I disagree with your conclusion. That's because a natural OG, which includes the laws of nature in its structure, would exist necessarily. It's logically impossible for an OG to have been designed.

On your other point: If there is a designer with free will, it could design creatures that lack it, so it seems irrelevant whether not the designer has free will.

That's a good example. What is impossible/contradictory is not always obvious. That is one of the risks when talking about potential/possibility in lose terms. We end up affirming the "possibility" of any words we can smash together without obvious contradictions.

This can get sort of out of hand in "bundle" and "pin cushion" theories of predication. E.g. a subject just is a "bundle of predicates," or "predicates attached to some bare haecceity" (the pin cushion that makes things individual). It would seem that anything can become anything else here, because the subject is completely bare.

Anyhow, an interesting thing is that "the first number that violates the Goldbach Conjecture" is a rigid designator. It uniquely specifies a number (if it exists). You could think of such a designator in terms of the shortest program that would retrieve a number too (it is easy to check if a number fits the criteria). But, strangely, this ability to uniquely specify the number fails to reveal its identity. It's a sort of recreation of the Meno Paradox. You don't really know what you're looking for until you've found it.

It appears like you understand this quite well, now try to convince Banno of this. Banno does not admit that incompatibility, and this is what supports fatalism. Yet Banno also denies fatalism, and that is a problem. — Metaphysician Undercover

Alright, I'll set out the basics and tell me where we disagree:

The fatalism issue arises in classic logic and is cured by modal logic. As in:

Classic Logic:

1. If it rains tomorrow, I will get wet
2. It rains tomorrow
I get wet

The fatalistic issue arises from fixing #2 as certain

Modal Logic (assuming both premises apply within the same possible world):

1. It is necessary that if it rains tomorrow, I will get wet
2. It is possible that it will rain tomorrow
It is possible I will get wet.

There is no fatalism because #2 is possible, not necessary.

Modal logic adds in two new qualifiers ((1) it is necessary, and (2) it is possible) that allows for the avoidance of fatalism. This cures the limitation of classic logic.

Are you saying that Banno is denying fatalism within classic or modal logic? I'm just trying to figure this out because you referenced Banno's other comments generally and I have no way of really figuring out what that refences because I've been bouncing in and out of this thread.

Nice.

Well, then, best you stop posting about logic, don't you think? — Banno

No, this is how we move forward by degrees, through an exchange of ideas. And opinions about logic are just as informative as opinions in other subjects, even though my opinion is that no one really understands logic.

Alright, I'll set out the basics and tell me where we disagree:

The fatalism issue arises in classic logic and is cured by modal logic. — Hanover

I don't think we disagree. The fatalism issue may be cured by modal logic. However, if one interprets modal logic as consistent with classical logic (as Banno seems to), then the fatalism issue reappears.

1. It is necessary that if it rains tomorrow, I will get wet
2. It is possible that it will rain tomorrow
It is possible I will get wet.

There is no fatalism because #2 is possible, not necessary. — Hanover

So, depending on how "possible" in #2 is interpreted fatalism may or may not be implied. If fatalism is not implied by one's interpretation, the three classical laws are violated in one way or another.

If we interpret "possible" when referring to the future, in the same way that we do with past possibilities, where we assume that one of the possible worlds is actual, as in the "Caesar crossed the Rubicon" example, then we have fatalism.

If we interpret two possible worlds, one with rain, and one without rain, with "I" as a rigid designator, then the law of noncontradiction is violated, because "I" gets wet and does not get wet, at the same time. The qualification of "different worlds" is just a facade to hide the contradiction. If we look at what Banno called "counterpart theory", then we have no continuity of the object "I", from the present time into the future, only possible similar objects in the future, therefore the law of identity is not applicable.

The conclusion therefore, is that modal logic provides an escape from fatalism, but only if it is applied and interpreted in a way which is conducive to this escape. That way of interpretation is to recognize that the classical laws of logic are not compatible. This is because it is the idea that these classical laws are applicable to the future which produces the fatalist mentality.

This is what Banno said:

The trouble here is that modal logic subsumes propositional logic. They are not inconsistent. — Banno

What I say is that the meaning of "possible" in #2 "It is possible that it will rain tomorrow" indicates that "it will rain tomorrow", cannot have a truth value. It could have a probability, but not truth. This is because the corresponding reality referred to by "possible" in this usage does not admit to truth or falsity. Therefore modal logic and propositional logic are not consistent.

