For anything that is contingently true, it is necessarily the case that its negation is logically possible. That is literally the definition of “contingent.”

If something is not contingent, then it is logically necessary (or logically impossible, and thus its negation is logically necessary; but that’s just the same thing the other way around).

In other words, something can only be either contingent or necessary—not both, and not neither. It’s one of the other. That is a logically necessary fact (it’s a proper dichotomy, exhausting all possibilities).

This means that if P1 is contingent, then its negation is logically possible, which entails there are some logically possible things that will not obey P1 (it will not describe them or be a property of them).

If there are some logically possible things that will not obey P1, then it is logically impossible that “all” things obey P1.

This is true even if we do not know what those logically possible things are. Because by definition, they must exist, or else P1 is not contingent but logically necessary. But that requires a formal proof, and there is none. So no one can assert P1 is logically necessary. That leaves it contingent.

It is possible, of course, that, unknown to us, it is logically necessary. But until we prove that, it must be contingent, so far as we know.

One might try to present an inductive argument for a probability of P1 being logically necessary (creating a fuzzy logic condition); but Alvaro never presented one. That would be how, in a well-argued debate, someone would respond to my argument here (assuming any such argument is to be had; I have yet to see one).

Science has also not established Premise 1. That is a claim to a physical law. Yet it is not logically necessarily true, and therefore must necessarily be only contingently true. But if it is only contingently true, it is logically possible for there to be states of affairs not subject to it. It is therefore logically impossible that ‘all’ things that begin to exist must come into existence by something else. Premise 1 is therefore logically impossible and therefore false.

Could you please explain more why the premise is logically impossible?
I understand the contingency objection but not how it leads to the logical impossibility of the premise.

And still no syllogism. So you have doubly confirmed you do not know what logical validity is and are incapable of even producing a formally valid syllogism.

So from now on I am ignoring you. Until you do what I ask and actually produce an actual syllogism that is actually formally valid and sound.

Until that happens, you do not know what you are talking about and you are not saying anything worth the bother of reading at this point.

If the universe began at a point in time, its past is finite.

That is not necessarily true. See other comment.

Conversely, if it has no endpoint, its future is boundless.

Ditto.

Within the block universe theory, which posits that all time exists simultaneously, we face the dilemma of envisioning a reality that is simultaneously finite and infinite, a contradiction.

I do not see how you get “simultaneously finite and infinite” from block theory. An infinite series is simply an infinite series. You can’t wish it away by saying there is only one infinite series and since one is a finite number therefore it is not an infinite series. That is joke logic.

You will necessarily have to proceed in the opposite direction and demonstrate that an infinite past can be conceived without contradiction

It can be. All contemporary mathematicians and scientists agree. There has never been a demonstration of any contradiction. Infinite series are logically possible and therefore physically possible. Just instantiate the logical set’s elements one-to-one with physical objects. Nothing in logic prevents that.

Otherwise, how does your universe differ from the Being of Parmenides?

I don’t think you know what you are talking about here. In modern relativity theory causality is a geometric relation on the asymmetrical axis of time. So causality is unaffected by block theory. That is why block theory is the position now held by all modern physicists: it is logically entailed by the observations of relativity theory (see The Ontology of Time).

If the universe began at a point in time, its past is finite. Conversely, if it has no endpoint, its future is boundless. Within the block universe theory, which posits that all time exists simultaneously, we face the dilemma of envisioning a reality that is simultaneously finite and infinite, a contradiction.

Thus, eternalism is tenable—or perhaps conceivable—solely under the condition of an infinite past. Yet, how can one claim that the concept of an infinite past derives from eternalism, when, indeed, the reasoning unfolds in the opposite manner?

You will necessarily have to proceed in the opposite direction and demonstrate that an infinite past can be conceived without contradiction, despite violating Ockham’s principle (“entities should not be multiplied beyond necessity”) and being foreign to all human experience, which is always finite.

Well, the demonstration you have outlined is astonishingly weak. You say: since we can conceive an infinity of ideas, we can also conceive an infinity of moments; therefore, an infinite past can be upheld, entailing no contradiction whatsoever.

The difference is that ideas exist in an ideal region, without succession, and time is only time if one state of affairs follows another. Otherwise, how does your universe differ from the Being of Parmenides? For what reason should we assert that there is a multiplicity of observable events—a presupposition that underlies all natural science—if, in reality, nothing happens and everything is one?

