So the reliance on counterfactual definiteness is here? That perhaps a coin was emitted in an indefinite state but we can’t observe indefinite states, only definite ones. This is like your grid-world example with the direction of the unobserved arrow. — Srap Tasmaner

Yes, exactly.

So the issue is that in some cases there might be no fact of the matter, no definite state, but if we take a measurement, we’ll always find that there is. — Srap Tasmaner

Yes.

And then counterfactual definiteness is specifically the claim that since our measurements always show definite states, then what we measure — or, more specifically, what we intend to measure or consider or imagine measuring, must always be in a definite state because indeed that’s what measuring it would show. — Srap Tasmaner

Yes, and this is a reason why some physicists and philosophers are not so happy with the term "measurement" here, because it seems to imply that the coin (or particle) is in a definite state prior to measurement.

Here's physicist Asher Peres on this:

In this review we shall adhere to the view that [state] p is only a mathematical expression which encodes information about the potential results of our experimental interventions. The latter are commonly called "measurements" - an unfortunate terminology, which gives the impression that there exists in the real world some unknown property that we are measuring. Even the very existence of particles depends on the context of our experiments.
...
The essential difference between the classical and quantum functions which change instantaneously as the result of measurements is that the classical Liouville function is attached to objective properties that are only imperfectly known. On the other hand, in the quantum case, the probabilities are attached to potential outcomes of mutually incompatible experiments, and these outcomes do not exist “out there” without the actual interventions. Unperformed experiments have no results. — Quantum Information and Relativity Theory - Peres, Terno

The point was that we cannot say whether or not "Alice has knowledge" under your description of "knowledge", unless we infallibly know whether or not it is raining. — Metaphysician Undercover

When I point out that a premise of the hypothetical is that it is raining, I'm not claiming that it's actually raining outside, here in the real world.

Before continuing with this, I want to point out that truth is very much the issue at stake in all of these apparent detours.
... — Srap Tasmaner

:up: I agree with all you said there.

Is this the claim? If each coin left box 1 with a definite state, then it would enter box 2 with a definite state, and if all of the coins entered box 2 with a definite state, then we should see some coins not in their initial orientation? — Srap Tasmaner

Yes.

Since we don't, it must not be true that coins leave box 1 and enter box 2 with a definite state. — Srap Tasmaner

Correct (given plausible assumptions, namely locality and no-conspiracy).

What I don't get is that the behavior of the boxes is defined only for coins entering with a definite state, and as emitting coins only in a definite state. — Srap Tasmaner

Not quite. What is defined is what happens when a coin in an initially definite state goes through one or more black boxes and then is finally measured to be in a definite state.

What are the boxes doing if not that? Isn't this a way of saying that the behavior of the boxes is not entirely definite? — Srap Tasmaner

Not necessarily. The boxes may operate in a well-defined (definite) way, but are instead able to input and output coins in an indefinite state. But that can't be directly confirmed since a coin is always measured to be in a definite state.

The example shows that human fallibility doesn't preclude Alice from knowing that it is raining.
— Andrew M

The example cannot serve this purpose, because it premises that we can know up front, infallibly whether or not it is raining. — Metaphysician Undercover

No, not infallibly. One can possibly be mistaken about what the premises of the hypotheticals are. But since they are clearly stated, there's no good reason why anyone should be mistaken.

all we need is this:

(Card) If and only if there is a one-to-one correspondence between the coins in a jar and the set of natural numbers less than or equal to k, for some natural number k, then the number of coins in the jar is k and there is a definite number of coins in the jar.

That’s just the definition of cardinality for finite sets plus existential generalization. We don’t need counterfactuals for that, and we don’t need them for this:

(Count) If and only if a jar contains k coins, then counting the coins in the jar yields the value k.

This definition of cardinality for finite sets might as well be a description of counting; there’s almost nothing else to say. — Srap Tasmaner

Looks good to me!

I see how your coins and boxes are analogous to photons and interferometers, but I’m still not getting the point here. — Srap Tasmaner

Assuming the coin always has a definite heads or tails state, even when not measured, what definite state could it have had when it was between the two black boxes? It seems that the coin couldn't have had a definite state, contrary to assumption. (Which is why it is modeled with a wave function, or a linear combination of definite states, or a sum over histories, etc.)

But! I think I have thought of the perfect example, because it also involves making calculations based on values that you should not be using: the two envelopes problem.

Refresher: The only right way to do this is to treat the envelopes as X and 2X; you don’t know which one you got, so you stand to gain X or to lose X by switching, and the expected value of switching is 0. But if instead, you call whatever you got Y, and then reason that if it’s the bigger the other is Y/2, and if it’s the smaller then the other is 2Y, then the expected value of switching is Y/4.

It could be that exactly what’s wrong with this analysis is that it relies on counterfactual definiteness. (Oddly, like the black boxes and the interferometers, there are points in the defense of this analysis that rely on the principle of indifference giving equal chances to events, and then relying on those chances as if they were real values. Among many many other issues.) — Srap Tasmaner

Definitely interesting to think about.

Talk of switching in either the X or the Y analysis is counterfactual. Why does one of them work and the other not? — Srap Tasmaner

Because the Y analysis solves a subtly different problem. Namely, when you choose an envelope, suppose the unchosen envelope is emptied and then randomly filled with half or twice the amount of your chosen envelope. So you should switch in that case.

