Interesting thread, @tim wood.

The question for me is, if ɸ is a priory, is ɸ also necessary?

Kripke takes Kant as saying this.

I like the entry Possible Worlds and Modal Logic in SEP.

It sets out how possible world semantics (PWS) solves the issue of substitution for modal logic.

I'm not a logician. I'm Happy to be corrected by those with a better understanding. But as I understand it, in PWS the existential and universal quantifiers are understood within each possible world, while the necessity and possibility quantifiers are understood across all possible worlds.

So within each possible world we can have different assignments of predicates to individuals.

We have lots of different possible worlds each with different bunches of the same individuals, being assigned different bunches of predicates.

If an individual or group of individuals has the same predicate in all possible worlds, it necessarily has that predicate: Bachelors are unmarried in all possible worlds.

If an individual or group of individuals does not have a predicate in any possible world, it is not possible.

If an individual or group sometimes has a given property, sometimes not, then it is a possible property.

But as I understand it, in PWS the existential and universal quantifiers are understood within each possible world, while the necessity and possibility quantifiers are understood across all possible worlds. — Banno

This is correct.

If an individual or group sometimes has a given property, sometimes not, then it is a possible property. — Banno

That's actually the definition of contingency. Possibility is just defined as truth in at least one world. Necessary truths, for example, are still possible truths because they fit that condition. Contingency means true in some worlds but false in others.

If an individual or group of individuals has the same predicate in all possible worlds, it necessarily has that predicate: Bachelors are unmarried in all possible worlds. — Banno

This has always been odd for me. It seems like one could have a married bachelor. What makes one married is to hold a certain legal status, yes? Well consider a state of affairs where there's a contradiction in the local laws. Law A says "Yada yada Those holding a marriage certificate are married" and Law J says "Etc etc Gay people cannot be married". Now some gay person managed to get married (certificate and all), and there is no judicial precedent in how judge which law overrules the other. On the usual assumption that law decides what is true in these cases (because that's how we know who is considered married), one would seem to have a married bachelor.

Kant:

b. The Common Principle of all Analytical Judgments is the Law of Contradiction. --- All analytical judgments depend wholly on the law of Contradiction, and are in their nature a priori cognitions, whether the concepts that supply them with matter be empirical or not. For the predicate of an affirmative analytical judgment is already contained in the concept of the subject, of which it cannot be denied without contradiction. In the same way its opposite is necessarily denied of the subject in an analytical, but negative, judgment, by the same law of contradiction. Such is the nature of the judgments: all bodies are extended, and no bodies are unextended (i.e., simple).

For this very reason all analytic judgments are a priori even when the concepts are empirical, as, for example, "Gold is a yellow metal," for to know this I require no experience beyond my concept of gold as a yellow metal. It is, in fact, the very concept, and I need only analyze it, without looking beyond it elsewhere.

The law of contradiction holds in PWS. In no world can there be a contradiction. But there can be differences between worlds; so while my cat is all black in this world, in another possible world it might be all white; yet in no possible world is my cat both all black and all white.

Now Kant says that it is part of the concept of gold that it be a yellow metal, and hence that being a yellow metal is a priori.

And yet it is eminently possible that gold might be a different colour. So in some possible world there might be red gold.

So being yellow is not a necessary characteristic of gold.

SO it seems that either Kant was in error about gold, or that a priori and necessity are different things.

That's actually the definition of contingency. Possibility is just defined in truth in at least one world. Necessary truths, for example, are still possible truths. Contingency means true in some worlds but false in others. — MindForged

Fair enough.

This has always been odd for me. It seems like one could have a married bachelor. What makes one married is to hold a certain legal status, yes? Well consider a state of affairs where there's a contradiction in the local laws. Law A says "Yada yada Those holding a marriage certificate are married" and Law J says "Etc etc Gay people cannot be married". Now some gay person managed to get married (certificate and all), and there is no judicial precedent in how judge which law overrules the other. On the usual assumption that law decides what is true in these cases (because that's how we know who is considered married), one would seem to have a married bachelor. — MindForged

That just looks like an invalid marriage to me. I don't see a philosophical issue here, just a legal one.

