There probably exists a necessary, external cause to the universe
Debate Rounds (3)
Universe - Everything which is, or ever has been, actual
Cause - Something which brings about some other state of affairs and is transitive such that if A causes B, and B causes C, then A causes C.
Existence - The state of being.
Necessary: Cannot not be.
Thank you to Pro for this debate.
Pro defines the Universe-everything which is, or ever has been, actual
If the universe is everything that is, or has ever been, then there can be nothing external to the universe. Therefore there can be no external cause.
Back to you Pro
Thanks Pro! I hope you enjoy this debate!
First for the introductory definitions.
i) S = everything that exists or has existed.
ii) --> on S = if some y-->x then y is a cause of x.
iii) x is at least one of the causes of x for all x in S
iv) :. --> is transitive.
v) If x-->y and y-->x then x=y.
vi) :. --> is a partial ordering of S.
vii) An External, Necessary cause is defined as an element G of S with the property that if X is another element of S such that X-->G, it must be the case that X=G. (G has no cause and cannot not be)
viii) Creation occurs when G-->X.
Now, onto the argument.
Premiss 1: The set S is a set in a universe of sets that satisfies the axiom of choice
Premiss 2: The set S is inductively ordered.
Theorem: If Premisses 1 and 2 hold, then an external, necessary cause of S exists.
Defence of Premise 1
This premise is uncontroversial, as it would be hard to deny that S exists, and it would be equally as hard to deny that the axiom of choice to hold, which states that the cartesian product of a collection of non-empty sets is non-empty - i.e., for every set whose elements are a disjoint (have no element in common) collection of non-empty sets, it is possible to choose another set which contains precisely one element from each of the sets in the original set.
Why should we believe this? Well, it seems self-evident. Imagine there is a set of boxes, each with 100 items in them, and there is a non-empty subset in each box (each box has more than one item). The axiom of choice will say that it is metaphysically possible to pick exactly one item out of each box. Simple, right? Now, simply apply this principle to S, and premise 1 is established.
Defence of premise 2
This states that in some chain C in S, there exists some X in S such that X is the cause of everything in C. Some chain C in S means that there is a set in S such that if x and y are distinct elements of C, then either x-->y or y-->x. Thus, C is totally ordered by causation.
In other words, imagine that a causes b, b cases c, c causes d and so on in an ordered chain. If this chain is inductively ordered, then a will be the cause of everything else in the chain in a causal sequence. 
The most basic view of dependence states that a is the cause of b iff if a were not to exist, then neither would b. 
If so, then in any ordered chain (i.e., the universe), if a were not to exist, then neither would b,c,d...., quod erat demonstrandum.
But even if we reject this view of dependency (but I see no reason to), I fail to see any other view of dependence which does not imply the same principle. So, this premise must be accepted.
Proof of Theorem
Lemma 1 (Zorn's Lemma)
Every partially ordered set P has the property that every chain (i.e. totally ordered subset) has an upper bound. Then the set P contains at least one maximal element. Now, replace P with the inductively ordered (partially ordered) set S in premise 1. Then, S contains at least one maximal element. In this case, the maximal element must cause every other member of S. Moreover, to avoid a vicious causal regress, this must result in G-->G and thus G is necessary. So we have a necessary being who is the cause of all members of S.
Proof of Lemma 1:
For a reductio, assume Zorn's Lemma is false. Then, there exists a partially ordered set or poset such that for every totally ordered subset, every element has an upper bound ad infinitum. Therefore, we need to define each element a1<a2<a3<a4..... In the set. But this will include not only all natural numbers but also all ordinals (a proper class) in the set, and consequently, there will be more ordinals than elements in the set and thus a contradiction arises. 
I have shown that, via certain axioms of maths, that the existence of a necessary first cause must be admitted. For if there exists an inductively ordered set where the axiom of choice applies, then via Zorn's Lemma, there must exist a maximal element of that set. This is equivalent to an external, necessary cause of S, which is equivalent to the universe.
Thank you Pro for that creative argument.
I find it interesting when one claims to prove things through analogy. Seems to me, if you can prove the thing you wish to prove, then an analogy is unnecessary. Pro wish to prove that there is a most likely an external cause to the universe through a math analogy.
Has Pro proved his case? No. Why? 3 reasons.
Analogy Fallacy. (1) Pro's conclusion to his opening argument, "I have shown that, via certain axioms of math, that the existence of a necessary first cause must be admitted." Pro wishes to equate, that "certain axioms of math" translate to the universe. Pro's assertion, certain (C1) axioms of math require a necessary first cause, (C2) therefore the universe requires a necessary first cause. C2 does not follow from C1, therefore Pro hasn't proved that the universe requires a necessary first cause.