In terms of counterfactual definiteness, in the original scenario the envelopes have a definite and unchanging state throughout the experiment. Whereas the in latter scenario, the state of the envelopes can change, depending on your choice, so in a sense is indefinite. Though, of course, at each point in time the envelopes have a definite state.

If you didn't know which scenario was in play then you would have to collect data, compare the switching strategies and come up with a model of how the envelopes were filled.

The issue was, if it must be raining in order for Alice to know that it is raining (i.e. true in your sense), then knowledge is infallible. How does this example show that knowledge is fallible? — Metaphysician Undercover

It doesn't. The example shows that human fallibility doesn't preclude Alice from knowing that it is raining.

What type of knowledge do you assume that a "hypothetical" gives someone? — Metaphysician Undercover

A hypothetical (or thought experiment) shows the consequences of particular premises.

The ancient Greek deiknymi (δείκνυμι), or thought experiment, "was the most ancient pattern of mathematical proof", and existed before Euclidean mathematics,[6] where the emphasis was on the conceptual, rather than on the experimental part of a thought-experiment. — Thought experiment - Wikipedia

When you assume hypothetically that it is raining, this does not mean that you have knowledge that it is raining. — Metaphysician Undercover

No. But the hypothetical shows the consequences that follow when it is raining. Namely that Alice knows that it is raining when, in addition to it raining, she has a justified belief that it is raining.

What I have been claiming about the number of coins in a jar is simply that we can know a priori that if they can be counted then there is already a specific number of coins in the jar; we can only know a posteriori what that number is.

I do not think I have ever had occasion to make a claim to knowledge that so clearly fits the definition of a priori. Whaddya know. — Srap Tasmaner

Cool! Yes, I think that crystallizes the discussion.

Perhaps this also says something about how the word "count" is used. For example, if Bob was randomly adding and removing coins from the jar while Alice was endeavoring to count the coins, would we be willing to say that Alice was actually counting the coins in the jar?

The way I'm thinking about this is that we have a conceptual scheme for how things work (a priori), but this is continually informed by our experience (a posteriori), such that it is possible for our conceptual scheme to change. As part of that, our mathematics can also change. Not necessarily in the sense of x being wrong and y right, but instead that we find that y is a more natural fit than x in particular situations.

I'm reminded of Rovelli's paper that argues for the contingency of mathematics:

If there is a "platonic world" M of mathematical facts, what does M contain precisely? I observe that if M is too large, it is uninteresting, because the value is in the selection, not in the totality; if it is smaller and interesting, it is not independent from us. Both alternatives challenge mathematical platonism. I suggest that the universality of our mathematics may be a prejudice hiding its contingency, and illustrate contingent aspects of classical geometry, arithmetic and linear algebra. — Michelangelo's Stone: an Argument against Platonism in Mathematics - Carlo Rovelli

So to apply this to counterfactual-definiteness, here's a hopefully simple example of what might motivate the questioning of it based on experience (at least for some scenarios).

Suppose that we have a coin, a measuring device (or just observing is OK) and one or more black boxes. When we measure the coin, it is always heads or tails. When we send the coin through the black box and then measure it, it has the orientation it started with only half the time (and not with any discernable pattern). We put this down to the black box having a randomizing element that sometimes flips the coin, sometimes not. Regardless, there's no need to question counterfactual-definiteness.

One day, someone decides to link two black boxes together, send a coin through them both, and then measure it. To their surprise, they find that the coin is always measured with the same orientation that it started with.

As evidenced by their surprise, this is a case of experience potentially bringing their conceptual scheme into question. So the challenge is to come up with a natural explanation for all the above measurements (which may either preserve their conceptual scheme or require a change to it).

They are hypothetical scenarios, and you know up front whether or not it is raining in each scenario. In the first scenario, it is raining (that's a given premise of the hypothetical). In the second scenario, it is not raining.
— Andrew M

You're missing the point. Unless you explain how one could "know up front" whether or not it's raining (someone might be hosing the window), you are just begging the question. — Metaphysician Undercover

You and I know up front because I created the hypotheticals that way. The question is not about what you and I know, which is a given, but about what Alice knows.

You didn't even have to align your direction right on the North-South axis to get here: if it were pointing exactly Northeast (45° off North), or, you know, almost anywhere, it's not aligned on either of your canonical axes! Oh my god! Its direction is undefined! — Srap Tasmaner

That's almost exactly the point. Suppose that you live in a grid world where you can only move and measure things along the North-South or West-East axes. Now an unobserved arrow might be mathematically represented as North-East in grid world (i.e., a linear combination of North and East arrows). But an arrow is only ever observed pointing along one of the grid lines. Thus raising the question of which direction the arrow is actually pointing (if it has a definite direction at all) when not observed.

I'll give a real-world example now. Suppose that you have an interferometer (see Figure 3) and a photon travelling East hits the first beam splitter. The photon could reflect and travel North, or continue East. Since we don't know which way the photon went, let's represent it with a North-East arrow. But, assuming counterfactual-definiteness, it's definitely travelling the North path or definitely travelling the East path. In fact, if we place detectors on those two paths, we will indeed measure the photon on one or the other of those paths.