The semantics of possible worlds just says that we understand "it is possible that it will rain tomorrow" as stipulating for our consideration two possible worlds, W₀ in which it is true that it rains tomorrow, and W₁ in which it is true that it doesn't rain tomorrow. There is no contradiction.

Must be the fifth or sixth time this has been pointed out to you. In no possible world does it both rain and not rain. That only happens in impossible worlds.


Added: "It is possible that it will rain tomorrow" just says that there is a possible world in which it rains tomorrow. And this is true, and therefor "It is possible that it will rain tomorrow" has a truth value.

"It is possible that it will rain and not rain tomorrow" is false, since there is no possible world in which it both rains and does not rain.

And this adds to your idea, @Hanover, in that such things only ever happen in impossible worlds, and so "It is possible that it will rain and not rain tomorrow" is false in all the possible worlds, but perhaps true in some impossible world...

That's because a natural OG, which includes the laws of nature in its structure, would exist necessarily. — Relativist

Since the laws of nature are not tautologies, they are contingent facts that need an explanation outside of themselves, i.e., a cause. As such, the OG which has no cause cannot include the laws of nature in its structure.

Additionally, if the OG has necessary existence, it must be the OG in all possible worlds. Thus, if the OG included the laws of nature in its structure, then the same laws of nature would exist in all possible worlds and this would result in a modal collapse.

It's logically impossible for an OG to have been designed. — Relativist

Agreed, but what I meant was that the OG is a designer that designs the laws of nature, not that the OG is designed.

If there is a designer with free will, it could design creatures that lack it, so it seems irrelevant whether not the designer has free will. — Relativist

I agree that a thing with free will can design creatures that have or lack free will. I'm not sure what this is in response to.

People often conflate epistemic uncertainty with ontological possibility. The semantics of modal logic distinguishes between what’s true in at least one possible world (possibility) and what’s necessarily false in all (like contradictions). The “impossible worlds” idea can be fun for thought experiments, but it doesn’t change the logical status of statements like “it rains and doesn’t rain.”

Yep. It's rather a way of setting that logical status out, and in a broader context.

But what it does put the lie to are ideas along the lines that logical impossibilities are unthinkable or even inconceivable. Impossible worlds can be conceived of, thought about and put into formal systems.

Since the laws of nature are not tautologies, they are contingent facts that need an explanation outside of themselves, i.e., a cause. — A Christian Philosophy

Tautologies are statements that are necessarily true. The term doesn't apply to existents, like an OG. The question is whether or not there is an ontological basis for an OG being contingent- meaning that it could have not existed.

If X is caused to exist, then it is contingent on it's cause, if the cause could have failed to produce X. That can't be the case for a first cause, so how else can it be contingent? You can't just assert it, because you are claiming to have a proof.

Additionally, if the OG has necessary existence, it must be the OG in all possible worlds. Thus, if the OG included the laws of nature in its structure, then the same laws of nature would exist in all possible worlds and this would result in a modal collapse. — A Christian Philosophy

Modal collapse pertains to propositions - it means that every true statement is necessarily true. From the perspective of ontology, necessitarianism would entail modal collapse. Necessitarianism means everything that exists, exists necessarily. You seem to think necessitarianism is false. Why? Provide your proof (dismissing it based on the assertion it's "frowned upon" carries no weight).

Regardless, a necessary OG does not entail necessitarianism - other sources of contingency may exist, such as quantum indeterminacy.

what I meant was that the OG is a designer that designs the laws of nature, not that the OG is designed. — A Christian Philosophy

You are claiming to prove there's a designer, so you can't just assume it. A natural OG accounts for laws of nature which exist necessarily. This remains a live possibility (thus defeating your argument) unless you can show this is impossible - or at least, less likely than a being of infinite complexity with magical knowledge (not the product of learning or experience).

The semantics of possible worlds just says that we understand "it is possible that it will rain tomorrow" as stipulating for our consideration two possible worlds, W₀ in which it is true that it rains tomorrow, and W₁ in which it is true that it doesn't rain tomorrow. There is no contradiction. — Banno

If there is a rigid designator, such as "I" who gets wet, and I who does not get wet, then there is contradiction. If, W₀ and W₁ are distinct subjects, one with the property of rain, and one without, then the law of identity no longer applies to "our world", which is the actual world from the past to now. It divides into a multitude of possible worlds at the moment of the present, so there can no longer be identity. Without an object with identity the other two laws do not apply.

It's not the first time I've pointed this out to you.