"No analogy is perfect, there is always some difference between analogies." (1) I can create an analogy that proves cats exist. However, the cat analogy doesn't prove dogs exist. Why? Cats aren't dogs. Pro's analogy may prove that "certain axioms of math" imply first cause. The universe is very different from math, therefore the math analogy doesn't support the universe conclusion.
Knowledge Fallacy. A knowledge fallacy is when a person claims to know something that cannot be known by human beings. Whether or not there is an external to the universe is beyond the ability of human knowledge. There isn't a person who has ever existed, who now exists, or (most likely) who will exist in the future that could know if there is an external to the universe. There very well may be no outside to the universe, no external. Pro's premise contains this assumption. Pro cannot demonstrate that an external exist to the universe. If Pro cannot demonstrate an external to the universe exists, Pro cannot claim there is likely an external cause. This is the Knowledge Fallacy, Pro claims to know an external to the universe exist, despite Pro being unable to know that there is an external to the universe. Pro cannot claim a "probably" off of an unknowable.
Logical Problem with proposition and definition. Pro's proposition demands an external state to the universe. Pro then defines the universe to include all things that do exist, or have ever existed. Pro's definition defines away an external state to the universe. "Universe-everything which is, or has ever been." An external that exists now, or has ever been, is in violation of Pro's universe definition,"everything which is, or has ever been." Pro's proposition and Pro's definition have a logical contradiction between the two.
Pro accepts and takes the burden of proof.
Pro hasn't proved his case for 3 reasons.
1. Analogy Fallacy. Number sets don't equal universes
2. Knowledge Fallacy. Pro cannot claim probability off an unknowable.
3. Logical Contradiction in Pro's proposition and Definition
Back to you Pro.
Thanks Con! Onto the final round.
Con gives 3 objections; let's go through each of them.
Con argues that maths cannot be used to prove anything in the universe because it is an unsound analogy. However, it seems that the axioms of maths are universal, necessary and infallible. Even if I were creating an analogy, the very fact that we are dealing with logical truths makes it possible to create such an analogy. If I were to make an analogy which stated that in the universe there are no married bachelors, I say that because it is a logical truth. The same would be truth with maths, because mathematics is a necessary truth.
Indeed, this is how physicists create their calculations all the time! If it weren't for maths equations, we would know very little about numerous aspects of the universe. The reality is, however, that this exact analogy is used by scholars habitually.
In terms of knowledge, it seems that well that may be so. Especially considering that the argument just is an argument for a reality external to the universe, it hardly makes sense to dismiss it by claiming, without interacting with the premisses of the argument, through denying the epistemology involved, as the argument itself is an argument contra that form of epistemology - the objection, therefore, is very much an ipse dixit
And I would dispute Con's epistemology anyway. Why, exactly, can't we make such claims? No argument has been given, and I think certain models of epistemology, viz. properly basic foundationalism, and the Knowability Thesis, both provide answers constituting a de jure case against Con's premise . Indeed, if physicists can make predictions about multiverses, why can't we make similar claims?
I also think that the objection is counter-intuitive, for if Con is to even argue about the topic at hand (i.e. whether there is an external cause) then he himself must claim knowledge about it - i.e that there probably isn't such a thing. What, then, is the difference between claiming that there is such a cause, and that there isn't? It seems that both make some sort of claim to knowledge about the transgressions of the universe.
He states: "Whether or not there is an external to the universe is beyond the ability of human knowledge". It should, of course, be noted that Con is not taking an agnostic position on the matter, for he is Contra the motion that there probably exists an external necessary cause of the universe - i.e. a knowledge claim. His own premise goes against his position.
Con argues that because whatever caused the universe must be actual, it cannot be external per se. What might follow from this objection though? Well, not much. The nature of Kuratowski-Zorn's Lemma means that of any given set (i.e. the universe), there is a maximal element of that set . This necessitates its separation from the rest of the set and thus, at least titularly, is external.
Moreover, though I admit that the definition I gave was confusing, it doesn't cause any intrinsic problems, for I didn't specify what the cause was external to - the fact is that it only needs to be external to everything other than itself, of which, Zorn's Lemma proves, in order my onus to be fulfiled.
In any case, this objection is just semantics, which is hardly a cogent objection to the content of the argument.
First, thanks Con for a short but entertaining debate. Hopefully it was enjoyable for you too. In this debate, I have given an argument from maths for a necessary, external cause. Con objected by arguing from three fallacies; but I have shown how they fail in basic ways. It turns out that I can indeed use such an analogy, as mathematics is a tautology and is true in whatever it is applied to. I can also make such an epistemological claim concerning the external universe, for provided it is a truth, the knoowability thesis shows that it is knowable; the same premiss can moreover be applied to Con's stance. Finally, there are indeed no logical problems wit the argument, as it is only semantics which Con objects to; nonetheless, the nature of Kuratowski-Zorn's Lemma means that there is no issue anyway.
