Just take as accepted, anything not counted as physical is not counted as empirical, and anything not counted as empirical in some way is counted as a priori, and anything not counted as empirical in any way whatsoever is counted as pure a priori. It follows that whatever is there that makes changes in one’s subjective condition merely possible, is pure a priori. But it must be something, and thus is established and justified, a precursory condition. — Mww

That's a very clear explanation.

The sound a lead ball makes is different than the sound a rubber ball makes, and the sound a ball makes is different than the sound a trash compactor makes. That all these make a sound is determined by the the matter of each, but the matter of these, while affecting the senses with sound, do not carry the information of what form the matter has. It is impossible for us to get “ball” out of the sound an object makes when it hits something solid. Without antecedent experience, you cannot get “telephone” out of some arbitrary ringing/clanking/buzzing sound. — Mww

This points directly to what I said to Janus above. Empirical evidence in itself does not justify a belief, what is required is empirical evidence plus logic.

Justified cannot mean proven. When it comes to empirical beliefs, nothing we consider ourselves justified in believing can be proven. The provenance of proof is in logic and mathematics, not in inductive reasoning. — Janus

It seems you have a misunderstanding of justification. Empirical evidence, along with logic comprise justification. All logic requires premises, and most are grounded in empirical evidence. Justification is not limited to empirical evidence alone. I don't even know how empirical evidence without some form of inference would work as justification for a belief. You just observe evidence with no inference?

I haven't disputed that, but it does not follow that all kinds of know-how are forms of knowing-that, which is why I have been trying to point out to you that there are kinds of know-how that have nothing to do with justification, truth or even belief. — Janus

I fully understand that, but I don't see the relevance. As I said what I was looking for is what is common to all knowledge. Depending on how one defines "justified", justification may be conceived of as what sets knowing-that apart from other forms of knowing how.

You and I know up front because I created the hypotheticals that way. — Andrew M

What type of knowledge do you assume that a "hypothetical" gives someone? It's not true knowledge. When you assume hypothetically that it is raining, this does not mean that you have knowledge that it is raining.

I don't think you can claim to follow the traditional formulation, because your understanding of what constitutes justification and truth is not in accord with the usual understanding. The usual understanding does not demand "proof" to underpin justification, and does not consider truth to be dependent on human intentions, honest or dishonest. — Janus

I don't see that you have a point. Justified, in general does mean proven. To justify means to demonstrate the correctness of, and that is to prove. And the meaning of "true" is very problematic, as demonstrated by this thread. Some posting here want to reduce truth to a special form of justification, but that leaves knowledge as simply justified belief. And others want to consult common usage. That's what I did, and common usage of "truth" is grounded in honesty. If we tell the truth when making a proposition, we propose what we honestly believe. A proposition which does not present what the person honestly believes is not a truthful one.

JTB is a definition of propositional knowledge, not know-how. — Janus

As I said, I do not respect this separation. Knowing-that, or propositional knowledge is just a special form of knowing-how. Using language and logic is a type of acting, so this is a type of know-how.

Even if propositional knowledge could be, at a stretch, considered to be a kind of know-how; there are many other kinds of know-how which have nothing to do with truth or justification. — Janus

In categorization, if there is a category with sub-groups, then all the sub-groups have something in common which makes them all members of the broader category. So if all types of know-how are all types of "knowledge", then they all have something in common. To say what "knowledge" is, we need to determine what they have in common. I think that JTB, if understood in the right way, is a good proposal. It has been around for a long time, and stood the test of time. The most difficult issue is to determine what "true" means. As the title of the op suggests, we often ask, "what is truth?", without sticking around to determine the answer. And so JTB is rather useless if we do not understand what T means.

The independent property is having three edges and vertices. — Michael

That something has "three edges and vertices" is a judgement. Who makes that judgement?

They have a nature, including a mass, an extended position (i.e. a shape), and often a certain kind of movement. — Michael

As I said, these are all things which we say about objects. And all you are doing is confirming this by saying it. How are you going to justify your assertions? What makes you think that mass, extended position, and movement, are anything other than concepts?

That we decide which words refer to which properties isn't that the object only has these properties if we refer to it using these words. This is the fundamental mistake you keep making. If something has three edges and vertices then it is a triangle even if we do not call it a triangle. — Michael

All these shapes and things which you say are the real properties of objects, are just products of our perceptual apparatus. These images, like edges and vertices, are created within the mind, There is no reason to believe that they are part of the objects themselves. The images created in the mind are just representations, like symbols, and there is no reason to believe that the symbol bears a likeness to the thing it represents. We can learn this from language. Words generally are not similar to whatever they represent. So whenever the mind creates an image, like a taste, a sound, or a visual image, we ought to believe that the image is a representation, like a symbol, and there is no reason to believe that the thing represented is anything at all like the symbol.

Science has been very good to demonstrate the reality of this to us. A taste, or smell, consists of molecules, which have no similarity to the smell or taste. Sound consists of waves, which is nothing like the image we hear. And, since the light which reflects to our eyes is the result of an interaction between electrons and photons, the boundaries between objects are nothing like the edges of a triangle (these are presumed to be straight lines).

If I ask someone to tell me the truth of where my kidnapped wife has been hidden I'm not interested in where the person believes my wife has been hidden; I'm interested in where she's actually been hidden. — Michael

Sure, you are interested in where your wife is hidden. That's obvious. But you are asking the person to provide you with what they honestly believe when you ask them for the truth. Remember, the person honestly might not know where your wife is. This is the way communication works, you cannot demand of others, to give you what you want. Such demands get you nowhere. So you must ask them to give you what they are capable of giving you, rather than demanding that they give you what you want. You want to know where your wife is hidden. The best that the other person can provide you with, is their honest belief, whether or not they know where she is. That's a simple fact. Therefore it is a mistaken approach for you to demand that the person give you the information you want, when their honesty provides you with the best that they can give you anyway. This way you respect the fact that the person might not be capable of giving you what you want. So the proper approach is to encourage them to give you their honesty. And that is to encourage them to tell the truth (honesty), rather than demanding The Truth (absolute, what is the case).

The request to "tell the truth" is premised on the notion that things actually are as this person believes them to be. — Michael

This is incorrect. The request to "tell the truth" is clearly a request for honesty. This is evident because it is most commonly used to determine whether or not the person knows the information which is wanted. You do not necessarily know whether the person has correct information concerning the whereabouts of your wife, so you need honesty to determine this. In relation to the subject you are interested in, your wife's location, you must get people to speak honestly, before you can even determine who has the beliefs which you are interested in. And that is what "tell the truth" is premised on, the attempt to determine whether the person has beliefs which are relevant to your interest.