Added: "It is possible that it will rain tomorrow" just says that there is a possible world in which it rains tomorrow. And this is true, and therefor "It is possible that it will rain tomorrow" has a truth value. — Banno

That's an absolutely meaningless sense of "truth". By this standard, I could make any combination of words and claim this is true therefore it has a truth value.

The issue is that the meaning (content) of the words must be distinguished from the form of the proposition. So, "possible" must be assigned a meaning, in order that we do not equivocate between "past possibility", and "future possibility", which leads to fatalism. I'm accustomed to your response to this criticism, which is to deny a distinction between words and meaning, form and content, but that's nonsense as the reality of ambiguity and equivocation demonstrates.

"It is possible that it will rain and not rain tomorrow" is false, since there is no possible world in which it both rains and does not rain. — Banno

That's an arbitrary designation. As explained above, a "possible world" cannot have identity as an object because it represents one of many possible contradictory states of an object which has identity. It's simply an imaginary entity, without an identity, therefore the laws of noncontradiction and excluded middle cannot be applied, and any designations as to what is acceptable and what is not acceptable are arbitrary.

And this adds to your idea, Hanover, in that such things only ever happen in impossible worlds, and so "It is possible that it will rain and not rain tomorrow" is false in all the possible worlds, but perhaps true in some impossible world... — Banno

Again, that's an arbitrary designation of impossibility. If we analyze this supposed impossibility, we will see that any possible world must divide into further possible worlds at the moment of the present, as we do with our actual world to account for the reality of the future. Therefore, any possible world could be divided into two further possible worlds, one in which it rains tomorrow, and one in which it does not. And so, your designation which states that it is impossible to have a possible world in which it both rains and does not rain tomorrow, is a completely arbitrary restriction which you apply to the understanding of possible worlds. You allow the actual world to divide into possible worlds, to account for future possibilities, but you do not allow a possible world to divide into further possible worlds to allow for future possibilities in that possible world. What sense does it make to deny the reality of the future from all possible worlds? In reality, the only true restrictions to possible worlds are the limitations of the capacity of imagination. Those are restrictions of content and ought not be confused with formal restrictions.

Repeating your errors does not reduce them.

I wouldn't have to repeat myself if you could show me where I am wrong, instead of just insisting that I am wrong. In fact I would greatly appreciate it. Clearing up errors is always a good thing.

if you could show me where I am wrong — Metaphysician Undercover

I, and others, have. You can't see it. Indeed, you have quite explicitly refused to see it.

Not our problem.

Even an OG needs to fulfill the PSR. This is done by the OG having existence inherently, such that the statement "this being-that-inherently-exists exists" is a tautology, and is therefore self explained. I presume you agree with that given what you said:

Whatever it is, the OG cannot have been caused, because it's a first cause. Can an uncaused thing be contingent? To be contingent, something must account for that contingency - such as its cause (whatever caused it, might have not caused it). But if it exists uncaused then I suggest it must exist necessarily - any OG must exist necessarily. — Relativist

This self explanation does not apply to the laws of nature because they are not tautologies, i.e., they can be denied without resulting in a self-contradiction.


Modal collapse: Modal collapse is often used to critique arguments like the ontological argument for the existence of God (source), which shows that it is commonly agreed to be a weakness.


Quantum indeterminacy (QI): QI is incompatible with the PSR. QI allows for outcomes to occur without reason, and this goes against the PSR that demands a sufficient reason for everything that exists or occurs. I presume you agree with that as well based on your statement quoted above. Indeterminate outcomes are contingent, and thus something must account for that contingency.

Even an OG needs to fulfill the PSR. — A Christian Philosophy

That's logically impossible. There can be no explanation for an OG. It must exist autonomously - not dependent on anything else. But since the OG is not contingent, it exists necessarily, consistent with some versions of the PSR.

Even an OG needs to fulfill the PSR. This is done by the OG having existence inherently, — A Christian Philosophy

Autonomous is a better descriptor.

This self explanation does not apply to the laws of nature because they are not tautologies — A Christian Philosophy

Category error. Tautologies refers to PROPOSITIONS, not to existents.

Quantum indeterminacy (QI): QI is incompatible with the PSR. — A Christian Philosophy

Since quantum indeterminacy is likely to be real, you have a choice: reject the PSR outright, or accept the probabilistic result of a quantum collapse as adequately explained.

I, and others, have. — Banno

Actually, Hanover clearly agreed with me, that modal logic when applied to future possibility is not consistent with classical logic. So it is really you who refuses to look at your own errors, which have been pointed out to you. Instead, you simply assert that I am wrong, and that it is a waste of your time discussing this with me. While we could be progressing toward discussing the actual points of understanding/misunderstanding where we disagree, and hammering out what that difference amounts to, you simply refuse to accept fundamental facts, leaving us unable to proceed.

