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March 22, 2014

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"the Laws of Logic are simply a reflection of His nature"

So whilst saying logical absolutes arent accounted for in the 'atheistic worldview' (whetever that means), meanwhile you cant account for God. So you've just shifted everything back onto God and not moved anything any further forward.

So if you are saying atheists have to account for logical absolutes, theists have to account for God i.e his existence, qualities and nature.

Suprendo, we "account" for God's existence by realizing that He is the Necessary First Cause of Everything Else.

Asking, "What caused the First Cause?" is gibberish.

Mike

So you say God just is, I say logic just is. How is your explanation any better than mine? In fact, it's worse, because you add a layer of complexity and cant account for any of aspect of God's conciousness or existence. The explanation without God is more parsimonious.....

Meanwhile you allege that there must be a first cause (which for reasons I pointed out in Mr Warner Wallace's last post, isnt justified) and that further, because you can't think of a better explanation, pick God at the root.

The thing is - Im not the one saying that we have to account for these things for worldview x to be viable- Mr warner Wallace is. I'm just pointing out the double standard here. Im quite happy with the notion that if you peel away the layers, you have to come down to some assumptions.

What does it mean to say that the laws of logic are a "reflection of His nature"? Or that "they exist as an extension of His rational thinking"? I can't make heads or tails of 90% of this post.

Ben, follow the links in the post to see his explanation. This post is one of a series, and the full series is on the Cold Case Christianity blog. The links will take you there.

Thank you Amy, but I do not believe the other posts are very helpful in answering my question. They all use the same bizarre, mismatched language to give the so-called theistic explanation of logic. For instance, in the latest installment, he writes:

"The Laws of Logic are simply an attribute and reflection of God's perfect existence; God does not create these laws, they are an innate and immutable aspect of His nature... They are merely a reflection of His Being, and they permeate all of His creation."

To me, this seems like nonsense. I have no idea what it means to say that, for instance, the law of noncontradiction is an "attribute" of God.

To see where I'm coming from, let me give you an example. Suppose I say this: The number 1 is an attribute of reality. It reflects the perfect nature of reality to be unified and singular.

If I was to try to assert such nonsense, how would you respond? I think you would just have to say, "look, I don't know what you are talking about."

Ben,

I can't answer your specific question, but will highlight how I use the laws of logic: they are examples of immaterial entities that science "uses"/"presupposes" but can't "prove".

Therefore, science cannot be leveraged to determine the existence of all types of entities/knowledge/truth. We must access some forms of knowledge through other means.

I don't necessarily go as far as JW's claims. It gets close to the ontological argument for the existence of god, which is too abstract for most.

Cheers.


Ben, from reading J's posts on his other blog, I get the impression that what he means by saying the laws of logic are part of God's nature is that God thinks logically. Or being logical is the way God is, or something along those lines. To say that logic is an attribute of God is to say that the way God thinks is logically, or something like that. Logic is an aspect of God in the sense of it permeates his metal life.

I could be wrong. J didn't explicitly say what he meant. But that is the impression I get.

Isn't logic simply a matter of language and communication? Obviously you can make statements such as "A is not A" but in order to communicate clearly, your statements have to have some sort of internal coherence. The whole "there is no logic without God" does not really seem to follow from anywhere, since it is painfully obvious that one can make logical statements without any reference or assumption of theism. The circumference of 2-dimensional circle is necessarily going to be about 3,14 times its diameter, because if it were anything else, you would not be talking about a geometric circle.

Not sure if this is part and parcel of the discussion, but is it something akin to this: God is not just "good", God IS goodness. God is not holy, God IS holiness itself. God is not loving, God IS love. God is not forgiving, He IS forgiveness. All of these things are not merely attributes of God but are the actual essence of God. Might the concept of the laws of logic be something like this?

Sam,

It's fine to say that it's part of God's nature to think logically. However, it's not clear how that would constitute an explanation for the existence of logic and its laws, nor would it tell us what logic is.