So far so good. Now suppose we don't measure which path the photon takes. In this case, the photon will arrive at a second beam splitter where it will again either reflect or continue in the same direction. The classical prediction is that the photon will end up at either detector 1 or detector 2 with equal probability (i.e., a North path photon will either reflect or continue in the same direction; same with the East path photon). But what actually happens is that the photon is only ever measured at detector 1, as predicted by QM.

QM represents the photon as being in a linear combination of travelling both paths which results in interference at the beam splitter. One could say that the linear combination (the North-East arrow) is just a mathematical representation, and that the photon took one and only one definite path (a hidden variable that is definitely North or definitely East). But there are various no-go theorems that say, in effect, that that purported solution creates more problems than it solves.

Isn't this like asking for the z coordinate of a point plotted on a plane? — Michael

Not quite, since one can conceive of a z coordinate even if it is not plotted. For example, a bird (at z altitude) that casts a shadow (point) on the ground (plane). Or if there is no z-dimension, z is always 0.

Whereas in the analogy, there is only one arrow pointing North. So there is no sense in which that arrow points definitely either West or East.

The issue is, who determines whether or not it is raining. Here, you are asserting "In the first scenario it is raining, in the second scenario it is not". Do you know whether or not it is raining in each scenario, in an absolute way? If so, I can give you an answer. If not, I cannot. This is because I cannot say whether Alice has knowledge or not unless I know infallibly whether or not it is raining. You have provided no justification for your assertions, therefore I cannot honestly give you an answer. So I do not believe that you know infallibly whether or not it is raining in each of those scenarios — Metaphysician Undercover

They are hypothetical scenarios, and you know up front whether or not it is raining in each scenario. In the first scenario, it is raining (that's a given premise of the hypothetical). In the second scenario, it is not raining.

In the first scenario, Alice has a justified, true belief that it is raining, i.e., she knows that it is raining. In the second, Alice's belief is false, so she does not know that it is raining.

That is, according to your representation of "knowledge", which requires infallibility. — Metaphysician Undercover

No, as demonstrated by the first scenario, Alice knows that it is raining not because she is infallible (or because she had ruled out all other possibilities such as Bob hosing the window), but because she had a justified, true belief.

I think the mathematical vocabulary is clearer: if they can be counted, then the cardinality of the set of coins in the jar exists and is unique, though we do not know its value until we count. — Srap Tasmaner

Yes, but it still assumes counterfactual definiteness. Which makes total sense for coins in jars (I'm not disagreeing with your argument with MU).

A person who has no lap has nothing in their lap. Russell's analysis of definite descriptions works just fine here, but physicists don't read Bertrand Russell. It's also tempting here to give a counterfactual analysis: if a standing person holding nothing were to sit, they would have an empty lap; if a standing person holding a child on their back and nothing else were to sit, they would have an empty lap, until another child scrambled onto it; if a standing person holding a child against their chest were to sit and loosen their grip upon the child even a little, they would have a child in their lap, and they would sigh with relief. — Srap Tasmaner

I think Strawson's presuppositional analysis is a closer fit. To make a different analogy, if a pointer is measured to be pointing North along the North-South axis, then what direction is it pointing along the West-East axis? A counterfactually-definite East or West direction presupposes that the pointer is also aligned along the West-East axis, but it isn't. Yet a measurement along that axis will give a definite result (in QM, West or East with equal probability).

Quantum mechanics may have some specific prohibitions on the use of counterfactual values in calculations, but it is, for me anyway, inconceivable (!) that we could get along without counterfactuals. They're hiding absolutely everywhere. — Srap Tasmaner

"You keep using that word. I do not think it means what you think it means." But, yes, it's difficult to imagine a world without counterfactuals.

↪Metaphysician Undercover

I addressed in my posts a single issue you raised: must the coins in a jar actually be counted, by you, me, God, or anyone, to know that there is a specific number of coins in such a jar? — Srap Tasmaner

Physicist Asher Peres once said, "unperformed experiments have no results". Which is to say, he rejected counterfactual definiteness.

In quantum mechanics, counterfactual definiteness (CFD) is the ability to speak "meaningfully" of the definiteness of the results of measurements that have not been performed (i.e., the ability to assume the existence of objects, and properties of objects, even when they have not been measured). — Counterfactual definiteness - Wikipedia

Consider also Aristotle's future sea battle scenario. Regarding whether there would or would not be a future sea battle, he says:

One of the two propositions in such instances must be true and the other false, but we cannot say determinately that this or that is false, but must leave the alternative undecided. One may indeed be more likely to be true than the other, but it cannot be either actually true or actually false. It is therefore plain that it is not necessary that of an affirmation and a denial, one should be true and the other false. For in the case of that which exists potentially, but not actually, the rule which applies to that which exists actually does not hold good. — On Interpretation, §9 - Aristotle (Problem of future contingents - Wikipedia)

If these ideas applied to regular coin jars then prior to the coins being counted, their number would not merely be unknown, but also not able to be meaningfully talked about. So, for the agent, there would be a potential (but not actual) number of coins in the jar that is only actualized in the counting of the coins.