If we interpret two possible worlds, one with rain, and one without rain, with "I" as a rigid designator, then the law of noncontradiction is violated, because "I" gets wet and does not get wet, at the same time. The qualification of "different worlds" is just a facade to hide the contradiction. If we look at what Banno called "counterpart theory", then we have no continuity of the object "I", from the present time into the future, only possible similar objects in the future, therefore the law of identity is not applicable. — Metaphysician Undercover

The claim that "I get wet and do not get wet" violates the law of noncontradiction misunderstands how modal logic works. These are not simultaneous truths in a single world, but distinct evaluations across possible worlds, which is actually the reason modal logic exists. The law of noncontradiction applies within worlds, not between them.

Additionally, the entirety of the "different worlds" enterprise must be jettisoned and the resultant collapse of modal logic as well if we follow out your logic. The term "different" as applied here by you includes any dissimilarity whatsoever, even the simple fact they are in different locations. That is, it is impossible under your reasoning to have any metaphysically related universes because everything within each one would be relevantly different.

To make my point clearer: Suppose you had Universe #1, and within it you get wet and in Universe #2, you also get wet. In fact, every single thing within #1 and #2 are the "same," they would still not bear any metaphysical relationship to each other because they are all necessarily different since they occupy different time and space. That is, #1 and #2 do not collapse into being the same thing because they are not identical under your view. They are just curiously similar.

When we chart out all possible worlds, under your reasoning, an infinite number could be the same in every apparent regard because you deny the concept of rigid designation in theory.

This is to say that if you deny a rigid designation for "I," you must do it for all things. That means that not only does the fact that you're not the same you in #1 and #2, the rain isn't the same in #1 and #2. They must be different. You can't have a different you in #1 and #2 and share the same rain. When we say it will rain in #1, while that sounds like any old generic rain will do, if we were being more precise, we'd describe the exact identity of the rain that would strike you in #1 versus #2.

This I suggest is the logical consequence of demanding cross universe consistency.

This is why @Banno brings in counterpart theory, which holds there is a similar counterpart in another universe that satisfies the conditions needed to perform the modal logic. It dispenses with the impossible mental gymnastics needed to comprehend what it could possibly mean to have identical entities in different locations at the same time, when location is a component of identity. This concept of possible worlds is injected to expand our epistimological understanding of the hypothetical, but, if taken literally, it cannot be sustained because there really aren't multiverses outside of science fiction.

All of this is just to say:even if we allow for a rigid designator of "I" across multiverses, that does not create a contradiction as long as we assume contradiction applies only intra-universe and not inter-universe.

But back to the classic versus modal logic discussion:

If in classic logic I say:

All glurgs are glogs
I am a glurg
Therefore I am a glog

That is true, despite the fact there is no referent for any of this gibberish. That is why we can use symbols to represent these entities because their existence is irrelevant for the analysis.

Under modal logic we say:

It is necessary all glurgs are glogs
It is possible I am a glurg
It is therefore possible I am a glog

This is true as well, purely from a formal level, despite there are no glogs here, there, are anywhere.

The issue then becomes providing a definition of "possible," as you allow for pure meaningless formality under classic logic but not under modal logic. Since "possible" is the only new thing inserted, that must be the reason you treat these two systems different. What you then do is require metaphysical grounding in order for the possible to occur, but that I challenge. You no more need semantical validity for modal logic to work than classic. It's good to have semantically meaningful statements, but not required.

That is, the same tension occurs in classic logic. Typically those syllogisms do more than just mindlessly maintain truth value through vacuous symbols. Typically they have semantical truth, but not always. I would say the same of modal logic as well. But to demand that modal logic always be semantical results in its collapse, despite its pragmatic value. I think the discussion of impossible worlds makes that clear. You can use modal logic to consider events that did not and cannot occur.

My position is that we must fictionalize the idea of multiverses for the purposes of gaining epistimological clarity, without regard to whether they really exist. Maybe explain what is gained or lost by this approach.

The claim that "'I get wet and do not get wet' violates the law of noncontradiction" misunderstands how modal logic works. — Hanover

Thank you. This is the basic insight, as you go on to explain, "which is why modal logic exists."