Erkki probably has it close to correct. Logic seems to be primarily about language, or possibly symbolism more generally. So, I would conjecture that logic exists because language and symbolism exist, and work in an orderly, rule-driven way. So, to the extent that language is a human convention (or perhaps, primate convention), so too are the laws of logic which govern language.

Notice that Wallace's objections above don't hold up to scrutiny once we view logic as part of language. For example, Wallace insists that logic cannot be changed. However, this is evidently false since there are languages in which classical laws fail. If we only spoke in languages like that, then the classical laws wouldn't apply. Or, for another example, Wallace insists that logic existed before primates existed. But, if logic is necessarily tied up with language, then this too is false since language did not exist prior to the evolution of primates.

Nevertheless, I only call this a conjecture regarding the existence of logic. Maybe I'm wrong, and it's about more than just language. But, even if I'm wrong, that doesn't make Wallace correct about his view of logic. He needs to articulate his view, and defend it independently of competing views. As far as I can see, he has failed in both tasks. Indeed, it looks to me as though his view is incoherent and confused. But, even if he can clarify it, he will need to argue that it is true before we can accept it.

Carolyn,

I don't think it's correct to say that God is goodness. Goodness is a property. For example, an act of charity can have the property of being good. In contrast, God is a concrete entity---a conscious being, and not just an abstract property.

It seems to me there are two aspects to the laws of logic. Take the principle of contradiction which says that it is impossible for a proposition to be both true and false.

In one sense, the necessity of this law is based on our firm determination to use words a certain way. "true", "false", "possible" and "and" simply are not to be used to say "Possibly, X is both true and false". That formula is false by convention. Its denial is true by convention.

But convention only takes us so far. We are not free to adopt just any convention. There seems to be some underlying reality, a logical fact or facts, that grounds the limitations that exist in the adoption of conventions.

What could such a fact be? Well, facts are constituted by things and their attributes and relations. The fact that the cat is on the mat is constituted by the cat, the mat and the one's being on the other.

So the logical facts that ground the laws of logic is constituted by some thing (or things) and its (or their) attributes and relations. What thing or things? Some set of propositions? Seems likely.

What are propositions? They are the meanings of some sentences "Snow is white" and "neige est blanche" are sentences that have the same meaning. That meaning is the proposition that snow is white. Not every sentence-meaning is a proposition. Propositions have the distinguishing feature among meanings that they bear truth values. But in common with all meanings, propositions are mental entities.

And in whose mind do those meanings exist? Well, a lot of peoples' minds no doubt. But it seems that they must exist in some necessary being's mind...otherwise the laws of logic could not be necessary.

So the laws of logic are grounded by some set of attributes and relations that exist on propositions that reside in the mind of a necessary being. Is it so hard to imagine that those attributes and relations are essential qualities of the mind in question?

And if that's the case, then the laws of logic are grounded in the essence of this necessary being. And if that necessary being is God, as seems certain, then the laws of logic are grounded in the essence of God.

No doubt there are lacunae in the argument just given. I was not attempting to provide a knock-down argument for the proposition that the laws of logic are founded in the essence of God. I was attempting to show that the view need not be given up as incomprehensible as Ben suggests.

WL,

If you're going to say that the laws of logic exist in the minds of human beings, that explains their existence quite nicely, without the need to add that they also exist in the mind of God.

But in any case, I wasn't denying that there are views of logic out there as dependent on God, which are not obviously incoherent. James Anderson's view is the best-known example, I think. I was only pointing out that Wallace had failed to articulate such a view.

I don't think it does work to say that the laws of logic exist in the minds of human beings, because human beings are contingent beings, but the laws of logic exist and apply even if there are no humans.

They have to exist in the mind of a necessary being.

As for JWW's post, I think I just argued that the laws of logic are a "reflection of His nature" which was one of JWW's claims that you couldn't make heads or tails of.