(1) If it is raining outside, then Alice knows that it is raining outside. She knows that even though she didn't exclude the possibility that it was not raining and that Bob was hosing the window. She knows it is raining because her belief is both justifiable and true. Alice has satisfied the conditions for knowledge.
— Andrew M

OK, but someone has to judge "if it is raining outside", in order for us to call what Alice has "knowledge". We need to know the answer to this. And if we know the answer to this, then we have excluded the possibility of mistake. So we cannot say whether Alice has "knowledge", unless we determine that it is raining and there is no possibility that it is not raining, thereby excluding the possibility of mistake. — Metaphysician Undercover

In the first scenario it is raining, in the second scenario it is not. According to knowledge as justified, true belief, do you judge that Alice has knowledge in either or both of those scenarios?

I think this is just too vague. — Srap Tasmaner

Just trying to capture the essential idea here! Apparently not successfully...

The trouble is not our knowledge, but our beliefs, and around here it's our beliefs that we know that p, which clearly can be mistaken even though our knowledge cannot. — Srap Tasmaner

Indeed.

It's also possible that generally people only believe that they're probably wrong about something, and that's as much "fallibility" as they're committed to. — Srap Tasmaner

Yes, I think it's a bit abstract otherwise. I think the other issue is that standards can vary according to context. For example, Alice might know that it's raining outside, having looked. But when challenged with the possibility of Bob hosing the window, making that possibility salient, she might doubt it and go and look more carefully. Or when challenged by a philosophical skeptic, conclude that she doesn't know very much at all.

Even though the original claim was that my beliefs are overwhelmingly right, I have the epistemic problem of not knowing which are the good ones and which the bad. (But attaching a modicum of doubt to all your beliefs is so ham-fisted, I don't think anyone actually does it or can do it.) — Srap Tasmaner

Yes, I think the reality is that we're pragmatic about it. If a problem arises, then we investigate further.

an open question (which we can investigate the truth of).
— Andrew M

Gotta love a 3500yo tradition, huh? — Mww

:-)

Prior to this, you were insisting that if something which is thought to be "known" turns out to be incorrect, then we must conclude that at the time when it was thought to be known, it really was not known. — Metaphysician Undercover

That's correct.

That we "exclude the possibility of mistake" is not a condition of knowledge, as ordinarily defined and used.

For example, Alice claims it's raining outside as a result of looking out the window. We can conceive of ways that her claim can be false (say, Bob is hosing the window), and thus not knowledge. But if it is raining outside, then she has knowledge.
— Andrew M

I don't see how this is an example of anything relevant. — Metaphysician Undercover

As a result of looking out the window, Alice justifiably believes that it is raining outside. For Alice to know that it is raining outside, her justifiable belief also has to be true. Those are the conditions for knowledge. Let's look at two different scenarios:

(1) If it is raining outside, then Alice knows that it is raining outside. She knows that even though she didn't exclude the possibility that it was not raining and that Bob was hosing the window. She knows it is raining because her belief is both justifiable and true. Alice has satisfied the conditions for knowledge.

(2) If it is not raining outside (say, Bob was hosing the window which Alice mistakenly thought was rain), then Alice's belief is false. Thus she doesn't know that it is raining, she only thinks that it is. Alice has not satisfied the conditions for knowledge.

Sorry, I'm not familiar with "Cartesian certainty". Maybe you could explain how it's relevant. — Metaphysician Undercover

Let's return to the beginning of this exchange:

If anything which may turn out to be false in the future cannot be correctly called knowledge, then there is no such thing as knowledge, because we cannot exclude the possibility of mistake. — Metaphysician Undercover

That we "exclude the possibility of mistake" is not a condition of knowledge, as ordinarily defined and used.

For example, Alice claims it's raining outside as a result of looking out the window. We can conceive of ways that her claim can be false (say, Bob is hosing the window), and thus not knowledge. But if it is raining outside, then she has knowledge.

The issue is not about what language one uses to refer to a kettle. It's that someone can conceivably, and honestly, mistake something for being a kettle that is not, or for not being a kettle when it is.
— Andrew M

I don't see how such an honest mistake is an issue. The person is simply wrong, by the norms of word use. Therefore calling the thing a kettle will create disagreement requiring justification. — Metaphysician Undercover

If they were wrong that the object was a kettle, then they didn't know that the object was a kettle, by the norms of word use.

so shouldn’t it be taken for granted he means an answer to “what is truth?”, which must be a definition of it, to be just that? To repeat what he doesn’t mean would be disastrous. — Mww

Yes, agreed.

On the other hand, perhaps one could reject that “truth is.....”, is technically sufficient as a definition, but is rather merely an exposition of the conditions which make all truths possible. But the rejoinder to that would be that’s precisely what a definition does, serves as the criterion for the validity of any conception.

Personal choice, then? — Mww

Yes, or an open question (which we can investigate the truth of). ;-)

The flat earther will say he is justified in making his claim, you say he is not justified. It's your word against his.
— Andrew M

Right, but saying "I'm justified" is not acceptable justification. Nor is an appeal to authority, or to the norms of our society. — Metaphysician Undercover

The flat-earther is not claiming it is. He will point to what he regards as evidence for a flat earth. Is his claim thereby justified?