When we say it will rain in #1, while that sounds like any old generic rain will do, if we were being more precise, we'd describe the exact identity of the rain that would strike you in #1 versus #2. — Hanover

Right. The point is that nothing is the same in different worlds. Trying to import something that's the same automatically dissolves what "possible world" means in this discourse, if I can put it that way.

In short:

contradiction applies only intra-universe and not inter-universe. — Hanover

And you guys feel free to disagree with me as well. I'm sorting it out in real time too.

Hanover clearly agreed with me, — Metaphysician Undercover

Not so much, it seems.

But also, if what I have said erroneous, as you supose, then they are not my errors, since all I have done here is present the Kripkean view that is the established interpretation of modal utterances.

So my my view, but that agreed to by the body of people who have looked into such issues.

Some of them even read books about logic, unlike you.

The point is that nothing is the same in different worlds. — J

...on the counterpart interpretation. If one accepts rigid designation, then there are things that are the very same in different possible worlds. Which is the advantage of Kripke over Lewis - when we ask "what if this post had been about the weather?" we are talking about this post, in the actual world and in another possible world.

The claim that "I get wet and do not get wet" violates the law of noncontradiction misunderstands how modal logic works. These are not simultaneous truths in a single world, but distinct evaluations across possible worlds, which is actually the reason modal logic exists. The law of noncontradiction applies within worlds, not between them. — Hanover

"Possible worlds" is an interpretive term, and it's really irrelevant. It makes no sense to speak of a world which is possible. They are not actually distinct worlds, just distinct possibilities. And it is the human mind which conceptualizes distinct possibilities from the realm of future possibility. The employment of distinct imaginary "worlds" does nothing but add confusion.

So, let's look at these possibilities without the confusion created by that nonsensical idea of "possible worlds". Banno suggested two possible modes of interpretation. One had a rigid designator, in which case "I" in each possibility (or possible world, if you really must) signified the very same individual. This clearly violates the law of noncontradiction because we are talking about the same object at the same time, tomorrow. In the other case, the two instances of "I" are not the same, but similar. In this case we have no identified object, only similar objects and the classical rules are simple not applicable.

Additionally, the entirety of the "different worlds" enterprise must be jettisoned and the resultant collapse of modal logic as well if we follow out your logic. The term "different" as applied here by you includes any dissimilarity whatsoever, even the simple fact they are in different locations. That is, it is impossible under your reasoning to have any metaphysically related universes because everything within each one would be relevantly different. — Hanover

"Different worlds", and "different universes", are nonsensical and misleading conceptions. "Universe" by definition includes all that is. "Possibilities" are completely distinct, and categorically different from the world, or the universe. It makes no sense to talk about possibilities as if they are real beings, living somewhere in different worlds. The different worlds referred to here as "possible worlds" are nothing but conceptual structures, designed to deal with the reality of possibility. Possibility is something general, and when we conceptualize it as distinct possibilities, those specific determinations, this possibility and that possibility are purely conceptual. Speaking of a possibility as existing somewhere as a world, is no different from speaking of numbers, and other conceptions as existing in some Platonic realm of Forms somewhere. This is totally misleading and confusing. As distinct possibilities is not a realistic representation of "future possibility", it is a product of the imagination

To make my point clearer: Suppose you had Universe #1, and within it you get wet and in Universe #2, you also get wet. In fact, every single thing within #1 and #2 are the "same," they would still not bear any metaphysical relationship to each other because they are all necessarily different since they occupy different time and space. That is, #1 and #2 do not collapse into being the same thing because they are not identical under your view. They are just curiously similar. — Hanover

This interpretation makes the problem even worse. We have truth about the past, and the actual world, as well as the actual universe, and truth about now. One world, and one universe. From what you are saying, the future consists of a whole multitude of universes, possibilities. You say the separate universes would bear no metaphysical relationship on each other, but this is not true. They must all relate to the one actual (true) world at the present, or else they are simply arbitrary fictions. But possibilities are not arbitrary. Therefore they must share a time and space, as they all must relate to the true here and now.

The reason why I say it makes the problem worse, is because now we need to define how these many possibilities (universes) relate to the here and now (the true). The principle which relates them must be absolutely fair and equal to all of them, or else we'd be assigning arbitrary, or subjective preference, to one over the others. But this is logic, so it needs to be objective, therefore the relationship between the actual, true, here and now, and those other universes, must be based in principles which are fair and equal. Clearly it makes no sense to talk about these distinct possibilities as different universes in different time and space, because all the possibilities must be directly related to the true universe, here and now through equal principles. And, it would be very misleading, if not downright false to speak as if there is no metaphysical relationship between them.