It could well be that JWW expressed some of his remarks in a way that's more friendly to those who have already cottoned on to what he says.

it is painfully obvious that one can make logical statements without any reference or assumption of theism.

How is this remotely relevant?

One can do thermodynamics without making any reference to statistical mechanics.

One can do chemistry without making any reference to quantum physics.

One can do Java programming without making any reference to assembly code programming.

One can do poetry writing without making any reference to lexicography.

etc.

But for each of these sentences, the former activity depends on the truths of the unreferenced disciplines.

It is not painfully obvious, or even pleasantly obvious, that logic does not depend on theism. This is the case even though one can do logic without making any reference to theism.

WL,

When you say that the laws of logic "exist," what precisely do you mean? I cannot point to any law of logic in the real world. It is not a physical object, nor even a single object of my thought. That I can see, they do not exist except in the sense that we can think and communicate in certain, orderly ways. So, if there were no human beings around to do that, why insist the laws of logic would still exist?

I'm not saying they don't exist in any other sense. I'm just saying, if they do, it's not obvious how. I would be very careful in asserting that the laws of logic exist at all---much less that they exist necessarily---unless we have some particular sense of existence in mind.

Ben, maybe you're confusing the laws of logic with their articulation. I would agree if there were no humans, there would be no formulations we call "the laws of logic." But reality would still be a particular way. It would still be the case that there couldn't be square circles. It would still be the case that either reptiles exist or they don't exist. It would still be the case that the sun is the sun.

That's kind of why I think the transcendental argument is fallacious. It seems to assume that the laws of logic are laws of thought. That's how Greg Bahnsen put it in his famous debate with Gorden Stein. But, as Ronald Nash pointed out in Worldviews in Conflict (or Faith & Reason, I can't remember which), the laws of logic are not laws of thought, but laws of being. They describe the way reality is. Reality would be that way whether or not there was anybody thinking about or articulating the laws of logic.

I don't think the laws of logic depend on the mind of God. In fact, God's existence wouldn't even be a coherent thing unless the laws of logic were already true. It seems to me that the coherence of God existing or doing anything at all depend on the laws of logic being real.

If it happened that God didn't exist, then "God does not exist" would be true, and "God does exist" would be false.

The original question was what are the logical facts that ground the laws of logic that we express with formulae like "Everything is what it is and not something else"?

Like all facts, these facts must consist of things and their attributes and relations. I asserted, further, that these things were propositions.

Now, propositions do exist. If they did not sentences like "Snow is white" would have no meaning.

Where do propositions exist (not just the propositions that express the Laws of Logic and not just the propositions involved in the logical facts that ground the Laws of Logic)? Like all meanings they exist in minds. And the attributes and relations between those meanings that comprise the logical facts that ground the Laws of Logic exist, likewise, in minds.

But if they existed only in contingent minds, then they would not exist should those minds not exist. A proposition cannot be true or false if it does not exist in the first place. So these propositions, at least the ones involved in the logical facts that ground the Laws of Logic, must exist in a necessary mind. They could not be true in every possible world if they did not exist in every possible world in order to bear truth value.

You ask "What does it mean to say that the laws of logic exist?" Well, the existence of the propositions that express the Laws of Logic, and also the existence of those Propositions constitutive of the logical facts that make the Laws of Logic true exist like any other proposition and like any other meaning...by being thought about by a mind.

They are not true because they are thought about by a mind of course. But they must first exist in order to be true. And they must exist necessarily in order to be necessarily true.

And, just so as not to keep things in suspense, in order for them to be necessarily true, they must exist in the mind of a necessary being (God).

I don't think the laws of logic depend on the mind of God. In fact, God's existence wouldn't even be a coherent thing unless the laws of logic were already true. It seems to me that the coherence of God existing or doing anything at all depend on the laws of logic being real.

If it happened that God didn't exist, then "God does not exist" would be true, and "God does exist" would be false.

"A depends on B" just means that "A entails B".

Bearing that in mind, note that everything after the first sentence could be true even if the Laws of Logic depend on the mind of God.