Now, if states of affairs succeed one another, it is true that “All the past was future,” because a past that has never been future is a past that has never begun to be and will never cease to be, that is, it is an entity to which nothing precedes and nothing follows.

However, if the entire future has already occurred even though we do not perceive it, it will be false that the cause produces the effect, since all parts of the universe will necessarily be connected by metaphysical necessity rather than united by virtue of an intelligible physical law. And with this, all our knowledge of nature is destroyed and reduced to mere fiction.

Therefore, even if the eternity of the world were not logically contradictory (although it can be demonstrated that it is), it would be an absolutely superfluous and mystical hypothesis that we could only assume at the expense of discarding all scientific knowledge.

You still have not presented a formally valid syllogism, nor a sound one. Which confirms my suspicion that you do not even know how to do that.

And the way you rhetorically frame your inability to defend Peckham suggests you are not actually taking any of this seriously. You are simply engaging in apologetics, not a genuine understanding of how logic works.

So I’m calling it.

Produce a formally valid and sound syllogism or GTFO.

I don’t want to be impolite to my host, but not engaging with the substance of the arguments presented and dismissing them with fallacies of authority, ad hominem, and other dialectical trash, while also ignoring the responses to potential objections anticipated in the argument itself, is precisely the modus operandi of a con.

Avicenna’s argument is not “a list of unproven suppositions”. The statement “In the aggregate of an infinite series of causes and effects, either all members of the series will be effects, or some of them will not be effects” is valid by the law of excluded middle. And the subsequent analysis is a logical deduction from these two exclusive possibilities:

If all were effects, they would all have a possible existence, as they depend on a cause and not on themselves, so, since they exist by another, they necessarily presuppose an uncaused cause outside the series.

And if not all were effects, at least one of them would be an uncaused cause, from which it follows that the series would not be infinite, contrary to what has been assumed.

I will not dwell on Peckham’s arguments since you have made no effort to present a valid critique of them. The charge of circular reasoning is laughable, as I have already shown that to invalidate the premise according to which “All the past was future” one would have to assume that the past has always been in act, meaning it has never passed and has always been present, which does not correspond with the nature of time nor with the very notion of “past”.

My argument against an infinite causal succession does not directly invoke the same logical structure as Russell’s paradox. Instead, it explores the implications of universal causality on the existence of a cause for the universe as a whole, leading to a contradiction under the assumption that everything must have a cause. The paradox in the argument is not about self-membership or the formation of sets but about the relationship between parts and wholes in the context of causality. Your response does not directly invalidate the argument, but rather shifts the discussion to a different domain (set theory) where the premises and conclusions of the original argument do not directly apply.

In a word, it seems you are eager to leave the discussion even before it starts. I could present more arguments in the same line, but it holds no interest for me to engage in such superficial dialogue with someone who either fails to grasp them or aims to mislead us with tricks.

I concur with your analysis.

For example:

An infinite amount of physical matter cannot fit in a finite space. That doesn’t prove all infinities are impossible, only that a specific infinity is impossible (putting an infinity of spacetime-dependent matter inside a finite space).

Indeed this all depends on contingencies. For example, the statement that “an infinite amount of physical matter cannot fit in a finite space” is really just a restatement of the Pauli exclusion principle, which entails “matter” (particles or fields with a nonzero rest mass) has a nonzero volume. The geometric limitation then follows. But many particles (photons, for example) are not subject to the Pauli exclusion principle and thus can be stacked infinitely in a finite space. So you can have an infinite amount of energy in a finite space. Thus the limitation only follows from the specific definition of matter.

Likewise, we do not actually know there even is a finite space. The spatial extent of the universe could now be infinite (as some cosmological models entail). And time can be past infinite even for a finite space. And so on.

The problem with the Kalam is that it requires its premises to always be true. But if there are conditions in which they aren’t true, then the argument fails to produce its conclusion. But all arguments for its premises require positing contingent conditions (e.g. infinite stairs with a first and last step, which is not a logically necessary condition, and therefore the example has no pertinence to establishing Premise 2, because it is disanalogous to what Premise 2 needs to be the case).

This is self-contradictory and is thus one of the fundamental incoherences of the argument.

Likewise your point about the contingent possibility of matter that cannot be infinitely divided: what is then meant by divided?