When we chart out all possible worlds, under your reasoning, an infinite number could be the same in every apparent regard because you deny the concept of rigid designation in theory.

This is to say that if you deny a rigid designation for "I," you must do it for all things. That means that not only does the fact that you're not the same you in #1 and #2, the rain isn't the same in #1 and #2. They must be different. You can't have a different you in #1 and #2 and share the same rain. When we say it will rain in #1, while that sounds like any old generic rain will do, if we were being more precise, we'd describe the exact identity of the rain that would strike you in #1 versus #2.

This I suggest is the logical consequence of demanding cross universe consistency. — Hanover

I suggest that denying rigid designation is what allows for the reality of different possibilities. This is what you would call inconsistency between distinct universes, which is not actually inconsistency if it's not actually the same object across distinct possibilities. So, what appears like inconsistency, when we apply rigid designation, is not inconsistency if we remove rigid designation.

What I propose is that there is no individual, no object, indicated by "I" in any described future possibility, just like there is no world in "possible world". Since this is a an imaginary scenario, everything about it is a possibility, even the existence of I, and the supposed universe or world. What "I" or "universe" indicates is a possible entity, and that means it is a concept only. And, a concept does not have identity like an object, nor do the same laws of truth or falsity apply to concepts, which apply to objects with an identity. The laws which apply to conceptions are axioms which are designed for the specific system of logic, like those of mathematics. So there are different types of logic which deal with building conceptual structures like mathematics, modal logic, etc., and these types are completely different from propositional logic which is applied toward describing and understanding empirical objects. The two are not at all compatible, because the former is based in truth, the latter possibility. This is because empirical observations are always in the past, and possibilities are in the future, and there is a substantial difference between these two. Relating these two at the present is a significant philosophical problem which has one form of manifestation as the is/ought gap.

But back to the classic versus modal logic discussion:

If in classic logic I say:

All glurgs are glogs
I am a glurg
Therefore I am a glog

That is true, despite the fact there is no referent for any of this gibberish. That is why we can use symbols to represent these entities because their existence is irrelevant for the analysis. — Hanover

We ought to distinguish "true" from "valid" here. The argument is valid, but we still need to question the truth of the premises. If we accept the first as true, we still need to assess the second. This is where the law of identity, and the other two laws come into play, in assessing the truth or falsity of the premises. We have an object signified by "I", and the premise states "I am a glug". By the law of identity, there is a truth to what "I" is, which inheres within that object itself. . So there clearly is a referent, and the soundness of the conclusion is very much dependent on the accuracy of the description of the referent.

If we change the second premise to "tomorrow I will be a glurg", then my argument is that the referent is swallowed up by possibility, such that there is no referent. I can say "yesterday I was a glurg", and there is an actual truth or falsity, a referent at that time, but that is not the case with the future. Any supposed object signified by "I" may be annihilated before tomorrow, so "I" does not signify an object with identity in this case. Now, the logic of truth and falsity cannot serve us.

The issue then becomes providing a definition of "possible," as you allow for pure meaningless formality under classic logic but not under modal logic. Since "possible" is the only new thing inserted, that must be the reason you treat these two systems different. What you then do is require metaphysical grounding in order for the possible to occur, but that I challenge. You no more need semantical validity for modal logic to work than classic. It's good to have semantically meaningful statements, but not required. — Hanover

The issue is not the validity of the logic itself. The question is one of truth and falsity. That is why I keep insisting it's a problem of interpreting and applying the logic, not a problem of the logic itself. And, truth and falsity are metaphysically grounded in the object spoken about. That is what the fundamental three laws are concerned with, what we can say truthfully say about objects.

We can remove all metaphysical grounding from "possible", but that's what I explained to Banno would produce complete arbitrariness. To produce the conceptual structure of possibility (possible worlds if you wish), we must remove the grounding of truth and falsity. But then Banno wanted to sneak truth and falsity back in, as applicable within possibility (a specific possible world), and this is an arbitrary rule. If we remove the metaphysical grounding of truth and falsity, to create a logic of possibility, then we need some other form of metaphysical grounding for this realm of possibility. To go back to truth and falsity is a step in the wrong direction. So we start with something like absolute equality and fairness (as in mathematics) between all possibilities, the we need to weight them according to the truth of here and now. And in decision making, principles of preference.

So my my view, but that agreed to by the body of people who have looked into such issues. — Banno

I think you know by now, that I tend to disagree with a good number of so-called bodies of people. I don't follow mob rules, nor do I blindly accept authority.