Infallibility is a condition of "truth" as you use it, and "truth" is a condition of knowledge. So infallibility is a condition of knowledge, under those terms. — Metaphysician Undercover

Let me put it differently: Cartesian certainty is not a condition of knowledge, as ordinarily defined and used.

I define "true" with honesty. So if one honestly believes the item is "a kettle" then the person will truly call it a kettle, despite the fact that someone else might truly call it "une bouilloire". — Metaphysician Undercover

The issue is not about what language one uses to refer to a kettle. It's that someone can conceivably, and honestly, mistake something for being a kettle that is not, or for not being a kettle when it is.

Excluding the possibility of mistake is not required for a human being to speak truthfully. That is supposed to be a feature of God, but not human beings. — Metaphysician Undercover

That's exactly the point. Someone might be mistaken about whether the object before them is a kettle. Similarly someone might be mistaken about whether they have knowledge. People can make honest mistakes. They thought it was a kettle when it wasn't. They thought they knew something when they didn't.

David Lewis has a paper that addresses infallibility. I've not read it yet. — Srap Tasmaner

Nor I. But I agree with Lewis that the standards of knowledge depend on the context:

Lewis argues that S knows that p is true iff S is in a position to rule out all possibilities in which p is false. But when we say S knows that p, we don’t mean to quantify over all possibilities there are, only over the salient possibilities.
...
The kind of position Lewis defends here, which came to be known as contextualism, has been a central focus of inquiry in epistemology for the last fifteen years. “Elusive Knowledge”, along with papers such as Cohen (1986) and DeRose (1995) founded this research program. — David Lewis - SEP

But isn't truth infallible in the sense of its being incapable of being false? Your reference to Cartesian certainty suggests to me that we may be talking at cross proposes, so I'm not proposing that possessing knowledge means that one knows one is infallibly correct, but that the knowledge we possess, if it is to be knowledge, must be infallible. — Janus

I was referring specifically to human fallibility. I prefer to say that a true statement cannot be false, just as it cannot be raining outside and not raining outside. But word choice aside, we agree.

I have wondered whether it ought to be said that we possess knowledge in cases where we cannot be certain, that is when we do not know that we know, but that is a whole other can of worms. — Janus

I think it sometimes can (@Srap Tasmaner gives some examples earlier in the thread), even if they often are found together. There's an interesting quote by philosopher Timothy Williamson on that subject here.

There seems to be a contradiction here. The second quoted passage seems to be saying that if what we thought was knowledge turns out not to be true, then it was never knowledge in the first place. Doesn't it follow that knowledge (as distinct from what we might think is knowledge) cannot be false; and thus that it is infallible? — Janus

Yes, knowledge cannot be false. But human beings, being fallible, are always capable of making mistakes or being wrong.

For example, Alice claims it's raining outside as a result of looking out the window. We can conceive of ways that her claim can be false (say, Bob is hosing the window), and thus not knowledge. But if it is raining outside, then she has knowledge.

So infallibility is not a condition of knowledge, whereas truth is. Another way of putting it is that Cartesian certainty isn't a condition of knowledge.

What do you think....is there a definition other than the nominal, that defines what truth is? — Mww

I don't think so. Suppose Alice says that it is raining outside. There is no general criterion that we can use to determine the truth of her statement (i.e., independent of its specific context). Instead, we need to look at what the statement is about, in this case, the weather outside.

Regarding your question, what do you think?

A flat-earther can claim to know that the world is flat. He nonetheless doesn't know that.
— Andrew M

That's what you say. He says he knows it, you say he does not know it. It's your word against his. We can move to analyze the justification, and show that your belief is better justified than his, but this still doesn't tell us whether one or the other is true. And if you argue that his is not knowledge, it's not because his belief is not true that it's not knowledge, it's because it's not justified. So we cannot establish the relationship between knowledge and true, in this way. — Metaphysician Undercover

That's kicking the can down the road. The flat earther will say he is justified in making his claim, you say he is not justified. It's your word against his.

If anything which may turn out to be false in the future cannot be correctly called knowledge, then there is no such thing as knowledge, because we cannot exclude the possibility of mistake. — Metaphysician Undercover

Infallibility isn't a condition of knowledge, as ordinarily defined and used.

It's more accurate to define "knowledge" as the principles that one holds and believes, which they apply in making decisions. That is a person's knowledge, regardless of the fact that it may later turn out to be wrong. This way, we don't have to decide at a later date that the knowledge we held before wasn't really knowledge. — Metaphysician Undercover

If it is later decided that your "knowledge" was wrong, then that just is to decide that you didn't have knowledge, as ordinarily understood. Thus we have a translation between ordinary usage and your way of speaking.

And the knowledge we hold now will later turn out to be not knowledge, onward and onward so that there is no such thing as something we can truly call "knowledge" because we can never exclude the possibility of mistake — Metaphysician Undercover

By that argument, there is also no such thing as something we can truly call a "kettle" because we can never exclude the possibility of mistake.

I’ll have to leave that alone; I don’t see how classical can be derived from nominal, but that’s ok. Also....once again.....translator’s preference. The SEP quote is right, but mine on pg 45 herein, is also right, and different. In addition, the SEP quote, after “is assumed as granted”, leaves out “...and is presupposed”, which offers a clue as to what exactly definitions are supposed to do. — Mww

I take nominal to mean that the definition can't be employed to establish which statements are true (see Kant's comments here). That's the case with Aristotle's (classical) definition as with Kant's.