But what would make it valid or not would be for a precedent to be set by a judge ruling on the case. Prior to that it's a contradiction in the law. One law says they're married (they hold the certificate) the other says they aren't (they're a gay couple), and it's the law which establishes who is married or not.

indeed; and if they are married, they are not bachelors; and if they are not married, they are. It's not a case of one without the other.

"Gold is a yellow metal" or "a bachelor is an unmarried man" — tim wood

All those types of statements really tell us is how an individual has formulated their concepts. It's telling us either what they require to call some x (some particular) an F (some type term), or alternately it's announcing terms they use as synonyms.

The only necessity invoked there is the stringent stipulation of the individual in question.

I've no idea how this helps.

It explains what's really going on with those statements contra Kant's misconceptions, and it explains the only sense in which we could say that they're "necessary."

Have you ever witnessed something you can't imagine? IOW, do experience and imagination have the same boundaries?

You like the word really - what is really going on; what the statement really tells us. I'm not so keen. I still do not see how your post explains anything.

Let me try this: is gold a yellow metal? Is gold any other color? Assuming the answer to these are yes and no respectively, then it seems right to say that if there is gold, then it is a metal and it is yellow, and, if it is either not metal or not yellow, then it is not gold.

As to necessity or possibility, neither of these apply. Gold just is a yellow metal.

Now let's consider something else, the judgment that "gold is a yellow metal," this being one of Kant's analytic a priori judgments. The concept that gold is a yellow metal informs the judgment that gold is a yellow metal. The judgment expresses the concept. As such, it is a priori. and by content of the judgment, analytic. By all possible evidence, it's also true.

I like the entry Possible Worlds and Modal Logic in SEP. — Banno

I am glad you like it, I infer from that you can answer my question as to what possible worlds are. Were it clear, I would not tax you to make it clear. What it cannot mean is conceivable worlds. That leaves "possible." But what does possible mean? In part of the SEP article, possible worlds seems to be just those worlds that could alternatively have been, if something in the actual world had been other than it was. Which is to say that the possible worlds, by virtue of not being, and consequently of not being possible, are merely conjectural, and even that only minimally (for "minimally, read asymptotically not at all).

The notion of "all possible worlds" appears to be a created artifact - a tool - of a branch of logic. We can imagine a dialogue between Hiho the jeweler and Hoho the semanticist. Hoho consults Hiho about a ring for his sweetie. Hiho tells Hoho in the course of the consultation that "gold is a yellow metal."

"Not always," says Hoho, "Gold might be blue laundry detergent is another world."
"What world might that be," queries Hiho, "and where is it?"
Hoho: "Oh, it's not a real world; it's not anywhere. It's just a possible world."
Hiho: "And how would that be possible?" (Keeping in mind gold is an element.)
"it's not actually possible. We semanticists just talk these thing into being so we can solve certain problems in logic - not really anything to do with any real world. Your gold is, was, and always will be a yellow metal."

And it is clear that in speaking about the various golds of all possible worlds, that the entire phrase, gold-of-all-possible-worlds is in fact a noun substantive that has nothing to do with gold, AU, other than to share a few letters in common. And this is a common error in many areas where a name used uncritically is confounded with something else that the name in question properly applies to.

And further: the SEP article mentions necessity, true in all possible worlds, and possibility, true in at least one possible world. But how can anything be true in all possible worlds? It certainly seems to me that something true in one such world could be untrue in another. After all, it's all possible worlds, yes?

Necessary statements are commands or policies, i.e. speech acts, whose origin of force is the intentions of the speaker or institution who asserted them. This includes metaphysical assertions, ethical assertions and all universally quantified 'propositions' over infinite domains in science and mathematics.

So "Bachelors are unmarried men", when interpreted as expressing a necessary truth, is to declare a policy allowing the substitution of the former as a synonym for the latter without exception. Hence the image of it holding in "all possible worlds".

