The usual explication of these two and the distinction between them is that the a priori statement is universally and necessarily so. — tim wood

And a posteriori statements, of course, require access to some experience - they could be so or not so, depending on the verdict of that experience. — tim wood

That water is H₂O is something we discovered - it is a posteriori, and synthetic.

Kripke shows that, that water is H₂O is true in all possible situations; that is, if we discover or stipulate a substance that is phenomenologically the same as water, but with some alternate chemical structure, it is not water.

Since it water is H₂O is true in all possible situations, it is necessary.

So, that water is H₂O is a necessary, a posteriori fact. Necessary but synthetic.

Hence, not all necessary facts are synthetic.

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First, who said they were? Did you forget analytic a priori statements? — tim wood

OK - is, that H₂O is water, a priori? I wouldn't have thought so. Analytic, necessary - but a posteriori.

I'm under the impression that you are a professional philosopher and thus am astonished you don't have understandings of Kant that are very clear indeed.. — tim wood

Happy for you to correct me.

"It" is not something we discovered. "It" is not a posteriori. Nor synthetic. As to the discovery itself, that is not water. — tim wood

Not too sure what you are saying. That water is H₂O is surely not a priori?

have to be more than a little careful in matching Kant against certain modern discoveries. — tim wood

Wouldn’t Herr Kant freak if he was around about the time they broke water down into its constituent parts? (Vion, 1869) Actually, no, probably not. Being an astrophysicist and a professor of math and physical science, he’d hardy be amazed. Hell, he probably could have done it himself.

Kripke or no, modern science or no, because water is a real object “All water is H2O” is an empirical judgement, hence synthetic, and from the proposition, the predicates of hydrogen and of oxygen absolutely cannot be derived from merely the subject “water”, hence, still synthetic.

“....But now I extend my knowledge, and looking back on experience from which I had derived this conception of body (water), I find weight (H2O) at all times connected with the above characteristics, and therefore I synthetically add to my conceptions this as a predicate, and say, "All bodies (water) are (is) heavy (H20)”. Thus it is experience upon which rests the possibility of the synthesis of the predicate of weight (H20) with the conception of body (water), because both conceptions, although the one is not contained in the other, still belong to one another, only contingently**, however, as parts of a whole, namely, of experience, which is itself a synthesis of intuitions....”
**contingently, re: heavy water. The concept of water in and of itself is not altered by the additional mass of a neutron in the nucleus of one atom.

Parentheses are mine, obviously, because I didn’t want to delete or subvert what ws actually said in the quote, but to show the particulars are pretty much identical.

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Supposed the nebula theory for galaxy creation, actually. Along with tidal forces making the moon’s orbit decrease, the prediction that stars were uncountable, the abolishment of Newtonian absolute time, the requirement for a constant velocity related to the motion of matter. Course, it was all metaphysical theory with no math or experiment, and Newton ruled the scientific roost, so.......

Then along comes GR, and the synthetic a priori judgement of all geometric properties goes right square.....well, you know the rest of the story.

Ah. You see, Tim, at my school we were taught that a priori and a posteriori were about how we found things out.

a priori stuff was found out by considering only the concepts involved. It was what comes before.

a posteriori stuff was found out by looking around. It was what comes after.

Now, on that way of thinking, that water is H₂O is an empirical discovery, and hence a posteriori. And yet necessarily true.

implies that what is verified by observation/experience, is with respect to the quality of the verification, the same as what is "verified" by logic. — tim wood

Not sure I understand this properly, but assuming the quality of the verification to mean the strength or weakness of its agreement, then it seems to me there’s no conflict. Observation is supposed to qualify a logical proposition.

The empirical "judgement" that water is h2o, were that final, would imply there is water that is not h20, or that water might not be water. — tim wood

It isn’t final, it’s contingent, as are all judgements based on experience. And it does imply it is possible there is water that isn’t H20, re: heavy water. As long as we conceive water as the chemical bond between hydrogen and oxygen, we can allow certain different combinations of them without contradicting the physical substance called “water”. Can’t we?

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In other words, synthetic a priori metaphysical concepts are the pre-conditions of all experience. Hence, Kant distinguishes between the world as experience it (the world as it is experienced given the application of said concepts) and the world as it is independent of our experience. — philosophy

Gold is a yellow metal.

That's not an analytic expression. Nor is it a priori. Given a suitable arrangement of lights, one could make gold appear purple.