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.

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. — Andrew M

It's only justified by your begging the question, which is not justification at all.

The issue here is not all of metaphysics but a simple conditional: if they can be counted -- if -- then there must be a specific number of coins in the jar right now. — Srap Tasmaner

I've agreed to this already. We see a quantity of coins and we assume that they can be counted. If they can be counted, there is a specific number, as you say. So we are inspired to count them, assuming that there is a specific number, and therefore they can be counted. Then we do count them. And after we do, we need to rely on a premise of temporal continuity to say that there was the same number at the earlier time as there was at the time of the count.

Do you still have trouble with this?

But it is easily fooled because all it does is count, and counting doesn't require -- so the machine doesn't offer -- judgment. — Srap Tasmaner

Your counting machine does make judgement. That's what an algorithm is, instructions for making judgement. As human beings, we have created machines designed to make these simple judgements for us. But machines are now making more and more complex judgements for us. The AI is designed to be adaptable in its judgement capacity.

My question was concerning how to distinguish between belief and knowledge. Beliefs can be understood to be "principles used for willed actions". So "being intentional" cannot be a sufficient criterion for saying that someone has knowledge as opposed to merely having belief. — Janus

I follow the traditional formula, knowledge is a particular type of belief, justified and true. Justified is having been proven, and true is honest (that's my difference, how I define "true). Generally, being intentional shows knowledge, because we do things in set ways (justified beliefs), and we honestly believe in what we are doing.

Bear in mind I am not concerned with "know-how" but with 'knowing-that' (knowing how to do anything does not seem to have anything to do with justified true belief). So, do you have a way to distinguish between knowledge and belief, or do you reject the distinction? — Janus

Knowing -that is a type of knowing-how, just like knowledge is a type of belief.

No one determines whether or not it is raining. — Banno

Lots of people do. I do it every day before I go outside. Don't you? I do not see how you could be using "determine" in any way other than this here. So let's not regress back to the dishonesty.

Then, how do, or could, we know that something is knowledge, according to you? (A concise, short-winded answer will do just fine). — Janus

Your question is misleading. We do not judge if something is knowledge or not, because we do not see, or sense things which might be judged as knowledge. What I think is that "knowledge" is something which we infer the existence of, through people's actions.

As I said earlier. "knowledge" consists of principles used for willed actions. If a person acts intentionally then the person has knowledge. What is required is to judge actions, and if they are judged as intentional, then the person has knowledge.

If you mean that my argument is only valid in a world very much like ours, I agree. — Srap Tasmaner

No, that's not what I mean. I mean your logic is only valid if you state that premise of temporal continuity. You seem to have a habit of thinking that valid logic can rely on unstated premises. That is not acceptable. The premises required for inference must be stated.

To return to the issue at hand: I consider my arguments valid in worlds very much like this one. In worlds like this, if the number of coins in a jar can be determined by counting them, then you can know, without counting, that there is a specific number of coins in the jar. — Srap Tasmaner

You don't seem to understand the reality of "a world very much like ours". In our world, time passes, and things change as time passes. Change is primary, and change is what we take for granted, as we take for granted that time passes. Since time passing, and the associated "change", are what we take for granted in "a world very much like ours", the proposition that something stays the same as time passes, cannot be accepted without justification.

Because of the reality of change, we cannot count the coins in a jar at one time, and logically conclude that the number of coins in the jar was the same at an earlier time, unless we premise that there was no change in the quantity over that period of time.

Do you agree? — Srap Tasmaner

Obviously not, your argument is not valid because it is missing a very significant premise which is required to make the conclusion that you do.

No. A number is a value. It is the "propositional content" of one or more mathematical symbols. For example, 0.250.25, 1414, and 2828 are different mathematical symbols that refer to the same mathematical value. — Michael

OK, I'll agree with "a number is a value", but I think that "propositional content" is somewhat vague or ambiguous, so I'll leave that for now. I understand "a value" as a principle which a human being holds within one's mind, concerning the desirability or utility of different types of things. Values often serve as principles by which we make judgements. So a value, as I understand "value", very clearly cannot exist independently of a human mind.

Being called a triangle and being a triangle are two different things. — Michael

This is something which needs to be justified. If "a number" is a value, then "a triangle" is also a value. So "triangle", as a concept is a simplified version (a representation) of an underlying complex concept, just like 2, as a number. is a simplified version (a representation) of an underlying complex concept.

So we have multiple layers of representation here. We have the word "triangle". We have the value 'triangle' (which is other than the word, like the number is other than the numeral). Then we have the underlying complex concept, three sided, straight lines, 180 degrees, different types, and all the associated mathematical principles.

Further, we now have the application of the value (the principle of action), which is the naming of a thing "a triangle". You seem to be asserting that a thing which a person might name as a triangle, has an independent property, which you call "being a triangle", which is separate from being named a triangle. How could you justify such a claim?

What you are saying, in effect, is that when you name something as a triangle, you are correct in an absolute sense, because the thing already has the property of "being a triangle" before you name it as such, therefore you cannot be wrong in your naming. And if you accept the reality, that you might be wrong in your naming, then if the thing does have that independent property, how would you ever know this? And if you cannot ever really know if the thing has this independent property or not, how is your assertion that it does, ever justified?

This is where we disagree. Objects exist and have properties even if we are not aware of them. — Michael

Yes, we disagree here. A "property" is a concept, usually quite complex, like the mathematical concept of "triangle" referred to above. We simplify the complex concept by naming it with one word, like "triangle", "large", "hot", "red", etc.. The word is supposed to represent "a concept" which in Platonist words is an intelligible object. The intelligible object represents the underlying complex concept. So a property is a complex concept. Objects do not have properties, as properties are concepts, and in application we assign the concept to the thing. It's called predication.

By Andrew's definition, we can't honestly call anything knowledge, because we can't really know whether it actually is knowledge or not. I don't agree, that's why I argued against that.

Weather forecaster is a good example. Does the weather forecaster actually know something, or just pretend to know what is actually not known?

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? — Andrew M

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

That is, according to your representation of "knowledge", which requires infallibility. I do not represent knowledge like that though. I think Alice has knowledge whether or not you assert that it is raining. These third party assertions, "it is raining", "it is not raining", or "if it is raining", are actually completely irrelevant to whether or not the person has knowledge, because as mere assertions they do nothing to justify one's belief.

That question I answered as clearly as I could, and even provided informal proofs to support my position.