That's logically impossible. There can be no explanation for an OG. It must exist autonomously - not dependent on anything else. But since the OG is not contingent, it exists necessarily — Relativist

What kind of necessity are you referring to? There are only two kinds of necessity: internal and external; that is, logical (or inherent) necessity and causal necessity. You correctly reject causal necessity because the OG has no cause. It follows that it has existence by logical or inherent necessity. Existence by inherent necessity fulfills the PSR and is not dependent on anything else.

Tautologies refers to PROPOSITIONS, not to existents. — Relativist

It's both. Tautologies are necessarily true, and truth means conformance to reality. Thus, the outcomes from tautologies occur in reality. E.g. "2+2=4" is a tautology because II and II are inherently found in IIII. And sure enough, two and two of anything results in four of that thing in reality. Not just in our world but all possible worlds. On the other hand, outcomes described by the laws of nature also occur in reality, but these laws are not tautologies and so these outcomes do not occur in all possible worlds.

Since quantum indeterminacy is likely to be real, you have a choice: reject the PSR outright, or accept the probabilistic result of a quantum collapse as adequately explained. — Relativist

The solution to the QI vs PSR problem is discussed in this post. There is a long and a short answer. The short answer is that quantum experts themselves claim "I think I can safely say that nobody understands quantum mechanics", and something that nobody understands cannot be used as a valid argument for or against anything.


It sounds like you believe in the PSR but allow some exceptions. This is problematic because how do we decide when exceptions are made? You made an exception for the OG, but could have just as easily made one for the laws of nature directly, which would end the discussion right there.

.
~~

, , you have been continuing your discussion here, independently of thel parallel discussion of modality. I'd like to bring the two back together.

If we presume the accepted modal logics with a possible worlds interpretation, what can we say about ontological grounding and the principle of sufficient reason?

First let's look at the idea of ontological grounding. What we want is for an explanation as to why the world is as it is, and not some other way. If something could have been otherwise, it cannot explain why something is necessarily the case. So any ontological grounding must be necessary. But then it would be the same in every possible world. And in that case, it could not explain why this world is as it is.

Hence any explanation strong enough to constitute an ontological grounding must thereby fail to explain why the world is as it is.

Next, the principle of sufficient reason. Much the same argument holds here. Either the sufficient reasons are necessary but too weak to explain why the actual world is as it is; or the reasons explain why the world is as it is, but are contingent, and so are insufficient to explain why out of all the possible worlds, this is the actual world.

What kind of necessity are you referring to? There are only two kinds of necessity: internal and external; that is, logical (or inherent) necessity and causal necessity. — A Christian Philosophy

I'm referring to metaphysical necessity/possibility, which pertains to existence. Logical possibility pertains to the semantics of logic. Conceptual possibility refers to what we can conceive. Epistemic possibility refers to what is logically possible per the logical implication of a body of facts. That's the broad set of modalities.

There is no "internal" possibility - although it may refer to something like (Christian Philosopher) Alvan Plantinga's "de re necessity" -wherein he proposes "necessary" to be an intrinsic property of God. It's a contrivance to "prove" what he already believes: God exists. You're doing the same thing: contriving a metaphysical framework that entails God.

You correctly reject causal necessity because the OG has no cause. It follows that it has existence by logical or inherent necessity. Existence by inherent necessity fulfills the PSR and is not dependent on anything else.

My position is that X exists contingently (meaning it is metaphysically possible for X to have not existed) IFF there exists some C, such that C accounts for (X or ~X)

Laws of nature are typically necessitations; if C causes X, then C necessarily causes X. I.e. there are no exceptions*. Quantum mechanics seems to entail a contingent outcome: Q (a quantum collapse) results in X, but there's a suite of other results (a probability distribution) that it might have collapsed to. In this case, X is contingent; the other results that might have happened are non-actual possibilities..

* C may itself be contingent, but the outcome of its instance of caustion is necessary.
--------------------
Because nothing accounts for the OG, there are no non-actual possibilities.

You don't have to accept my account of metaphysical contingency/possibility - but this demonstrates that your proof depends on a metaphysical framework that you cannot show to be true. Your proof is thus epistemically contingent on that questionable framework.