But let's consider something easier-the question of the
yellowness of gold. Could we discover that gold was not in
fact yellow? Suppose an optical illusion were prevalent, due to
peculiar properties of the atmosphere in South Africa and
Russia and certain other areas where gold mines are common.
Suppose there were an optical illusion which made the substance
appear to be yellow; but, in fact, once the peculiar
properties of the atmosphere were removed, we would see
that it is actually blue. Maybe a demon even corrupted the
vision of all those entering the gold mines (obviously their
souls were already corrupt), and thus made them believe that
this substance was yellow, though it is not. Would there on
this basis be an announcement in the newspapers : 'It has
turned out that there is no gold. Gold does not exist. What
we took to be gold is not in fact gold.' ? Just imagine the world
financial crisis under these conditions ! Here we have an undreamt
of source of shakiness in the monetary system.

It seems to me that there would be no such announcement.
On the contrary, what would be announced would be that
though it appeared that gold was yellow, in fact gold has
turned out not to be yellow, but blue. The reason is, I think,
that we use 'gold' as a term for a certain kind of thing. Others
have discovered this kind of thing and we have heard of it.
We thus as part of a community of speakers have a certain
connection between ourselves and a certain kind of thing. The
kind of thing is thought to have certain identifying marks. Some
of these marks may not really be true of gold. We might discover that we are wrong about them. Further, there might be a substance which has all the identifying marks we commonly
attributed to gold and used to identify it in the first
place, but which is not the same kind of thing, which is not
the same substance. We would say of such a thing that though
it has all the appearances we initially used to identify gold, it is
not gold. Such a thing is, for example, as we well know, iron
pyrites or fool's gold. This is not another kind of gold. It's a
completely different thing which to the uninitiated person
looks just like the substance which we discovered and called
gold. We can say this not because we have changed the meaning
of the term gold, and thrown in some other criteria which
distinguished gold from pyrites. It seems to me that that's not
true. On the contrary, we discovered that certain properties
were true of gold in addition to the initial identifying marks
by which we identified it. These properties, then, being
characteristic of gold and not true of iron pyrites, show that
the fool's gold is not in fact gold.

Naming and Necessity, pp. 118-9

A world independent of our experiences is a world about which we can say nothing. And of that of which we cannot speak, we ought not speak.

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Just staying in my lane, doncha know. Kant said *ALL* mathematical expressions, particularly geometric formulations, are synthetic a priori propositions. He had to, of course, because he was looking for laws based on principles, which cannot have exceptions. Curved space was something he hadn’t envisioned, so he was wrong about *ALL* expressions, for some predicates of Euclidean geometry do not hold under Riemann configurations. For us guys with no use for Riemann configurations, we don’t care that much; I never fly far enough for minimal geodesics to make any difference I would notice, and event horizons are not in my immediate future. Well....unless something bad happens at CERN.

And that region of epistemology he did claim? He claimed it well and truly.

Fine.

Kant said:

First, as concerns the sources of metaphysical cognition, its very concept implies that they cannot be empirical. Its principles (including not only its maxims but its basic notions) must never be derived from experience. It must not be physical but metaphysical knowledge, viz., knowledge lying beyond experience. It can therefore have for its basis neither external experience, which is the source of physics proper, nor internal, which is the basis of empirical psychology. It is therefore a priori knowledge, coming from pure Understanding and pure reason.

But Tim said:

Reverting to the definitions of my youth, that the a priori are necessarily and universally so, then it follows that water, being just H2O, is so a priori.

The discovery that water is H2O is a different topic. All discoveries are empirical, aren't they? But the thing, fact, truth, discovered, as a thing, fact, truth.... I suspect you can complete, already have completed, this line of thought. — tim wood

I find this hard to reconcile.

I could be wrong, but looking at this debate, it seems that the basis for your confusions as to each other's arguments and conclusions is not clearly defining the difference between something that is "synthetic a priori" (pace Kant) with something that is necessary (analytic?) a posteriori. I think much of the confusion will dissipate if these two are clearly differentiated.

“.....For this very reason all analytical judgments are a priori even when the concepts are empirical, as, for example, Gold is a yellow metal....”
Preamble, Sec2b,

This I grant willingly; gold is an elemental substance to which the law of contradiction would necessarily hold. Water, a compound substance, on the other hand, doesn’t have to be H2O necessarily.

Maybe. For my part, roughly...

Synthetic Vs. analytic: it's synthetic if it brings two distinct ideas together; it's analytic if one idea is contained in the other.

a priori vs a posteriori: it's a posteriori if you have to look around to find it out. Otherwise it is a priori.

Necessary Vs. contingent: it's necessary if it is true in all possible worlds; otherwise, it's contingent. This is where I would expect Tim and I to disagree.

Hence: synthetic a priori: two distinct ideas that are associated without looking around.

and, necessary a posteriori: found out by looking around, but true in all possible worlds.