If you have no rebuttal besides "maybe coins spontaneously appear and disappear," then we're done here. — Srap Tasmaner

What I said, is that your logic is not valid without a premise of temporal continuity. That a coin might disappear without one noticing, is just a simple example as to why such a premise is necessary. If you do not agree, and think that your logic which concludes that the number of coins in the jar at a later time will necessarily be the same as the number at an earlier time will be valid, without such a premise, then so be it. But I think your refusal to continue is just a recognition that you are wrong. The premise of temporal continuity is a requirement for a valid conclusion.

In the sense that the numeral refers to a number and that number is the number of coins prior to being counted. — Michael

Well, here we have an ontological difficulty. What is "a number"? Are you taking a position of Platonic realism here? If not, maybe you can explain what you mean by "a number". I tend to think that a numeral refers to the situation in application, through the medium of some mental ideas, rather than through the medium of "a number", just like other words do.

We can however, use mathematical symbols, like numerals, in practise, without any particular situation of application. This is like when we practise other forms of logic, using symbols without any referent. The symbols have meaning, but they effectively refer to nothing. So in mathematics when we do practise exercises like "2+2=?", the symbols have meaning, but they effectively refer to nothing. And it is a mistaken notion, that "2" refers to a number in this sort of exercise. In reality "2" has a complex meaning of order and quantity, which cannot be represented as a simple object, the number two.

t's not magic. We agree to use the word "triangle" to refer to the shape of some object that we have seen. Now, every object with that shape -- even objects we haven't seen -- are triangles, even though we haven't explicitly used the word "triangle" to refer to each of those objects individually. They are triangles by virtue of having the same shape as an object that we have referred to as having a shape named "triangle". — Michael

I don't understand how you can truly believe this. How do you honestly believe that there are objects called "triangles" which have never been called by that name? This is blatant contradiction. There is an object called a triangle which has not been called a triangle.

It appears to be a simple confusion of what is potentially the case, with what is actually the case. I might agree to the possibility that there are objects which if seen, and named, would be called triangles. That's a type of potential, a possibility. Obviously, I cannot say that any such potential is actually a triangle, because no one has apprehended these things and designated which of them are triangles. You clearly conflate the potential for triangles with actual triangles.

We've already agreed that the numeral "66" refers to a specific number.. — Michael

No, we haven't yet discussed this premise of Platonic realism. The problem, as I said above, is that numerals have multiple uses and therefore complex meaning. I learned from fishfry on this forum, that modern mathematics assumes order as the primary defining feature. Then, to establish consistency between order and quantity, quantity is assumed to be a sub-type of order. The problem which I see is that order is a concept based in continuity, while quantity requires discrete entities. So there is a fundamental incommensurability between order and quantity which makes it so that one numeral, "66" for example, cannot refer to one coherent intelligible object, the number. There is a dual meaning and the two are not consistent with each other.

You make the mistake of saying that because we need to explicitly assign a particular word or numeral to a particular kind that we need to explicitly assign that particular word or numeral to every individual of that kind. This is false. We need to do the former to establish meaning, but we don't need to do the latter. — Michael

The issue is, that the thing must be judged to be of that kind. because a "kind" is something artificial, created by human minds, a category. A natural object isn't just automatically of this kind or that kind, because it must fulfill a set list of criteria in order to be of any specific kind. And, whether or not something fulfills a list of criteria is a judgment. So a natural object really does not exist as any specific kind until it is judged to fulfil the criteria. We cannot claim that a thing is judged to be of a specific type, without it actually having been judged to be of that type.

That this is truly the case is evident from the fact that there is continuous disagreement as to whether some objects are of this or that kind, disagreements which sometimes cannot be resolved. And the fact that all people might agree on some things, doesn't prove that kinds are naturally occurring. However, the fact that some people do not agree on some things demonstrates that kinds are artificial, and things just aren't naturally of this kind or that, they are judged. Things are classiified, and placed into categories, through judgement. They do not just naturally exist in categories.

The T-schema is useful here. There are 66 coins iff "there are 66 coins" is true, there are 67 coins iff "there are 67 coins" is true, there cannot be both 66 and 67 coins, therefore "there are 66 coins" and "there are 67 coins" cannot both be true. — Michael

This does not tell us whether "there are 66 coins" is the product of a judgement, or whether it's something independent from judgement. Nor does it tell us if there is 66, or 67 coins. It really tells us nothing. It is a useless statement. And, since it is possible that the person who counts 67 is using a different numbering system, in which "67" is equivalent to "66" in the other system, it is actually your claim, that there cannot be both 66 and 67 coins, which is incorrect. That is why my proposal, that when both 66, and 67 are both claimed as true assertions, we must move to justify and understand, rather than simply asserting that one person must be wrong.

This is consistent with how we actually understand the meaning of the word "true". I don't know why you're trying to make it mean "honest belief". What evidence or reasoning is there for that? — Michael

This is how "truth" is most commonly used. When someone is asked to tell the truth, the person is asked to state what they honestly believe. Epistemologists have attempted to give "true" a meaning which is independent from this, signifying what is the case, in some absolute sense, independent from human judgement. But it really makes no sense at all to argue that there is some type of true correspondence, or true relation between a group of symbols, and the reality of the situation, without a judgement in relation to some criteria for "true". So this proposed form of "true" is really nonsense.

On the other, you would be claiming that "there are 64 coins in the jar" is neither true nor false. That is, you are rejecting bivalence, the view that all statements are either true or they are false. — Banno

That's right, in cases where a human judgement is required, we ought to reject bivalence. This was argued extensively by Aristotle, in order that we can account for the reality of potential, and the nature of the human will. He proposed that we reject the law of excluded middle in these situations, while some modern philosophers propose we reject non-contradiction. Aristotle's famous example is the sea battle tomorrow. There may or may not be a sea battle tomorrow. It has not yet been decided, so there is no truth or falsity to "there will be a sea battle tomorrow". And, we cannot turn retroactively, after tomorrow, and say that one or the other was true the day before, because there simply was no truth or falsity to this matter at that time, due to the nature of the human will.

His argument, was that since we all deliberate on our decisions, we act as if there really is not truth or falsity concerning those questions we deliberate on. And if it really was ture that there was already a truth or falsity to the questions which we deliiberate on, we would have no need to deliberate, we would just let the event occur the way it is predestined to.

(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.

Your reasoning appears to be that there are 66 coins in the jar because we have counted 66 coins, whereas my reasoning is that we have counted 66 coins because there are 66 coins in the jar. — Michael

Yes! This, I believe is the situation. And I think that to coming up with this is a very good example of philosophizing on your part. The use of the term "because" signifies that you recognize that this is a matter of a difference in opinion concerning causation.