Tautologies are necessarily true, and truth means conformance to reality. — A Christian Philosophy

The statement "The morning star is the evening star" is a tautology because both the morning star and the evening star refer to the same object. This is semantics, with no ontological implications about necessary or contingent existence. So substituting tautolgy for necessity is misleading, such as your next error:

outcomes described by the laws of nature also occur in reality, but these laws are not tautologies and so these outcomes do not occur in all possible worlds. — A Christian Philosophy

For there to be a "possible world" in which it is not the case that F=ma, there would have to be some C that accounts for the truth of F=ma, and C could have accounted for ~(F=ma) - some non-actual possibility. Here's a case where I think you're conflating metaphysical possibility with conceptual possibility (i.e. you can conceive of F=ma being untrue).

The solution to the QI vs PSR problem is discussed in this post. There is a long and a short answer. The short answer is that quantum experts themselves claim "I think I can safely say that nobody understands quantum mechanics", and something that nobody understands cannot be used as a valid argument for or against anything. — A Christian Philosophy

Actually, there are multiple coherent interpretations of QM. Some treat quantum outcomes as contingent (as I described). Others treat it as a necessary outcome. My earlier comments are based on the premise the outcome is contingent. My purpose was to illustrate the concept of contingency, not to insists there is true, metaphysical contingency.

It sounds like you believe in the PSR but allow some exceptions. This is problematic because how do we decide when exceptions are made? — A Christian Philosophy

I consider the metaphysical basis of necessity/contingeny that I described to be the correct principle. The PSR generally conforms to it, but it is more vague.

First let's look at the idea of ontological grounding. What we want is for an explanation as to why the world is as it is, and not some other way. If something could have been otherwise, it cannot explain why something is necessarily the case. So any ontological grounding must be necessary. But then it would be the same in every possible world. And in that case, it could not explain why this world is as it is. — Banno

Several issues.

1. An OG exists autonomously. This means without dependencies of any kind (causal or otherwise). If it had such a dependency it could not be the OG
2. For an object, X, to be ontologically contingent, there must be some C that accounts for X, but C could have accounted for ~X. Example: assume quantum collapse is not determinate, and C is a quantum collapse in which X emerged. X is contingent because C could have collapsed to Y. I express this as:
C accounts for (X or Y), or more generally: C accounts for (X or ~X).
3. If an object is not contingent (as identified in #2) then it is necessary.
4. Compare this to the outcome of a deterministic law of nature: the law: C causes X. Because it's deterministic, it means: C necessarily causes X. If C is contingent, then there X inherits this contingency (whatever accounts for the contingency of C, also accounts for the contingency of X).
5. An OG is not contingent because there is no C that accounts for the OC (that would entail a dependency - see#1). Therefore it exists necessarily.
You have 2 general choices:
6. If you embrace a version of the PSR that requires everthing to have an explanation, then you are committed to an infinite series of dependencies, and should reject the existence of an OG.
7. If you are committed to an OG, then you should reject any version of a PSR that requires everything to have an explanation. You could accept "necessary" and/or "autonomous" as sufficient explanation.

IMO, possible world semantics can obfuscate the issues. It's valid, but one should avoid conflating conceivability with metaphysical possibility. IOW, you could conceive of possible worlds with OG1, OG2, OG3 as their respective ontological grounds, but per my analysis the actual OG is the only METAPHYSICALLY possible one.

You can, of course, reject my view of contingency. But this is my basis for rejecting the theistic argument that was presented.

Maybe this will help:

It is necessarily true that if someone is a person, then they are a physicist.
Einstein is a person.
It is necessarily true that Einstein is a physicist.

This is modal logic. See what just happened? If we necessitate a rigid designator across all worlds onto a non-essential trait, we elevate a contigent statement into a necessitated one and we destroy modal logic by eliminating hypothesizing what Einstein might have been in another world.

What this means is that the law of non-contradiction is not violated when you have an Einstein across different worlds because the entire modal structure demands he be different across differing worlds in non-essential ways.

Yep.

I'd caution agains attempting to show that there is an inconsistency in Meta's logic. He may simple add ad hoc hypotheses in order to escape.

But also, his premise, p(x)⊃□p(x) does not lead to an inconsistency within the logic.

it does lead to modal collapse. There can be no modal statements in such as system.

p(x)⊃□p(x) says that nothing can be other than it is. It describes a world in which there is no change.

Also, p(x)⊃□p(x) ↔︎□p(x)⊃p(x), so all truths are necessary truths. All truths in this system are necessary, and all falsehoods are impossible.

There are no counterfactuals, no contingency and as a result, there can be no free will. Given that maintaining free will was one of the reasons Meta gave for adopting this system, that's a big problem for him. Look out for the ad hoc reply.

So his system is consistent, but useless for any sort of modal reasoning, and leads directly to fatalism.