Nevertheless, there is rather apparently an intended difference between Kant and Aristotle, insofar as the former’s definition contains cognition, while the latter’s does not. They would have been much less different if Aristotle had said, “to think that what is is......”. — Mww

As I mentioned earlier, for Aristotle, to say something presupposes cognition. Keeping in mind, of course, that people sometimes do speak without thinking...

Yes, that is how "knowledge", as the subject of epistemology, is normally defined. But we were not talking about "knowledge", the epistemological subject, we were talking about normal use of "know" as an attitude. — Metaphysician Undercover

That's an artificial distinction. Knowledge, and thus epistemology, is grounded in ordinary life and we use ordinary (and, if need be, specialized) language to talk about it.

And the fact is that people often claim to know things, which turn out to be not the case. — Metaphysician Undercover

That's correct, and no-one disagrees. A flat-earther can claim to know that the world is flat. He nonetheless doesn't know that. So there's a distinction between knowledge and knowledge claims.

So the definitions which epistemologists prescribe as to what "knowledge" ought to mean, do not accurately reflect how "know" is truly used. — Metaphysician Undercover

Actually, it does. For example, people once said that they knew that Hilary Clinton was going to win the 2016 election. But since she didn't win, they didn't know that at all, they only thought they did. The term knew is retracted because of the implied truth condition.

This is somewhat analogous to Alice saying that "Trump won the 2020 US election". Is Alice misusing the word "won"? Does she need to consult a dictionary so she can correct her mistake? Presumably, the problem is not with her use of the word "won", it's that her perfectly well understood claim is false.

But if we conceive of "true" as I proposed earlier in the thread, to be a representation of one's honest belief, then knowing entails truth, as commonly said by epistemologists, but truth does not necessarily mean what is the case. — Metaphysician Undercover

I see that Oxford Languages lists that as an archaic usage, as in "we appeal to all good men and true to rally to us". But that context isn't propositional truth.

Just to play devil's advocate: The Myth of Factive Verbs.

The SEP article on knowledge summarises Hazlett's view as:

Hazlett takes this to motivate divorcing semantic considerations about the verb “to know” from knowledge, the state of traditional epistemic interest. Even though “knows” is, according to Hazlett, not a factive verb, even Hazlett accepts that knowledge itself is a state that can only obtain if its content is true.

This is almost exactly what Metaphysician Undercover is saying — Michael

Yes. I will have to take a look at the paper. Note that SEP put knew in scare quotes with the above Clinton example, which I think also says something about the ordinary use of the term.

So we have statements concerning that which is true or false, but....again....not what true or false is.

As well, it is logically inconsistent to contain the word being defined within its own definition, which Aristotle does, but Kant does not. From that alone, it may be said Aristotle is not defining what truth is, but simply relating truth to that which is not false. — Mww

First, Aristotle says that he is defining truth and falsehood. Second, the word is not defined within its own definition. Truth is defined as "to say of what is that it is, and of what is not that it is not". Falsity is defined as "to say of what is that it is not, or of what is not that it is".

For example, to say of white snow that it is white snow, is true.

Besides, a cognition qua procedural mental event, is far antecedent to its representation in language form in the saying of it. To say a thing is true presupposes, albeit perhaps only metaphysically, the cognition from which the language representing that truth, is assembled in the form of a particular judgement.

Yes? No? Maybe? — Mww

Maybe? For Aristotle, to say something is a cognitive act. Kant says that “The nominal definition of truth, that it is the agreement of [a cognition] with its object, is assumed as granted” (1787, B82) (SEP) Which to me implies that Kant isn't intending to differ from the classical account.

The point is, that for the logic to be valid :"know" must be defined as a "factive" term as a premise. — Metaphysician Undercover

That is how knowledge is ordinarily defined. As the following sources show:

1. Socrates: knowledge as true opinion that stays with us (Plato, Meno 97)

2. Knowledge as justified, true belief (SEP - The Analysis of Knowledge)

3. '... one cannot have "knowledge that" of something that is not true. A necessary condition of "A knows that p," therefore, is p.' (Britannica - epistemology)

4. factive: denoting a verb that assigns the status of an established fact to its object (normally a clausal object), e.g. know, regret, resent. (Oxford Languages)

That's not a premise in Srap's proposal, because it's not stated as a premise. If it were stated then we could judge the truth or falsity of it. — Metaphysician Undercover

So let's state it:

$\ \ \ \ \ Kp\ \vdash\ p$

Which is to say, if it is known that p is true then p is true. And from which follows, by modus tollens:

$\ \ \ \ \ \neg p\ \vdash\ \neg Kp$

Which is to say, if p is false then it is not known that p is true

When people say "I know that X is the case", they are most often not claiming absolute certainty, that it is impossible for things to be otherwise — Metaphysician Undercover

Whether people are claiming absolute certainty or not isn't relevant. That knowledge entails truth means only that if someone does know X then X is the case.

Does "imagining something" imply that the imagined thing is what is the case? How does "knowing something" elevate itself to a higher level than "imagining something", without the required premise, or definition? — Metaphysician Undercover

As @Srap Tasmaner has pointed out, know is a factive [*] term while imagine is not. One can imagine that Trump is still the president of the US but one can't know that he is, since he isn't. The required premise (Kp ⊢ p) comes from observing how the term know is ordinarily used in language.