What is the cause of this specific numeral, "66" being related to the coins in the jar. I say that it is an act of human will, the act of counting, which causes "66" to be related to the coins in the jar. You seem to be saying that the numeral "66" is already related to the coins, prior to being counted, and this causes the person to count "66". So, I say that the freely willed act of counting causes the person to say "66", and establish this relation between "66" and the quantity, while you say that the relation between "66" and the quantity is already established, and this established relation causes the person to say "66".

Notice that I say the act is freely willed. This is because the difference between your perspective and mine, as a matter of causation, manifests in the difference between determinism and free will. The issue is that I believe we freely choose "66" to represent the quantity of coins in the jar, and we are not caused by the coins in the jar to represent them with "66", as you seem to believe.

The problem with your reasoning is that it doesn't explain why it is that we counted 66 coins (and not, say, 666), and also that it can lead to the contradiction which I reject in (b). — Michael

You never asked me to explain this, but I will say that it is simply a matter of how we as human beings created the numbering system. That we count the coins as "66" is a feature of the system we have devised for measuring quantities.

What do you mean by a number being assigned? — Michael

Assignment in this case is a matter of judgement, and it must be an honest or true judgement, or it's not a true assignment.

If, as in the example of (a), a person randomly guesses "66", this would not produce a true statement, because "true" as I've defined it requires the person to state what one honestly believes, to the best of their ability. "There are 66 coins in the jar" would not be a statement of one's honest belief, if the person is just guessing, and therefore is not true under those circumstances.

In the case of (b), it is very common to have contradiction in true statements, "true" meaning a statement of one's honest belief. If one counts "66" and another counts "67", then they both make true statements which conflict, and require justification. In this case, another counting is required. It is also possible that two different people could use two different systems. That's why knowledge requires both, truth and justification. Truth alone cannot resolve contradictions, because two people will both insist on knowing "the truth", even though they contradict each other.

And (c) is simply wrong. For there to be "66 coins in the jar", it is necessary that "66" is the symbol which has been associated with the quantity of coins in the jar. You seem to think that the symbol "66" is somehow magically associated with the coins in the jar, without anyone making that association. How do you believe that this comes about, that the symbol "66" is related to the coins in the jar, without someone making that relation? Doesn't meaning require intent in your understanding of the use of symbols?

Suppose we say that the meaning of "66" is already related to the coins in the jar, prior to them being counted. How could we interpret this? What is that meaning, and where is it if independent from human minds?

No, we needn't take that as a premise. We can argue for it. — Srap Tasmaner

The point was that to make the logical conclusion that there was the same number of coins at an earlier time, as there is at the later time, when counted, we need some sort of premise of temporal continuity. You can argue for it, saying that the jar was watched for the entire time and no coins disappeared out of it, etc., but in the end all possibilities for change must be covered. If there is no temporal continuity of existence, then the quantity can change randomly from one moment to the next. If the quantity can change randomly, then we cannot say that it was necessarily the same at the earlier time as the later time. Therefore we need a premise of temporal continuity.

If we remove a coin from the jar, then there is some time t1, after t0 and after we have removed one coin but before we have removed another. If the jar is empty at t1, then the initial state of the jar at t0 was that it contained 1 coin, and 1 is a natural number. If the jar is not empty at t1, we go again. If we remove another coin, then there is a time t2, after t1 and after we have removed another coin but before removing any others (if there are any). If the jar is empty at t2, then it contained 1 coin at t1, and 2 coins at t0, and 2 is a natural number. If the jar is not empty at t2, we go again. — Srap Tasmaner

As I said, I do not deny that we can make these logical conclusions, so long as we recognize the required premise of temporal continuity. And the problem with the premise of temporal continuity is that we really do not understand temporal continuity, it's just something we take for granted. Newton's first law of motion is an example of a law concerning a temporal continuity which we take for granted.

Let's return to the beginning of this exchange: — Andrew M

That's not the beginning. 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.

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

I know that excluding the possibility of mistake is not a condition of "knowledge", as commonly used. But according to your assertions, excluding the possibility of mistake is very clearly a condition of "knowledge". That's why I am saying you are wrong.

You say that when something which is thought to be known, turns out to be mistaken, then it is not "knowledge". So anything mistaken cannot be called "knowledge". Therefore anything which we can truthfully call "knowledge" must exclude the possibility of mistake, according to what you are asserting.

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.

The temporal continuity of what? I don't understand the point you're making here. — Srap Tasmaner

We must premise a temporal continuity of the quantity in order to conclude that the quantity at the time prior to being counted was the same as the quantity at the later time of being counted

The procedure I described, if it terminates at all, yields a unique value. It cannot do otherwise unless the procedure is undermined by other premises. Did you have such a premise in mind? — Srap Tasmaner

Yes, I agree that the procedure if carried out according to standards of what qualifies to be counted, as you described, will turn out a unique value. The point though is that the unique value does not exist prior to the procedure being carried out. The issue is not whether the coins can be counted, I have no problem with that. The issue is whether or not there is "a count", "a measure", 'a number", which corresponds with the quantity, prior to being counted.

Suppose a jar contains some coins, but for no natural number n is it the case that the jar contains n coins. Then for no natural number n is it the case that removing exactly n coins from the jar would leave the jar empty. If the number of coins in the jar could be determined by counting to be some natural number k, then removing exactly k coins from the jar would leave the jar empty; therefore the number of coins in the jar cannot be determined by counting to be any natural number k. — Srap Tasmaner

I can't understand this example. I agree that when we say that there is a quantity of coins in the jar, we assume that they can be counted. And, this assumption implies that there is necessarily one of an infinite number of possible numbers which will be the unique value. But to say that there will be one number, after being counted, out of a present infinite number of possibilities, is not the same as saying that there is one number presently.

What, in your wisdom, is math after all? — Real Gone Cat

Math is based on made up axioms, like Tones described. It's imagination, fiction, not truth. The majority of the axioms which get accepted into the mainstream do so because they prove to be useful. Some though, may be accepted simply for beauty or eloquence. Usefulness is quite distinct from truthfulness.

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? — Andrew M

I cannot answer this. I cannot judge a justification without seeing the specifics of the justification.

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

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

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.

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. — Andrew M

I don't agree with this at all. First, knowledge is not the same type of thing that a kettle is. A person has knowledge prior to knowing that one has knowledge. And, a person may learn how to use the word "kettle" prior to knowing what a kettle is. That's simply the way we learn as children. We learn things before we learn how to describe what it is that we have learned. We learn how before we learn that. Therefore by the time that a person learns that oneself has knowledge, it is impossible that the person does not have knowledge.