For indeed, if the Laws of Logic were not true, God's existence would not be coherent. If the Laws of Logic weren't true, nothing would be coherent. What's more, if the Laws of Logic weren't true, they would also be true! Any time you set up an if-then statement that has a logical impossibility for the if-clause, pretty much anything goes for the then-clause. And "the Laws of Logic are not true" is a logical impossibility.

And indeed, the coherence of God existing or doing anything at all depend on the laws of logic being real. That is to say that both "God exists" and "God is coherent" entail (individually or jointly) "The Laws of Logic are real".

But, then again, anything entails that the Laws of Logic are real, even something that, in turn, is entailed by the reality of the Laws of Logic. Or, to put it in the lingo of dependency...everything depends on the Laws of Logic, even those things on which the Laws of Logic depend.

And indeed, if it happened that God didn't exist, then "God does not exist" would be true, and "God does exist" would be false.

Then again, if it happened that God didn't exist, then "God does not exist" would be false, and "God does exist" would be true.

Once more, put a logical impossibility in your if-clause, and anything goes for your then-clause.

"It happens that God does not exist" is a logical impossibility, even if God doesn't exist. God, if He exists at all, is a necessary being. He doesn't just happen not to exist. If He fails to exist, it's because the whole idea of God is a contradiction.

So because "It happens that God does not exist" is a logical impossibility, anything goes for the then-clause of an if-then statement that uses "It happens that God does not exist" for its if-clause.

    How is this remotely relevant?

It is relevant in the sense that if one can construct logical statements that can be proven to be coherent and exist necessarily without any reference or assumption of theism, it's not really the case that non-theist must "borrow" his worldview from theist or that it is fair to accuse him not following his worldview to its "necessary" conclusion.

My mopeds engine does not work without gas, this is certain. Perhaps the gasoline contains the essence of magical ancient dragon whose soul fuels the necessary chemical reaction to stroke the cylinder. I can't prove that this is not definitely the case. However, as I can explain the gasoline and chemical reactions in much more simple terms, adding magic dragons to my worldview seems superfluous and unnecessary.

WL,

Although I feel a lot less confident than you apparently do about swinging the sword of propositions, I nevertheless can tentatively agree that the laws of logic are propositions, and that they exist insofar as minds use and/or conceive them. But then, this seems not to help you establish that the laws of logic exist without people.

I asked before: If there were no human beings around to use/conceive the laws of logic, why think they would still exist? You answered (my paraphrase), because if they did not then they would not be true in every possible world.

But, I don't think they are. Some philosophers (e.g. Kit Fine and Robert Adams) have distinguished between truth in a world, and truth at a world. I think this distinction is natural and essential to understanding possible worlds. In those worlds where sufficiently-developed minds do not exist, neither do propositions, and hence what is true at those worlds will not be true in those worlds, since truth in a world requires the existence of propositions.

Motivating the in/at distinction is, in part, the observation that the propositions about a given possible world, which we want to evaluate for truth/falsity, exist here. From the vantage point of the actual world, we can formulate propositions and ask whether they accurately describe some other possible world. But the propositions are still located here with us, in the actual world.

So, it seems to me that you must either deny the in/at distinction, or else you can try to show that the laws of logic are true in every possible world, and not merely at every possible world. I don't see how you can hope to do either.

By the way, this is exactly James Anderson's problem. I wrote up a paper about it, which should appear in the next few months in the secular web library.

If Fine and Adams were right, then, if human beings, or some other mind, did not exist in the actual world no propositions would even be true at any world (because there would be no propositions to even be true at a world).

But necessary truths are true at every world no matter which world is the actual one.

So that in/at distinction actually buys you diddly-squat in avoiding the consequence that there must be a necessary mind in which necessary truths (at least) exist.