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[*] factive
adjective
1. (of a verb, adjective, or noun phrase) presupposing the truth of an embedded sentence that serves as complement, as realize in I didn't realize that he had left, which presupposes that it is true that he had left.

HA!!! My post on pg 45 didn’t even get a response, even though it contained a distinct and irreducible answer to the question. Might not be correct, and is certainly open to disagreement, but at least it was there. — Mww

Is Kant's definition of truth, "the accordance of the cognition with its object”, much different to Aristotle's definition "To say of what is that it is ... is true"?

No, it's called skepticism, — Metaphysician Undercover

Well, you've raised it to a fine art!

The issue, as I see it, is that observational data and evidence should inform our philosophy. When there's a conflict, that's a signal that we need to check our premises.

Obviously, what I disagree with is what you say "science" tells us. So clearly I will not be producing a "scientific" source to back up my disagreement. The "science" is what I disagree with. So, I produced a philosophical source, this being a philosophy forum. I don't think we should be moving toward "scientific" sources.. — Metaphysician Undercover

It's poor philosophy to reject well-established facts about the world.

Assume that "green" was used to denote the colour white.
...
IE, "snow is green" is true IFF snow is white.

In that event, doesn't this mean that Tarski's T-sentence would be false ? — RussellA

Not at all. The object language is in quotes (let's call it Greenglish), while the metalanguage is conventional English. If the object language were instead German, it would be:

"Schnee ist weiß" is true IFF snow is white.

The RHS is an English translation of the German sentence in quotes on the LHS. If snow is white, both sentences are true. If not, both sentences are false.

Similarly, in your example, the RHS is a conventional English translation of Greenglish. If snow is white, both sentences are true. If not, both sentences are false.

This is a mistaken supposition, explained well by Kant. The name "snow" does not refer to some sort of object which preexisted the appearance within the mind, as you seem to think scientists claim. — Metaphysician Undercover

I said that snow was white 200,000 years ago, as scientists would tell us. That's common knowledge - if you disagree, perhaps you could provide a scientific source.

Today, we have Tarski's T-Sentence "snow is white" is true IFF snow is white. The left hand side is the object language, the right hand side is the metalanguage. — RussellA

The T-sentence is in the metalanguage, while the quotes name a sentence in the object language.

I agree that in our world snow is white. — RussellA

Cool.

However, in the world of the metalanguage, snow may or may not be white. — RussellA

Certainly if the word "white" were used to denote the color green then the sentence, "snow is white" would be false (since snow is not green).

It's like if you call a tail a leg, then how many legs does a horse have? We can be in agreement as long as we avoid ambiguity.

I am curious why naming plays no part in Tarski's T-sentence, as naming seems to affect the truth or falsity of the T-sentence itself. Am I missing something ? — RussellA

Maybe - the quoted part on the LHS is the name of the sentence on the RHS.

A sentence such as "snow is white" is true if in the sentential sentence "x is white", x is satisfied by snow.

200,000 years ago snow had not been named. Today, snow has been named, whether "white" in English or "schnee" in German. Therefore, there must have been a point in time when snow was named "snow", ie, what Kripke calls "baptised". — RussellA

Yes, but naming it doesn't affect what it is. 200,000 years ago, snow wasn't named "snow", and the color white wasn't named "white", yet snow was still white. At least, so the scientists tell us.

Before naming snow as "snow" and white as "white"
As "white" didn't exist, in the sentential function "x is white", there is no x that satisfies "white", therefore "snow is white" can never be true.

After naming snow as "snow" and white as "white"
As snow has been named "snow" and white has been named "white", in the sentential function "x is white", x is always satisfied by snow. Therefore, "snow is white" is always true.

In summary, the T-sentence is false before snow had been named "snow" and white named "white". The T-sentence is always true after snow had been named "snow" and white named "white". IE, the T-sentence itself may be either true or false dependant upon how its parts have been named. — RussellA

The names didn't exist but the things named did. The T-schema didn't exist either, but the things that we might later schematize did.

In seeking an answer to the question, “what is truth”, that passage says, in a modernized, which is to say, seriously overblown, manner, nothing effectively superior to the entry on pg 45. — Mww

Yeah, kids these days with their logic and stuff...

@Banno

The Revision theory, discussed in some other posts, appears to offer a way to map out the circularity of the T-sentence definition of Truth.
— Banno

...
As I mentioned before, Tarski didn't think of the T-sentence as being a definition of truth, only as something that must be entailed by the definition of truth. — Michael

As Michael noted, Tarski didn't think of the T-sentence as being a definition of truth and, I'd add, neither was his actual definition of truth circular. Here's Tarski's comments from his 1944 paper:

(T) X is true if, and only if, p.
...
It should be emphasized that neither the expression (T) itself (which is not a sentence, but only a schema of a sentence) nor any particular instance of the form (T) can be regarded as a definition of truth. We can only say that every equivalence of the form (T) obtained by replacing 'p' by a particular sentence, and 'X' by a name of this sentence, may be considered a partial definition of truth, which explains wherein the truth of this one individual sentence consists. The general definition has to be, in a certain sense, a logical conjunction of all these partial definitions.
...
A definition of truth can be obtained in a very simple way from that of another semantic notion, namely, of the notion of satisfaction.