So such a mistake, as thinking oneself to have knowledge when one does not, is impossible. And so it is also impossible that the person thought they knew something when they didn't. It seems like it would be more of a case that the knowledge which one had was not quite what the person thought it was. They really did know something, it just wasn't exactly what they thought they knew.

But as I said, the findings of science are that the position of an electron isn't like the number of coins in the jar. The former is in a superposition, the latter is not. If you want to use science to support your position then you cannot pick and choose which bits you like. — Michael

You seem to be missing the point. In each case, there is no measure until the measurement is made. There is no number assigned to the supposed quantity within the jar, until the coins are counted, and there is no location of the electron until the measurement is made. "Superposition" is irrelevant, and something you just brought up as a distraction from the real issue, as if it had some relevance. It's really just a fancy word meaning that the position is undetermined, just like the number of coins is undetermined.

I'm not even sure what you're asking. If you're asking if somebody has determined the number of coins before somebody has determined the number of coins, then of course not. If you're asking if there is some number of coins before somebody has determined the number of coins, then yes. — Michael

I think you are using dishonest language Michael, to avoid the question. "Some number" is a general reference, and it does not mean a particular number. When the coins are counted there is a particular number, a specific number, which is assigned to the quantity of coins in the jar, as "the number" of coins in the jar. That is what I have been arguing is a matter of judgement, the decision as to which specific number gets assigned to that quantity. If you really think that there is a particular number assigned to the quantity before it is counted, I'd like to hear your explanation as to how this occurs.

We are not discussing whether there is a quantity of coins in the jar, in that most general sense, we can see that there is a quantity without counting them. We are discussing whether there is a particular number assigned to that quantity, prior to being counted, whether or not the coins in the jar have a specific number. Do the coins in the jar have a number? So the question is, do you honestly believe that there is a particular number which has already been assigned to the quantity of coins in the jar, prior to them being counted?

Your argument seems to commit a fallacy of equivocation. — Michael

No, I think it is you who is equivocating, now saying that "the number" of coins in the jar is "some number". See, you have moved from your assertion that the coins in the jar have "a number" to the claim of "some number", where "some number" now means any one of an infinite number of possibilities. Do you see the difference in predication? The quantity has a number, or, the quantity has many possible numbers. The latter is the reality, because the number is determinable, not determined.

If the procedure terminates, then the number we have reached is the number of coins that were in the jar before we started counting. — Srap Tasmaner

Yes, that is a logical conclusion, which validates the act of counting. Counting the coins in the jar justifies the claim that the number of coins in the jar is determinable. Retroactively, after counting, we can now employ a premise about temporal continuity, to conclude that this was the number before counting. But notice, that this number is not produced until after counting, and is applied retroactively. So we still cannot truthfully say that we could have said, that before counting, the coins had that number. The number is produced from the counting and applied retroactively.

This would be the same sort of faulty temporal argument that some determinists try to employ against free will. After a person acts in a specific way, it is claimed that the person acted this way, so it is impossible that the person could have acted otherwise. But it's really just a faulty application of retroactive logic. Yes, after the fact, it is impossible that the fact can be otherwise, but prior to the fact there is a multitude of possibilities. The same sort of thing is the case with the coins. After counting, it is impossible that the count could be otherwise. But prior to counting, we have to admit numerous possibilities. The retroactive application of logic, after the act of counting, to say that there was X number of coins before the counting, does not negate the fact that prior to the counting there was no such thing as the number of coins, only a multitude of possibilities.

But if we do agree what to count as a coin and which coins to count, we know there is a procedure available, and that we will be able to determine the number of coins currently in the jar, even if we have not yet made that determination. — Srap Tasmaner

I agree, that prior to counting, we can truthfully say that we might count the coins, apply logic, and say how many coins are in the jar now. But that does not mean that the coins in the jar have a number now. The coins in the jar now, prior to being counted have no number, and even though we might apply logic at a later time to say how many coins were in the jar at this earlier time, that still doesn't change the fact that the coins in the jar at this earlier time have no number, because the count, and the logic haven't been applied yet.

It's a very simple principle. After the fact, we can make all sorts of conclusions about what happened, and why it happened, causation etc.. But this does not imply that we could have made the same conclusion before the occurrence of the event. So, after counting, we can make conclusions concerning the quantity of coins in the jar, which we could not make before counting.

That was quite the rant Tones. I hope you're feeling better now, to have gotten that off your chest. And if so, I'm very happy to have been able to assist you, in feeling better about yourself: if that was even possible. If it wasn't possible, for you to feel better about yourself, as I fear is the case, then I'm sorry, for you.

somehow the truths of math have been revealed to no one else but you. — Real Gone Cat

Really, where did you get that idea? I am in the habit of dismissing what are commonly touted as the "truths of math", for being in some way faulty. How do you get from this to the point of saying that the real "truths of math" have been revealed to me.

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.

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

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.

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. — Andrew M

No, I don't think that's right. People just change their minds about things, and sometimes if encouraged to, they will admit to having previously been wrong. But they are more inclined to say that their information (knowledge), was incorrect when the mistake was made, than that they didn't have knowledge at the time. This is because having incorrect knowledge allows them to pass blame elsewhere, toward the source of that incorrect knowledge.

If we look back, in retrospect, we see two possible principal causes of mistaken action, one being a lack of knowledge, the other being incorrect knowledge. The two are not the same, and we must maintain a distinction between them to be able to understand and prevent the causes of mistake in the future. You seem to be claiming that there is no difference between these two in ordinary usage of "knowledge", as if people don't distinguish between lack of knowledge and incorrect knowledge when assigning blame, and in other situations.

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. — Andrew M

No, this is an incorrect conclusion as well. 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". 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.

So are you saying that the number of coins in the jar is in some sort of superposition of all possible numbers until someone counts them? — Michael

No, not really. I used the example of quantum mechanics to elucidate the type of problems which adhering to your principles brings about. We look at an electron as a particle, and we think, a particle has a determinate location, therefore the electron has a determinate location. The issue at hand is that "determinate" is not the same thing as "determinable".

Now, if you and I look at the jar of coins, you would say that there is a determinate number of coins in the jar, and I would say that there is a determinable number of coins in the jar. I differ from you, because I insist that an act of determination (measurement) is required to determine the number of coins, before we can truthfully say that the number is determinate. You seem to take this act of determination for granted, as if there is already a number assigned to the coins without an act of measurement. That, I say is a mistake. There is no number already assigned to the coins prior to being counted, just like there is no location already assigned to the electron prior to being determined.