@Ben: I believe one can say that God IS goodness for the very reason that He is a being unlike any other. When a man does something good, like preventing a person from stepping off the curb into oncoming traffic, we rightly say that it was a good thing. Are there greater good things that a man can do? Well, suppose a man commandeers a bus full of school children whose driver just had a heart attack and is slumped over the wheel, and pulls the bus to safety--wouldn't that be an astonishingly great thing, an heroic act that saved sixty youngsters? So, as believers in God, we rightly look at Him who sacrificed HIMSELF to save the entire world from the penalty our sins deserve, and we can correctly call that the greatest goodness possible--He did what we could never do for ourselves. He IS goodness personified.

WL,

If no minds existed in the actual world, then there would be no possible worlds semantics. To even engage in the language of possible worlds seems to require there to be minds in the actual world.

To put it another way, I don't think it makes sense to talk about an "actual" world which is not actual. At least, I don't see how to make that work.

If no minds existed in the actual world, then there would be no possible worlds semantics. To even engage in the language of possible worlds seems to require there to be minds in the actual world.

Right. And so no propositions could be true at every world and so there could be no necessary truths.

But the funny thing about necessary truths is that they are necessary. Not only are they necessary, it is a necessary truth that they are necessary. It is true at every world, even the non-actual ones, that they are true at every world.

Now, I'm not sure that with this claim:

I don't think it makes sense to talk about an "actual" world which is not actual. At least, I don't see how to make that work.
So you don't think the expression "If a different world were actual" is coherent?

I don't see how to make that work.

WL,

Permit me to rephrase my objection. You seem to be arguing as follows:

Premise: in order for propositions to be true at a given possible world, they must exist in whichever world is actual.

Conclusion: Every necessary truth exists in every possible world.

I agree that the conclusion follows from the premise, but I do not agree that the premise is true. In particular, I need not assert that true-at propositions must exist in whichever world is actual, but only that they must exist in this world (which just so happens to be actual).

I do not assumed that any proposition must be true in any possible world. So that is not a premise in my argument. I do assume that necessary propositions must be true at every possible world. I further noted that if the actual world did not contain any minds, this would be impossible, because there would be no propositions to exist at any world. I finally affirmed that necessary truths are true no matter which possible world is the actual one.

WL,

You wrote: "I do not assumed that any proposition must be true in any possible world. So that is not a premise in my argument. I do assume that necessary propositions must be true at every possible world."

Yes, I understand that, and I agree---as long as we interpret the word "must" sufficiently carefully.

But, to make your argument work, you require the following:

"necessary truths are true no matter which possible world is the actual one."

This seems false. If the actual world contained no minds, and hence no propositions, then since propositions must exist in order to be true, no proposition would be true in such a case.

But, to make your argument work, you require the following:

"necessary truths are true no matter which possible world is the actual one."

This seems false. If the actual world contained no minds, and hence no propositions, then since propositions must exist in order to be true, no proposition would be true in such a case.

Aren't you, in effect, just saying that my premise seems false because if it were true, then my conclusion would be true?

WL,

It seems false to me based on my intuition that there is a possible world where no sufficiently-developed minds exist, and my understanding of propositions as mind-dependent, i.e. only existing where sufficiently-developed minds do. From these two assumptions, I believe, follows the rest.

But, if you do not want me to assume in advance that there is a possible world where no sufficiently-developed minds exist, then the best I can say is this: I see no reason to think that necessary truths are true no matter which possible world is the actual one.

Ben:

"I see no reason to think that necessary truths are true no matter which possible world is the actual one."

Then, you are not using the word necessary in it's normal philosophical meaning.

I see all the way through the posts Ben wanting to make sense of what the Christian worldview proposes using a atheist starting point. Early on, he says:

"I can't make heads or tails of 90% of this post."
Even when Amy refers him to JW's blog posts, it doesn't help...he says. No suprise really-it shouldn't make sense when you bring a contrary starting point and then view everything as contrary from then on. Also, most of his assertions along the way are really question begging because he assumes atheism as he rates the Christian system. I think it'd be helpful to rate the atheist worldview internally, and to the same with the Christian worldview....for some reason, it seems hard for an atheist to only imagine God Is, and then consider the coherency internally. I think this is something that JW's pre/post Christian topics turn on--his own personal pre Christian thinking rated internally as a comprehensive system of thought VS. his own personal post Christian thinking rated internally as a comprehensive system of thought.