Necessary Vs. contingent: it's necessary if it is true in all possible worlds; otherwise, it's contingent. This is where I would expect Tim and I to disagree. — Banno

First thing that might cause confusion is the addition of necessary and contingent. Though very related to synthetic and analytic, it is different, and by the time of Kripke there might have been further refinements as to analytic vs. necessary and synthetic vs. contingent. Thus, we might not be speaking in the same languages and creating a sort of category error.

To move forward we should give examples. Banno said:

Hence: synthetic a priori: two distinct ideas that are associated without looking around. — Banno

So what would be your ideal example? Kant uses certain scientific truths that can only be gained through our a priori psychological predisposition for space/time/causality (and other categories).

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First thing that might cause confusion is the addition of necessary and contingent. — schopenhauer1

And yet,

(for what is declared to be known a priori is thereby announced as necessary)

And it is this necessity in which I am interested.

So, is being a priori the very same thing as being necessary? Or is it rather that all a priori things, amongst others, are necessary?

So, Tim: if some thing is true a priori, is it also necessary?

And what do you make of the case, in the Kripke text I quoted above, in which we ponder what it might have been like of gold were not yellow?

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So, is being a priori the very same thing as being necessary? Or is it rather that all a priori things, amongst others, are necessary? — Banno

I believe he thought a priori truths to be necessary and/or universal. I would assume he is saying they are the same thing. Really the tricky part with Kant is his idea of analytic and synthetic. Analytic seems to be a sub-set of a priori that are tautologies. The meaning is in the subject- you don't have to look any further. Many philosophers think that math is just this.

However, if a priori means necessary and universal, then there is another sub-set people don't think about- synthetic truths that are always necessary and universal. Thus, many proofs in math are universal and necessary, but are not tautologies, they have to be found out in the world. Where does this ability come from to gain universal truths that are not just odd pairings (pace Hume)? It comes from a priori synthetic categories of our psychology.

That water is H₂O is something we discovered - it is a posteriori, and synthetic.

Kripke shows that, that water is H₂O is true in all possible situations; that is, if we discover or stipulate a substance that is phenomenologically the same as water, but with some alternate chemical structure, it is not water.

Since it water is H₂O is true in all possible situations, it is necessary.

So, that water is H₂O is a necessary, a posteriori fact. Necessary but synthetic.

Hence, not all necessary facts are synthetic. — Banno

I wonder to what extent this bears on Kant. You've had your hands full discussing Kripke with people who want to discuss Kripke, but not on Kripke's terms. In threads specifically discussing Kripke, their's seems like a bad approach. But once you leave Kripke's province....I've seen you say, elsewhere, that you think Kripke is confusing metaphysics and grammar. And so...

(the above being, largely, a self-serving apology for commenting on Kripke, without really knowing Kripke, just like everyone else, but...)

We've identified something as water. Then we learned some. And we learned that what we identified as water always has the structure H2O. Now:

if we discover or stipulate a substance that is phenomenologically the same as water, but with some alternate chemical structure, it is not water. — Banno

Here's a scenario that it seems like Kripke would admit is possible (seems that way to me anyway, correct me if wrong). Let's say some group of people coined the word 'water' talking about a pond in their town X. Visitors to this town (there's a trade route or something. the water people have silk, say, so people go there a lot, to get silk) ---but visitors to this town pick up this term. "water. That's like the stuff we have at home! We'll call it water too!." Years go by, science grows. Less syphilis, more television. People in town x learn chemistry etc. Water, in their pond, is H20. For whatever reason, though, what's called 'water' everywhere else has a different chemical structure. There is only one place with H20 water as far as we know, and its in the pond of town X. All the other 'water' is something else entirely.

What are we talking about when we talk about necessary, a-posteriori facts? And what does it have to do with Kant?

What are we talking about when we talk about necessary, a-posteriori facts? And what does it have to do with Kant? — csalisbury

Kripke introduces "all possible worlds" to the idea of natural kinds. So, in all possible worlds, the term "water" is always H20. This means that water is necessarily H20.. It didn't have to be H20 before it was named thus, but once someone used it as a name for water, it became a necessary truth "after the fact". It didn't have to be from the outset like a synthetic a priori truth. If it was a synthetic a priori truth, H20 would always have to have been named water, but that would be silly. So at least in the cases of proper names and natural kinds, there may be a kind of truth statement that Kant didn't account for which is necessary a posteriori truths.

It didn't have to be H20 before it was named thus, but once someone used it as a name for water, it became a necessary truth "after the fact". — schopenhauer1

I think I follow so far. That's why, in my example, I talked about a specific village who named the substance in their pond.

This wouldn't change much I think. Just like there can be two Johns who are not the same person, so too do you have two waters. It is not the name itself but the idea that it is fixed to a referent in all possible worlds.