Taking things like this for granted is a pragmatic principle which is extremely useful. If we want to know the quantity of coins, we assume that there is such a thing as the quantity of coins, therefore it is determinable, and we are motivated to count them. Further, we can use this assumption to state premises for logical procedures, like you did, which I said was begging the question. However, that there is a determinate quantity is just an assumption, which is not completely justified until after the count. So in the case of the electron, we might assume it is a particle, therefore it has a location which is determinate, and then we could proceed to determine it. In the end though, the original assumption, that the electron is a particle with a determinate location, is never justified. What is justified is that it has a determinable location

What this demonstrates, is that we must be very wary of these pragmatic principles, which we accept without proper justification, for the sake of facilitating our logical procedures. The principles are extremely useful, and even appearing to be infallible in the circumstances where they are heavily used, and so they appear to be universal. But then, when we expand the use of them, because of that appearance of universality, outside their range of applicability, this misleads us. Because the principle is so extremely useful, and infallible in its original application (there is a determinate number of coins in the jar), we are not inclined to use the tool of skepticism, to question that premise and see where it is faulty.

Forget the word "true" for the moment: what kind of (meta)physics are you suggesting describes the nature of the world? — Michael

Come on Michael, if I knew the answer to that, I'd have reality all figured out. And of course, so would everyone else because when one person gets it right everyone else jumps on board. I think metaphysics is an inquiry into the best way to describe the nature of the world. If one already knew the best way there would be no need for inquiry.

I am asserting what our best understanding of the world entails. You brought up quantum mechanics earlier to support your argument, so you appear to accept the findings of scientific enquiry, and the findings of scientific enquiry are that the number of coins in the jar isn't in a superposition of all possible numbers until counted.

I would say that you are begging the question, saying that "there is no such thing as the number of coins in the jar [until counted]" without any evidence or reasoning. — Michael

Look at it this way, it's very simple really. The truth of the phrase "the number of coins in the jar" implies that there is one specific number attached to, associated with, or related to, the quantity of coins in the jar. Can you agree with that? Now do you honestly believe that a particular number has already been singled out, and related to the quantity of coins in the jar, prior to them being counted? How is that possible?

I think the real problem here is that we've come from a tradition of religious beliefs. We have a religious history. So there are many old principles that we now take for granted, which are only properly supported by the concept of God. Isaac Newton for example, stated that his first law of motion (which we tend to take for granted), relies on the Will of God. This is similar to what I think about your belief, that there is a specific number already associated with the coins in the jar. It is a belief which was developed under the assumption that God has already counted them, and assigned that number to the quantity of coins in the jar.

Time, however, is a concept and it can be defined as what clocks measure, but time is not limited to this definition. — val p miranda

As a concept, time is the measurement of motion. — val p miranda

See the difference between these two concepts of "time" val? The one says that time is what is measured. The other says that time is a measurement. Clearly these are not the same concept. The clock measures something, time in sense 1. And, we also produce a measurement, time in sense 2. It is impossible that the thing measured, and the measurement itself, are one and the same thing. Therefore we have two principal senses of "time".

There is some number n where n >= 0 such that “there are n coins in the jar” is true even if nobody has counted them. — Michael

You are just begging the question Michael. Sure it is true that someone could count the coins, and determine how many there are. But until someone does, there is no such thing as the number of coins in the jar. This requires that someone draws (judges) a relation between a particular number, and the quantity which the jar contains. Until then, the number of coins in the jar is undetermined.

All you are doing here is mentioning every possible number, and saying that one of them will be the number of coins in the jar, if counted. So you are assuming that it is possible that the coins can be counted and you say that one of the infinite possibilities will match. I would assume the same thing. But I think it's quite obvious that until they are counted, there is no such thing as the number of coins in the jar. No specific number has been assigned to that assumed quantity. Therefore there is no number to that quantity. And what you are saying above, is that out of all the possible numbers, you are quite sure that one will prove to be the correct number. So you apply some logic to justify your claim that the coins can be counted and one number will prove to be the correct number. However, this does not produce the conclusion that there already is a correct number, as you seem to think it does.

And how do you account for two people making contradictory judgements, much like you and I here? Is it just the case that we disagree or is it also the case that one of us is right and one of us is wrong? — Michael

This is a good question. If the two people honestly believe what they are saying, and are stating it to the best of their capacity, they are both making true statements, regardless of the fact that they disagree with each other. This is why knowledge requires justification as well as truth. We move to resolve these disagreements through justification. Right and wrong are judgements based in justification, whereas "true" is a judgement based in what one honestly believes. You can see a lot of overlap here, and that is "knowledge" as justified true belief.

I didn't say the axioms are wicked, I said they are wlly nilly. And it was Tones who stated that idea. I just went on to draw the conclusion that when you create your principles in such an undisciplined way, you need luck in the application of them. Here:

I've told you about a million times already, you can have axioms for whatever you want*, even inconsistency if that's your thing. — TonesInDeepFreeze

I can say "there are 66 coins in the jar" and that claim can be true even if I haven't counted the coins in the jar and even if nobody knows how many coins are in the jar. — Michael

So you say, but as I explained, I think you are being dishonest in your statement. You are using "can be true" which honestly implies possibility, to make it appear as if "66" actually is true. It is not.

To "be true" is very clearly a judgement. And if no one has counted the coins, who do you propose has made that judgement, God? Obviously, you are not even proposing that the judgement has been made, you only say "can be true", meaning it is possibly true. Yes, just like 65, 64, etc., are all potentially true answers. But that does not justify the claim that there is a true answer.

It's not the case that my claim retroactively becomes either true or false after someone has counted them. And it's not the case that if two people count the coins in the jar and come to a different conclusion that both of them are right. — Michael

This does not address the issue. Prior to being counted your answer, 66, "can be true", meaning it has the potential to be true, just like other numbers. When the coins are counted, there is a correct answer. There is no retroactivity involved. Prior to being counted, all the answers had the potential to be true, and after counting, the judgement is made.

Retroactivity is the mistaken route which the others proposed. After determining that what was accepted as "knowledge" is determined to be incorrect, they propose that we retroactively declare that it was really not knowledge. But then everything which we commonly call "knowledge", may at any moment, be shown to be not knowledge. Retroactive judgements is a mistaken venture.

This issue was very well discussed by Aristotle thousands of years ago. His solution was an exception to the law of excluded middle, to account for the reality of potential. So things which require a judgement, like the famous sea battle example, are neither true nor false, prior to the judgement being made. "There will be a sea battle tomorrow" is neither true nor false. And, after tomorrow passes, we do not retroactively say that there was a truth or falsity to that statement yesterday. We simply must face the fact that there neither is a truth nor a falsity to these statements which require a judgement, prior to the judgement being made.