As far as the other back and forth with WL, hard to follow when Ben doesn't get plain statements. I used to think he was being obtuse on purpose, but it may just be a resolute commitment to materialism that wont let his conscious thought go there.

Brad,

You say that I'm "not using the word necessary in its normal philosophical meaning," but this is incorrect. A proposition is said to be necessarily true just in case it could not have been false. And that's fine with me. However, philosophers are not agreed on how to relate necessary truths to possible worlds semantics. I gave the examples of Kit Fine and Robert Adams who distinguish between truth-in and truth-at, and these are just examples. Undoubtedly, there are others who agree with them. Like me :)

On second thought, I'm not sure that is fine with me. But, it's pretty darn close.

"I gave the examples of Kit Fine and Robert Adams who distinguish between truth-in and truth-at."

Do you think that Kit Fine and Robert Adams would deny that necessary truths are true no matter which possible world is the actual one? Because I don't. The truth-in/truth-at distinction does not have this consequence.

Ben,

Is it possible that there are necessary truths?

WL,

I don't have a reference, but I'm pretty sure Fine and Adams would have rejected that view of necessary truths, since it is a standard criticism of the in/at distinction (cf., e.g., Thomas Crisp in "Presentism," 2005). Also, Iris Einheuser recently (2012) published a paper called "Inner and Outer Truth" which discusses this notion. I haven't read it carefully, but it seems at first glance that Einheuser rejects the view that you espouse.

Unfortunately I'm not a philosopher nor philosophy student, so I'm not too familiar with the literature. But, if a view is threatened by some notion, don't you think the proponents of that view would reject the notion in question?

It seems the finite attempts to, but cannot, source the infinite. Abstractions / Forms are not only contextually relational in nature, they are mind-dependent, though, the contingent mind in question, man’s, sees beyond itself into the infinite, numbers alone being such a contextually-relational-something too innumerable for the mind of man to account for, though there is a wide array of other such intangibles, eternals, infinites, and immeasurables as that odd affair of discovery proceeds. All of the anxious appeals of Universal Possibilism make of themselves non-entity and the necessarily true becomes unavoidable, and that in all worlds. As in all things, the landscape of the Triune dissolves the tensions of contextual relationality within abstractions as the Word/Logos ever in reciprocity’s relations is that manifestation of Words/Logoi as the Word/Logos ever flows through reciprocity’s unsearchable relations as the source of all Words/Logoi for abstractions and forms are simply the casual speaking of the thoughts of an Infinite, and Necessary, Mind. We find in the Triune the In-Here/Out-There to be perpetually in communion. It seems Mind knows Mind within Mind. It seems Mind is Mind, is with Mind, begets mind. Logic sees In/At, In/Out, sees to the end of ad infinitum from the outside of experience as we spy from afar that infinite ocean which we cannot actually touch, swim in, and experience, and, Logic also sees from inside of perception’s brutally repeatable experiences as our own In-Here’s/Out-There’s, though not knowing infinitely, touch that Hard Stop that is the Infinite Mind in which the Immutable Semantics of an Eternal Language finds That-Mind touching this-mind in all contexts, in all worlds. We can only pity those who insist on having their supposed round square in some possible world somewhere as that volitional jettison of Truth from one’s own mind leaves only an insufficiency of being that is that mind’s privation.

But Fine and Adams' view isn't threatened by the notion that necessary truths are propositions that must be true no matter what (even no matter which possible world is the actual one).

The only thing that's threatened is the conjunction of the idea that propositions exist by existing in minds and the idea that there is no necessary being.