Satisfaction is a relation between arbitrary objects and certain expressions called "sentential functions." These are expressions like "x is white," "x is greater than y," etc. Their formal structure is analogous to that of sentences; however, they may contain the so-called free variables (like 'x' and 'y' in "x is greater than y"), which cannot occur in sentences.
...
Hence we arrive at a definition of truth and falsehood simply by saying that a sentence is true if it is satisfied by all objects, and false otherwise. — The Semantic Conception of Truth: and the Foundations of Semantics - Alfred Tarski, 1944

For example, consider a model [*] where there are a set of objects including white snow. In that model, the sentential function "x is white" is satisfied by snow. Regular sentences, such as "snow is white", are special cases of sentential functions and are satisfied by all or no objects (for technical details, see Haack, p206-207). Thus truth (in a model) is defined in terms of satisfaction which, in turn, is defined in terms of inclusion in a set of objects.

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[*] "... in his original paper, Tarski gives an absolute rather than a model-theoretic definition; 'satisfies' and hence 'true' is defined with respect to sequences of objects in the actual world, not with respect to sequences of objects in a model or 'possible world' (e.g. 'there is a city north of Birmingham' is true, absolutely, but false in a model in which the domain is, say, {London, Exeter, Birmingham, Southampton}" - Haack

I guess this is why nobody can agree on whether he was a correspondence theorist or not. Ironically he's less clear and unequivocal than we'd like. — Michael

Though he was, at least, clear and unequivocal that the sentence, "Tarski is a correspondence theorist" is true iff Tarski is a correspondence theorist. :wink:

I believe there isn't much agreement amongst philosophers on that. — Michael

Yes, that seems to be the case. They are based on fairly technical discussions of what constitutes correspondence, with a good review here (Truth, Correspondence, Models, and Tarski - Panu Raatikainen, 2007).

So it seems to me at least that he doesn't endorse the correspondence theory but does endorse the Aristotelian theory, which he thinks of as different. — Michael

Tarski was certainly critical of modern correspondence formulations, but also said that "One speaks sometimes of the correspondence theory of truth as the theory based on the classical conception.":

The conception of truth that found its expression in the Aristotelian formulation (and in related formulations of more recent origin) is usually referred to as the classical, or semantic conception of truth. By semantics we mean the part of logic that, loosely speaking, discusses the relations between linguistic objects (such as sentences) and what is expressed by these objects. The semantic character of the term "true" is clearly revealed by the explanation offered by Aristotle and by some formulations that will be given later in this article. One speaks sometimes of the correspondence theory of truth as the theory based on the classical conception. — Truth and Proof - Tarski, 1969

We can explain Tarski's view as follows: There are two modes of speech, an objectual mode and a linguistic mode ('material' mode, in Medieval terminology). The correspondence idea can be expressed in both modes. It is expressed by:

'Snow is white' is true iff snow is white

as well as by:

' "Snow is white" is true' is equivalent to 'Snow is white.'
— Andrew M

I don't know if Blackwell got this right. — Michael

The sentences are equivalent in the sense that they are satisfied by the same object(s). Whereas redundancy is a philosophical view about usage.

So he seems quite opposed to the redundancy view. — Michael

Yes, Tarski endorsed the correspondence theory of truth. Sher notes this at the beginning of the chapter where she says:

Tarski's philosophical goal was to provide a definition of the ordinary notion of truth, that is the notion of truth commonly used in science, mathematics, and everyday discourse. Tarski identified this notion with the classical, correspondence notion of truth, according to which the truth of a sentence consists in its correspondence with reality. Taking Aristotle's formulation as his starting point - "To say of what is that it is not, or of what is not that it is, is false, while to say of what is that it is, and of what is not that it is not, is true." (Aristotle: 1011b25) - Tarski sought to construct a definition of truth that would capture, and give precise content to, Aristotle's conception. — Truth, The Liar, and Tarski's Semantics - Gila Sher (from Blackwell's A Companion to Philosophical Logic)

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Makes sense, cheers. Question though. The source uses the word "correspondence" in the context of mapping expressions of language and concerned objects, is that meant as fleshing out a correspondence theory, or is it meant in an informal sense of "an explanatory relation of equivalence" — fdrake

Yes, it's meant as fleshing out a correspondence theory - see the above quote. But that wasn't Tarski's only goal. As Sher goes on to say:

Tarski’s second goal had to do with logical methodology or, as it was called at the time, metamathematics. Metamathematics is the discipline which investigates the formal properties of theories (especially mathematical theories) formulated within the framework of modern logic (first- and higher-order mathematical logic) as well as properties of the logical framework itself. Today we commonly call this discipline ‘meta-logic.’ The notion of truth plays a crucial. if implicit, role in metalogic (e.g. in Gödel's completeness and incompleteness theorems), yet this notion was known to have generated paradox. Tarski's second goal was to demonstrate that ‘truth’ could be used in metalogic in a consistent manner (see Vaught 1974). — Truth, The Liar, and Tarski's Semantics - Gila Sher (from Blackwell's A Companion to Philosophical Logic)