However, when interpreted as expressing a publicly verifiable proposition "Bachelors are unmarried men" is both contingent and under-determined.

...then it seems right to say that if there is gold, then it is a metal and it is yellow... — tim wood

I don't see that you can escape modality quite so easily. Suppose a mine starts digging out red gold. Same mailability, same atomic mass, same melting point. Would you say it is red gold, or not gold?

If being yellow is a part of the very concept of gold, you must say it is not gold.

Possible worlds.

The best way to understand them is by seeing how they are used in possible world semantics.

It's simply a way to parse any modal statement. Possible worlds are specified by our speculations. What if Tim Wood had been Jim wood? That can be parsed as: In some possible world, Tim wood is known as Jim Wood.

In some possible world, gold might be red. In no possible world could gold have a different atomic mass, because no longer would it be gold - it would be something else.

But how can anything be true in all possible worlds? — tim wood

2+1=3 in all possible worlds. If it did not, we would not be talking about 2,3,+, or =.

Water is H₂O in all possible worlds. If it were not, we would not be discussing water.

Relevance?

Have you forgot that gold is an element? Alloyed, it can be all kinds of colors. And alloyed, it is alloyed gold, not gold. But in my opinion you're missing a deeper point. Perhaps this way. Posit something certain. Then subject it to your criticism that maybe someday somebody might dig up or discover.... Allow that, and absolutely nothing stands. I argue that we do have our certainties, perhaps fewer than most folks would like to think, but certain nevertheless. But, you say, understandings change! And indeed they do, and it matters, if you have in mind our absolute presuppositions. But as they are the constitutive concepts for what we call reality, and reality seems pretty stable, they - the concepts, the absolute presuppositions - change but seldom.

Have you forgot that gold is an element? Alloyed, it can be all kinds of colors. And alloyed, it is alloyed gold, not gold. — tim wood

no - hence my specification of atomic mass.

no - hence my specification of atomic mass. — Banno

And you don't see how this upends your apple cart thus annoying you donkey?

But in my opinion you're missing a deeper point. Perhaps this way. Posit something certain. Then subject it to your criticism that maybe someday somebody might dig up or discover.... Allow that, and absolutely nothing stands. — tim wood

Perhaps I see see beyond your deeper point...

let's debar the Humpty Dumpty world where words mean whatever we choose.

Then if we find a red substance with otherwise the same properties as gold, we have a choice: is it gold, or is it not-gold? what attributes are essential to gold? Kant, and perhaps you, say colour is; i say it isn't.

So set it out for me. I'm a slow old man.

On the contrary, I think of you as a father figure of TPF - or maybe granpaw.

Anyway, you want your gold; you want to call it gold; you want it to have the same atomic structure; but you want it to be different. Can you reconcile those, without going all Humpty-Dumpty? And I don't know about you, but I think I'm done till tomorrow. Domestic bliss calls....

TPF — tim wood

TPF?

The Philosophy Forum.

Ah. Said I was slow.

you want to call it gold... but you want it to be different. — tim wood

That's not an issue: I want my cornflakes not as they are in the pack, but slightly soggy from cold milk. I want my I want my beard longer. Such things do not make these not my cornflakes or this not my beard.

Achieving almost complete incoherence! Is it the wanting that does not make these not your cornflakes or not your beard? Are possible worlds just a thought? We joke, but I'm serious. Semanticists can create any animal they feel they need for their ow purposes, but as with any errant creativity, their's is subject to disciplines and controls, and being kept in its cage. "Possibility" is possibility, not license.

Relevance? — Banno

The limits of imagination are the limits of the knowable. So for all practical purposes, the limits of imagination are the limits of what is. In cases where we can't imagine X, it seems we know a priori that X doesn't and can't exist. Necessarily, there is no X.

With a posteriori knowledge, we are being informed about what's out there. As long as we can imagine things being other than they are, there are only contingently true statements related to a posteriori knowledge.