WL,

Fine and Adams were concerned about the existence of propositions. If I remember correctly, they believed that there were possible worlds where (certain?) propositions do not exist. To defend their view, they independently developed the in/at distinction. (Fine called it by a different name, the inner/outer distinction.) The "if w were actual then..." criticism was originally aimed against their view that a given proposition may not exist in some possible world, and can be found, as I said, in Crisp's 2005 paper, "Presentism."

Here's what Adams has to say in "Actualism and Thisness" (1981):

In reply to this objection I deny, then, that "it is possible that p" always implies that the proposition that-p could have been true. Philosophers have often found it natural to characterize possibilities and necessities in terms of what propositions would have been true in some or all possible situations (or possible worlds, as we like to say). This seems harmless enough so long as it is assumed that all propositions are necessary beings. But it is misleading if (as I hold) some propositions exist only contingently. From an actualist point of view, modalities (especially non-qualitative modalities) are not to be understood in terms of a non-modal property (truth) that propositions could have had, but in terms of modal properties that actually existing entities do have. To say that I might never have existed is not to say that the proposition that I never exist could have been true. There is such a proposition; but if I ever exist it is false, and if I never existed it would not be true because it would not exist.

I should add, Adams is a Christian, and although I don't know for sure if he believes God is a necessary being, it seems likely that he does. And yet, he disagrees that every proposition exists necessarily.

"And yet, he disagrees that every proposition exists necessarily."

While I disagree with Adams on this point...I think every proposition does exist necessarily...what's really important is to note that my argument above does not require that. It is enough that necessary truths exist necessarily. And as far as I can tell, nothing that Adams says in the passage above contradicts that.

WL,

That is true, but the point is, we cannot be assured propositions exist in (or at) those worlds where they otherwise would be true. In other words, you need to actually show that necessary truths exist necessarily---which seems an impossible task.

Or, at least, that's the point I've been trying to make.

Ben-

I've got to deal with some other matters at present. I'll see whether I can't craft a reply a bit later this evening or early tomorrow morning.

Modal Logic is complex, but, for some more digestible looks at “necessary truth” one can look at this link here for a basic form. One can look at this link here to see a move to redefine terms, and there is this link here to see a brief look at the move toward universal possiblism, the basic assertion that there is no necessary truth. The Stanford Encyclopedia of Philosophy has several essays on Modal Logic as well but you may have to join / pay a fee to download PDF’s. Eventually this will bring one into that “Y” in the road where Abstractions / Forms / Logic seem to be something God is enslaved to, or, such “things” are the thoughts of an Infinite, and Necessary, Mind. Two brief looks at that arena are this link here and at this link here. As for the unavoidable contextual geography of relationality that just is the language of abstractions / forms, such just is housed within the Triune interior of the Christian God.

Ben-

I'm sure you won't like this, but I'm still not sure what's wrong with this proof:

  1. Necessary truths are true no matter which world is actual.
  2. For that to be the case, they must exist in every possible world.
  3. Therefore, Necessary truths exist in every world.
I think premise 1 is true because necessary truths are true no matter what. That's what I think "necessary truth" means...propositions that are true no matter what.

Notice that I need not understand the necessity of necessary truths in terms of truth in or at possible worlds. I may understand it, per Adams, in terms of modal properties that actually existing entities do have. Such propositions, whatever else you might say, are actually existing entities. Those actually existing entities have the modal property of being true no matter what.

But because necessary truths have the property of being true no matter what, they have the property of being true no matter which possible world is the actual one. Thus premise #1.

WL,

I don't think that's what "necessary truth" means, for the reasons outlined above. After all, by your definition, it's not clear that there are any necessary truths, since we don't know whether propositions exist in all possible worlds.

To put it another way, I think our definition of "necessary" should be guided at least by that special collection of what you might call purely logical truths. If we cannot verify that, say, the law of identity is necessarily true according to some suggested definition of necessity, then so much the worse for that definition!

But, on your definition, there doesn't seem to be any way to verify that the law of identity is necessarily true. So, that's why I think your definition is insufficient.

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