"We brought nothing into this world, and we take nothing out. The Lord gave, and the Lord has taken away; blessed be the name of the Lord" - Job 1:21
Thank you Pro for that response.
Before I begin this final round I would like to return to Pro's round 1 ground rules/definitions. Pro "BOP will be on me." Pro is the instigator and has accepted the burden of proving his proposition. I commend Pro for setting a high bar and taking such a strong position. Proof is a tough thing to meet, and I don't feel as though Pro has meet this bar, for the previous reasons and the following reasons.
Pro's objections to the Analogy Fallacy. The argument I made was that analogies are different than the thing they are being compared to. It is this difference that prevents things being proved off of an analogy. In Pro's rebuttal to this objection I've raised Pro doesn't refute this point. He goes back to discussing axioms of math, logical truths and a few other small points. He never makes a case as to why the math analogy is so similar to the universe that the conclusion he draws from the analogy applies to the universe. Analogies by their very nature are different from the thing they are being compared to, this is why they are analogies. Analogies cannot be used as proofs because they require a difference between the subjects being compared. Pro hasn't proved his case because of this simple fact regarding analogies. Pro hasn't proved his case because he hasn't established a strong (any) link between his math analogy conclusion and the properties of the universe.
Pro's objection to the Knowledge Fallacy. I would like to commend Pro for acknowledging this is a valid point made by Con. Pro speaking, "In terms of knowledge, it seems that well that may be so. Especially considering that the argument just is an argument...." The thing about this debate is that Pro stated "BOP is on me." I claimed that Pro cannot establish a probability (meaning more likely than not) off of an unknowable. Pro never refutes this point. So the objection remains and Pro is in general agreement, effectively acknowledging he hasn't proved his proposition.
Pro raises a few other points in this section, multiverse and a claim on what my position really is. My position is that Pro cannot prove his position. Yes, I'm Con to the proposition. But Pro accepts BOP in round 1, which is before I accept the debate. My position is that Pro cannot prove the proposition, he hasn't.
The multiverse, this isn't even a scientific hypothesis at the moment. There is a significant amount of discussion of whether it even qualifies as science in scientific circles. In the NOVA series, "The Fabric of the Cosmos" several physicists are questioned about their thoughts on the multiverse idea. One's response was, "is it science, philosophy or religion?" Several dismissed the topic because it is beyond our ability to test the idea scientifically. The point is, the multiverse is an idea that hasn't been proved and this minor objection to the multiverse idea doesn't help Pro prove his case.
Pro's objection to Con's logical objection. Pro speaking, "Con argues that because whatever caused the universe (nice assumption) must be actual, it cannot be external." No this isn't what I argued. Back to round 1, Pro defines the universe as everything that is or every was. This is simple logic here. If the universe is everything that is or ever was, then logically there is nothing external to the universe (the universe contains everything). If there is no external (because the universe contains everything) then there can be no external cause. This is simple logic. When Pro defined the universe as everything that is or every was, Pro defined away his external to the universe and his cause to it. In chess we would call this a blunder. A move that has cost you a piece because you simply missed seeing something obvious. If Pro believes the universe is everything, he did define it that way, then there cannot be an external or an external cause. This point remains unrefuted.
Conclusion. Pro is the instigator in this debate. Pro, "BOP is on me." Pro must prove the proposition to be correct. Pro hasn't proved this in the debate for three reasons. Reason 1, the Analogy Fallacy hasn't been refuted by Pro. Reason 2, the Knowledge Fallacy, Pro does concede this point. A probability cannot be proved off a unknowable. And the clear logical problem with defining the universe as everything then claiming something outside of it. Needless to say Pro didn't refute this since it is unrefutable. The BOP hasn't been meet.
Thank you Pro for this debate.
1 votes has been placed for this debate.
Vote Placed by Envisage 2 years ago
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Reasons for voting decision: I buy Toviyah's analysis that truths can be known about the universe via. purely logical deductions (which he attempted to use in this debate). My vote is ourely cast on rhetorical grounds. I am sorry Toviyah, but you may well have proved a groundbreaking truth, but it's horrific rhetoric for people unfamiliar with the mathematical system you are implementing. I don't think Con addressed the argument here directly very well, I personally suspect the assumption that everything within an inductive set has a cause is an unsound one, but Con did not raise this. Thus I would have awarded the win to Pro IF it were not for the rather simplistic argument that Pro has literally ruled out an external to the universe by definition, which seems cogent. Thus I am left with either accepting that the mathematical proof Pro provided is flawed, or that it is correct but it entails a rather trivial deduction such as this is false. I am more convinced by the latter. Sorry Toviyah, feel free to correct me
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