Geometrically, matter can always be infinitely divided. That’s why the irreducible Planck length is nonzero: the smallest possible division of space appears to be around 10^33rd of a meter. But that means there are an infinity of geometric points spanning one Planck length that sum to 10^-35 meters, a nonzero value. That infinite sums can be finite is a basic principle of calculus and has been formally proved so there is no issue with that (this is BTW the solution to Zeno’s paradoxes: infinite spans of space can be crossed in infinite spans of time, so there is no division problem for movement: because time is also being divided along with space, and their ratio always remains finite and the same).

So if all one means is that matter cannot be physically divided further than 10^33rd of a meter, one is positing specific contingent conditions that are not logically necessary; there are therefore conditions in which the limitation doesn’t exist (like dividing matter geometrically rather than physically, or a physical world without a Planck length limitation).

Your point about A and B theory is also sound.

Indeed, because the laws of probability entail that all any continuously repeated nonzero probability approaches 100% as t approaches infinity, there will never be any span of time infinitely long even on past eternalism: a Big Bang like event will always reset and scramble the information, starting a new span of informational time that will in turn end eventually the same way. So all spans of time are finite.

The sequence of those isolated time segments can then be infinite without any concern over why infinite information has not accumulated into ours (e.g. why we have not reached an infinite entropy state etc.). This is true on A and B theory, and is partly even confirmed by physical observations.

So none of the “predictions” claimed for past eternalism that are supposed to refute it are actually predicted by it. And there is no logical barrier to it. So there is no way to exclude it (or even render it improbable), as Premise 2 requires we do.

“Where in the world do we get the idea” is what Dr. Alvaro is providing answers for in his entries. Whether they are good answers is a separate question.

But that the Kalam is either incoherent or vacuously trivial is the point I will be arguing in my entries. Either there is no way to have both premises be true at the same time, or the conclusion simply states the innocuous fact that “if everything began the first state of it will be in some sense different from subsequent states of it,” which no one denies (least of all atheists).

How one gets “intelligence” as a property of the first state is still not addressed by Dr. Alvaro, but he promises to get to it in his third entry (in his second entry, which just went live). But that’s the only thing that would count as a god in any relevant sense. Otherwise it’s just physics.

There are several demonstrations that conclude the logical impossibility of an infinite causal succession in act.

No, there are not.

See my citations and quotations of the literature in my Marshall debate (e.g. here and here).

I have proposed one, formulated by Avicenna, which you have not deemed worthy of consideration.

That is not a formally valid syllogism. Nor is it sound. It’s just a list of unproven suppositions. That’s why modern mathematicians are not impressed with it. It’s in the junkyard of obsolete medieval ideas. Modern mathematics is vastly more advanced, particularly on the question of the coherence of transfinite sets.

John Peckham has two demonstrations in this sense.

Not a scientist or a mathematician.

And the syllogism you attribute to him is again neither formally valid nor sound.

Indeed it is laughably circular. As soon as he says “But when all time was future…” he has presupposed his conclusion in his premises. On past eternalism, the condition “all time was future” never exists in that set.

You really need to be sharper than this. You are being taken in by a con.

One would have to maintain that the first premise, “All past was future”, is false. But it does not seem to be.

Um. That all past was future is false is by definition past eternalism. That is literally what past eternalism is. You cannot presuppose the set to be impossible to argue the set is impossible.

This is like saying I have to prove the set of all mammals lacks a lizard. By definition it lacks a lizard. I do not have to prove that it does. You are the one who would have to prove that the set of all mammals would contain a lizard. And this is precisely the proof no one has ever produced and why all contemporary mathematicians deny this claim that infinite sets are logically impossible.

All the other arguments you list are likewise sham arguments.

You do not appear to understand what logical necessity is or even how to produce a formally valid argument, much less validate its soundness.

For example, that cause-whole argument relies on what is known as Russell’s paradox, arguments from which have long since been refuted (particularly by modern set theory): the premise is void because it posits a logically impossible set, therefore any argument depending on that premise is automatically unsound.

That Peckham doesn’t know this demonstrates he knows nothing at all about the history of transfinite mathematics and thus is wholly unqualified to even have an opinion in the matter. That you were so easily taken in by an amateur making a bad argument is a bad sign. You need to check things more carefully before falling for them. Gullibility is not a virtue. Please learn how to vet the validity and soundness of an argument; and how to research the past history of the matter being argued.