonstrative power” to your argumentation.

This is your argument:

1. 
   *]If A then B
   *]If B then C
   *]If C then A
   *]Therefore, A and B and C
   
   Which, as you can verify if you build the associated truth table, is incorrect.
   

   Although what you say is technically true: if B prevents A from falling, and C prevents B from falling , and A prevents C from falling, and if nothing else is needed to prevent the whole set from falling, then the whole set will not fall down.
   
   Techically true, but a silly mechanism.
   
   What I said to start with. Go back and read it carefully.

   I don’t know what you mean with “technically true”. My counter example is silly, as you have said, and it is incorrect: Silly and incorrect as your own “argument”, as you can hopefully see above.

 

[ethereality]

I don’t know how much time is appropriate to spend writing letters online; I am extremely busy … so I will try to be succinct.

The argument from contingency assumes from the start the possibility of an eternal universe. It does not assume a beginning as a starting assumption. That part of your argument is a strawman.

Where did I declare this? I think you have misunderstood what I wrote.

Contingent just means the answer is Yes to the question of “Is it possible for ____ not to exist?” Are you proposing thay there is any matter or energy to which the answer is no?

This is overly simplistic to the point that it overlooks the problem I have identified: The question is whether it is possible for both matter and energy in combination to cease to exist.

Let’s assume for a moment that energy always existed. What causes energy to convert into matter? What causes matter to convert to energy? Is it not some outside force or event?

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.

I don’t necessarily agree with him, because I find it foolish to hold a philosophy I cannot live (like Hume’s denial of free will?). That said, I’m not sure what is necessary for energy-mass conversion: Energy apparently has statistical fluctuations, i.e. we don’t understand everything about energy yet. But sure, I’d grant that other things exist as well to facilitate this mass-energy back-and-forth. Perhaps stars, for example.

If energy was sitting there for infinity what would cause a change to occur which resulted in our universe’s current state]?

You start to make an argument from ignorance here, because the fact is we don’t know the past history of our universe. Might we have always had stars in some configuration prior to the Big Bang?

If the conditions that created the universe were simply unconscious forces at work like say energy then why is the universe not infinite?

How do you know it isn’t?

But, if it always existed then why haven’t the stars burned out by now? Since it has had infinite amount of time to exhaust their fuel.

Again, this is an argument from ignorance. We don’t know everything about the universe yet. There could be some physical mechanism whereby energy is fed into new stars in a cyclical, sustainable process, like how the death of animals yields biomass resulting in new animals. Our Second Law of Thermodynamics does support your argument, but there could be something we haven’t discovered yet causing us to reformulate it, just as Newton’s Theory of Gravity was replaced by Einstein’s. It is just as much a leap of faith to “therefore God” as it is to “therefore future scientific revision”: We simply don’t know.

Gorgias, you seem to have missed the point that if matter and energy are both always present, then the set containing them necessarily exists. Hence the assumption that the set is contingent is unjustified.

Actually, it is a claim of science not theism that the expansion of the universe means a beginning.

"The universe began from a state of infinite density. . . . Space and time were created in that event and so was all the matter in the universe. It is not meaningful to ask what happened before the Big Bang; it is like asking what is north of the North Pole. Similarly, it is not sensible to ask where the Big Bang took place. The point-universe was not an object isolated in space; it was the entire universe, and so the answer can only be that the Big Bang happened everywhere. "

Richard J. Gott, et.al., “Will the Universe Expand Forever?” Scientific American (March 1976), p. 65.

You’ve found a well-published straw man: This is simply a bad explanation to popularize scientific theory, akin to saying the Trinity is like a three-leaf clover to popularize Christian dogma.

Actually, this assumption is what science builds on. If this assumption were not true then we could not do science.

Yes, but we must be clear that it is an assumption (hence uncertain), and that science does not produce truth claims: It produces approximations to observation.

One could easily imagine a different arrangement of those parts and systems such that …] the universe [is] not metaphysically necessary. …] This also, I think, leads us to the divine simplicity of God who is not composed of parts requiring an explanation for how those parts came together.

Actually, you are assuming the existence of God by denying that the universe can contain the explanation for its existence. You’re merely begging the question here. I can imagine a tree floating in midair but that doesn’t negate the necessity of its soil.

Taffy, if you think you have a demonstration (that I am wrong …] present it.

I wish you would stop bickering: You apparently argued that your backpack would support your wall, or that a pebble would stop a planet, which are both ridiculous and regrettably misunderstand the discussion. They merely have semantic similarity.

 

[DrTaffy]

You should check out William Lane Craig’s arguments for the universe having a beginning and for God’s existence.

Have done. Not impressed.