We're not talking about quantum states though. — Michael

I used quantum mechanics as an example of how that type of dishonest thinking, which you display, causes problems in application. The particle "can" (potentially) have a location, but that does not justify the claim that it does actually have a location.

Good luck with that. — jgill

Thanks, but unlike the undisciplined mathematicians who make willy nilly axioms however they please, we don't rely on luck here.

A proposition being true and a proposition being determined to be true are two different things. — Michael

That's exactly what I don't agree with obviously.

There is a correct answer to "how many coins are in the jar?" before we actually count them. — Michael

If you think so, explain to me who has counted the coins in the jar and stated the answer. An "answer" is something stated as a reply to a question. If no one has counted the coins, and it was not determined at the time of placing the coins in the jar, and the jar has been watched, then no one knows how many there are, and no one has stated the "correct answer". The "correct answer" will be determined when the coins are counted. Therefore, there is not a correct answer to that question before the coins are counted. The number of coins is undetermined, no "correct answer".

This, I propose to you, is where we cross the line between honesty and dishonesty in our philosophy. We honestly know that unless the number has been determined, there is no correct answer. The correct answer is undetermined, it does not exist. However, we assume that since the coins could be counted, there is potentially a correct answer, and we allow that this potential answer has actual existence, and we say as you do, "there is a correct answer". This, I tell you, is a dishonesty, because we know very well that there is a difference between what actually exists and what potentially exists, yet we allow this division to be nullified, because it simplifies our use of mathematical language. We do not have to account for the process of counting, (See the difference between actually and potentially infinite for example). The abundant consequences of this sort of dishonesty are very evident in the issues of quantum mechanics.

It's not just a judgement. See above. — Michael

That's right, it's not just a judgement, it's a special type of judgement, a dishonest judgement made for the sake of facilitating our language use, especially mathematical languages (See above). When we are well convinced that "the truth" could be determined, we jump to the dishonest conclusion that the truth already is determined, for the sake of avoiding philosophical discussion about the required process of determination. The fact that this is a mistake is fully exposed in quantum mechanics. The particle's location really is not determined before the process of determination, and it is obviously mistaken to think that it is. Therefore it is only the process of determination (the act of measurement) which can determine "the correct answer". And the character of that assumption, that there is a correct measurement, prior to the measurement being made, is fully exposed for the lazy, and dishonest, attitude that it truly is.

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.

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. — Andrew M

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. This is what Plato demonstrated in The Theaetetus. So, it's much better to allow that what people claim to know right now, is "knowledge", regardless of the fact that it may later turn out to be wrong. It was still knowledge, at that time, before it was proven wrong.. So, if at a later time they decide against it, it is no longer knowledge, but it still was knowledge back when it formed the principles upon which they based their decisions.

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. 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..

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". — Andrew M

It isn't archaic usage. It is the principal meaning of "truth", employed in courts of law etc., and any time or place where people are asked to "tell the truth".

As I said to another poster a few days ago, all this says is that we determine the meaning of a proposition. It doesn't follow from this that we determine the truth of a proposition. — Michael

But I said more than that. I said that whatever the proposition means must be related to what is actually the reality of the situation, and through this comparison, it is judged for truth. That's how we determine the truth of a proposition, through judgement. How could the truth of a proposition be determined, except by a judgement?

Our language use determines the meaning of the proposition "water is H2O". John believes that this proposition is true and Jane believes that this proposition is false. The laws of excluded middle and non-contradiction entail that one of them is right and one of them is wrong, irrespective of what they or I or anyone else judges to be the case. — Michael

Actually, what you've just stated, that one must be right and the other wrong, is just a judgement itself, made by you, as Mww has already pointed out.

True or not true can be nothing other than a judgement. The question of the thread, I believe, is what exactly constitutes a true judgement. But we cannot remove the judgement aspect without leaving "true' as completely meaningless. That would be like asking what is "red" while insisting it's not a colour.

There is no judgement. It just either is or isn't true. — Michael

This cannot be correct. A proposition requires an interpretation and a comparison with what is the case, to be determined as either true or not true. That is a judgement. With no such comparison or relation, between the words of the proposition, and the reality of the situation, there is no truth to the words.

This is where Banno ran into trouble with the claim that a proposition is always already interpreted, and I accused him of dishonesty with that claim. We cannot ignore the simple fact that symbols symbolize, and therefore need to be read. Apokrisis has a unique way of dealing with this, claiming that the interpretation, (or rules for interpretation, or something like that), are actually encoded within the symbol itself, so the symbol actually reads itself. This, it is claimed, is derived from biological foundations.

pi is not a ratio of two rational numbers.

pi is the ratio of the circumference of any circle and its diameter. But if the diameter is rational then the circumference is not. So still pi is not the ratio of two rational numbers.

So there is not a contradiction. — TonesInDeepFreeze

The measurement of one is incommensurable with the measurement of the other, therefore the relation between the two measurements is an irrational ratio. So I wouldn't really call it a contradiction, it's just an attempt to do the impossible, to establish a relation where one cannot be properly established due to that incommensurability. A straight, one dimensional line is incommensurable with a curved two dimensional line. Likewise, an attempt to give the cardinality of an infinite set is an attempt to do the impossible.

Since music is numinous in nature, it being somewhat of a bridge between us and the universe, the Pythagoreans probably extrapolated the math found therein to the universe itself. — Agent Smith

This was primitive wave theory.

The discovery of irrationals, kind courtesy of Hippasus of Metapontum who was thrown overboard to prevent word of this getting out, threatened to overturn what was up to that point a perfect world. A simple and yet magnificent way mathematics could serve as the foundation of the universe had to be abandoned. I wonder what Max Tegmark has to say about this? — Agent Smith

The temporal nature of waves always seems to throw a wrench into the cogs of the application of mathematics toward understanding the foundation of the universe.

I know, I know, pay no attention to the man behind the curtain. — jgill

Step out from behind that curtain. On with the show this is it!

Mathematicians come up with general formulas, involving pi and other irrational numbers. Isn't it the case that engineers make use of those general formulas, from which they can decide what specific specific values to use as close enough for the task at hand? — TonesInDeepFreeze

Yes sir! But what happens when understanding the foundation of the universe is "the task at hand"?

You clearly refer to negative knowledge of p (i.e. ~Kp); not to positive knowledge of not-p (i.e. K~p). You say that it is not knowledge: "not allowed to be called knowledge", "said not to be knowledge". It is unreasonable to deny this; it is there in black and white. — Luke

You clearly misunderstood what I said. Or, as is often the case with you Luke, you intentionally misrepresented what I wrote. Whatever, I will repeat myself as usual. The same ideas which are knowledge at one time are not knowledge at another time.