I could say: You should go to university for a decade or two to get a good understanding of both physics and philosophy. Have you done so? Do you think that that is a reasonable response, or should I at least try to present the argument I think should convince you? :ehh:

Let’s assume for a moment that energy always existed. What causes energy to convert into matter?

You tell me. When a vacuum particle pair of particles comes into existence, what ‘causes’ that? Note that the pair does not ‘come from’ the ‘vacuum foam’ as CAF posters like to claim, the vacuum foam is the spontaneous pairs of particles and similair phenomena.

So what is the ‘cause’ in that case? The laws of physics? In that case there is your unmoved mover right there.

Similarly energy or matter can not be converted from one form or another without something outside acting on it.

Unsupported assertion.

For example, if you had ice for an infinite amount of time would you all of sudden some finite time ago get water?

Ice is water. And one instance where we can point to a cause is not proof that every effect has a cause. Which would, in any case, undermine the catholic definition of God. :nope:

However, if the agent that caused the universe was not unconscious but a mind that can choose to create a universe then that would explain the universe coming into existence a finite time ago.

‘Choice’ is a temporal proposition. So a ‘God’ (or anything else) outside of time (and therefore changeless) cannot ‘choose’ anything.

And I draw your attention to the title and explicit topic of this thread. Do you have anything relevant to that to add?

 

[DrTaffy]

Yet, this doesn’t prove what (I think) you think it proves.

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”

The fact that such a system is able to be modeled, and therefore exists in theory, does not demonstrate that the universe is such a set.

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.

The argument from contingency only presumes that the universe itself (as an entity) is contingent.

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?

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

 

[DrTaffy]

One could easily imagine a different arrangement of those parts and systems such that we would have a different universe. Thus, it’s possible to have a different universe then the one we have, making the universe as it is not metaphysically necessary. Even the underlying physics of the universe are particles and systems which could be different. There could be more or less atoms in the universe making the number of atoms in the universe not metaphysically necessary.

Thank you - an excellent illustration of my point about the ambiguity of ‘contingent’.

Can we agree, for at least this thread, what we mean by it? Suggestions:
A ‘contingent’ thing can exist without relying on anything outside of itself
A ‘contingent’ thing must exist - there is a logical contradiction in it not existing
A ‘contingent’ thing must exist in its current form - there is a logical contradiction in it not existing other than in its current form

 

[ethereality]

‘Choice’ is a temporal proposition. So a ‘God’ (or anything else) outside of time (and therefore changeless) cannot ‘choose’ anything.

There have been many issues raised, and I encourage you to spend more time with some of them (hopefully in a separate thread per topic). Perhaps you have not spent enough time on this one: Christian theologians say that God does everything in a single perfect act from the first moment of time. This side-steps the issue you’ve raised: God doesn’t choose things one at a time like we do. (Though I must admit I get lost rather quickly, because they also God is pure act, and many other things besides…) Choice is temporal for us because our brains operate in spacetime; I see no reason to suppose that choice is inherently temporal: All that is required is for a mind to hold two propositions and make a conclusion. The time it takes to do such appears to be a function of the mind, and while the choices of our minds are (apparently) linked to brains, God is not like us, as the Bible reminds us repeatedly.

the term ‘contingent’ is ambiguous. Does it [mean] 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?

I don’t think it’s ambiguous: It means merely that, as Copleston said (did you listen to that clip?) that an explanation for a thing’s existence does not reside in that thing, just as we are explained by our parents, or the elements in the earth explained by a supernova, etc. (It is unfortunate that an earlier poster introduced confusion by asserting that it meant something that had to exist. The matter can be reformulated in those terms, but those are indeed different terms.)

 

[JuanFlorencio]

I wish you would stop bickering: You apparently argued that your backpack would support your wall, or that a pebble would stop a planet, which are both ridiculous and regrettably misunderstand the discussion. They merely have semantic similarity.

Not semantic similarity, Ethereality (that would have no impact at all); it is logical similarity what is important. When we design a proof it needs to be formally correct. If it does, then you can use the same form with any interpretation you wish. Any interpretation of a correct formal argument would make a good argument.

My counter example of the backpack was just a fast way to show that Taffy’s argumental form was incorrect. Taffy and you have easily noticed that there is something wrong in the counter example. It is the form.

I have shown the form of the argument in my previous post and, as I said, it’s incorrectness can be seen by building its truth table. If the argument is correct, then the conjunction of the premises plus the conclusion should be a tautology; but it is not.

 

[DrTaffy]

My counter example of the backpack was just a fast way to show that Taffy’s argumental form was incorrect. Taffy and you have easily noticed that there is something wrong in the counter example. It is the form.

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

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

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.