It cannot be known that not-p is true if p is true, due to non-contradiction. This applies at any given time. — Luke

Again, you are using "true" in a deceptive, sophistic way, as I explained in my last post. That a statement is "true" or "not-true" is a human judgement. The same person can judge the same statement as true at one time, and not-true at another time, yet a person cannot judge the same statement as true and not true at the same time (contradiction). The same idea is judged as "true" at one time and "not-true" at another time, and there is no contradiction.

This is completely consistent with my definition of truth, as an expression of what one honestly believes. You however, seem to be assuming some sort of "truth" which is independent of human judgement, as an unstated premise. Your use of this unstated proposition is simply an attempt to deceive. Who would make such a judgement of truth, God?

The same person or people making the judgment that p is true in your example. It makes no difference.

Obviously it's not the person who knows not-p.
— Metaphysician Undercover

Obviously not. Nobody can know that not-p is true if p is true. — Luke

The question is, in your statement "Nobody can know that not-p is true if p is true", who is making the judgement that "p is true". A person can know that not-p is true, when that person is not making the judgement that p is true. Therefore you need to disclose who is judging p as true, in your statement. If it is not the person who knows not-p, then there is no problem.

Your use of "true" here is deceptive, because you do not disclose the person who is making the judgement that p is true. Clearly it's not the person who knows that not-p is true, so who is it making the judgement that p is true? I honestly believe that you are simply employing a counterfactual here, for the purpose of deception. When the person knows that not-p is true, then "p is true" is proposed as a counterfactual unless justified, in which case it would be an attempt to change the person's mind. You have made no attempt to justify "p is true", so I conclude the counterfactual is proposed for the sake of deception.

Is it a coincidence that the word "irrational" means illogical/makes zero sense? — Agent Smith

Consider the root of "rational" is "ratio". Now think about an irrational ratio such as that expressed as pi, and you'll get a glimpse at the problems which pervade mathematics.

That a verb like "know" isn't factive.

One of my aims here has been to convince you to abandon the idea that the 'factive verbs' form a sui generis semantic or syntactic category. Perhaps there is some sui generis semantic or syntactic category of expressions that deserves the name 'factive verbs' or 'factive expressions', but the list that philosophers usually offer does not comprise such a category. I have made a case for denying that an utterance of "S knows p' is true only if p is true, i.e. that "knows" is factive. — Michael

The other way to go is to allow that if S knows p then p is true, but define "true" differently. As I propose, "true" would mean a statement of what S honestly believes, i.e. p would be an expression of what S honestly believes. Of course this definition of "true" has its problems, but I think it's much better than what some here propose, which is to reduce "true" to a special form of justified, like justified in an infallible way. Then "knowledge" simply becomes justified belief regardless of whether the justification is done in honesty or not, because infallible justification is impossible unless we invoke an omniscient God who holds real knowledge.

I would rather take the inference rule as primary and say that our usage of "know" mostly, though imperfectly, follows that -- that this is the nature of knowledge -- rather than saying the inference rule rests on an analysis of how we use the word "knows." — Srap Tasmaner

The problem is that this is not the nature of knowledge. This is the way that some epistemologists think knowledge ought to be. In reality, knowledge changes and evolves, and things accepted as knowledge at one time (geocentricity for example), are later rejected, becoming no longer justified. Knowledge naturally contains much which is not consistent with the reality of things, therefore not "true" by common definition.

That was one of my two options: At one time the person claimed to know p, but it turns out later that they did not know p. — Luke

That's not what I said. I said the person did know p, then later came to know not-p. I thought I made that clear. At one time the person knew p. At a later time the person knows not-p. This is not a case of it turning out that the person did not know p at that time. Nor does the person know not-p at that time, because the person knew p at that time.

What I am saying is that p was a part of the person's knowledge at one time, and not-p was a part of the person's knowledge at another time, because knowledge changes. The person clearly knew p, as p may have played a significant role in the person's body of knowledge. So we clearly cannot change this to say that the person did not know p, because this would involve the contradictory conclusion that the knowledge possessed at the time was not really knowledge.

And how did they "decide" this? — Luke

The person decides not to believe p any more for a number of possible reasons, but most likely because other evidence is brought to the person's attention, which the person did not have access to before.

My understanding on the factivity of "know" is that you cannot know ~p where p is true. — Luke

You are using "true" in a deceptive way here. That p is true is a judgement. And of course, if one judges that p is true, then this person obviously does not know not-p. So, who is making the judgement that p is true in your example? Obviously it's not the person who knows not-p. This example is just deceptive sophistry.

The problem, as I've explained, is that your statements do not give an accurate representation of what knowledge really is. In reality, knowledge consists of many mistakes. That's why the knowledge of yesterday is always being replaced by the knowledge of today. Things which were accepted as fact, and which were a part of our knowledge are later demonstrated to be not accurate. That's the nature of justification.

This is the issue Plato faced in "The Theaetetus". They sought to determine the true nature of knowledge. But they set out with the prerequisite condition that knowledge could not contain any mistakes. Then they found out that of all the possible descriptions of knowledge that they examined, none of them had the capacity to exclude mistakes. So they ended up concluding that this prerequisite condition, to exclude falsity. was itself a mistake, therefore not really a defining feature of knowledge.

Grice claims that conversational implicature is "triggered" by an apparent violation of a maxim of conversation, which suggests that what you mean by uttering p must be different from the plain meaning of p, in order to preserve the assumption that you are cooperative (and not after all violating a maxim). — Srap Tasmaner

Here lies the problem. Intentional violation of the maxim is dishonesty. But if you mean something different from p than what others take from it ("the plain meaning of p"), this could be either dishonesty (intentional violation of the maxim) or an honest mistake. Now we need principles to distinguish one from the other, to determine whether the person practises deception.

You are repeating the same error that I pointed out to you before.

Does it turn out that the person does not know that the proposition, p, is true (i.e. ~Kp), or does it turn out that the person knows that the proposition, p, is not true (i.e. K~p)?

That is, does it turn out that they don’t know p, or that they know not-p?

If the former, then it’s irrelevant to what Srap said. If the latter, then what does it mean that they claim to know p but it turns out they know not-p? How is that possible? — Luke

Your two options do not contain the correct choice. What is correct, is that what is at one time called "knowledge", is at another time not allowed to be called knowledge. So the same ideas at one point in time qualify to be called "knowledge", yet at a later time are said not to be knowledge. The person knew proposition p as true, then later decided proposition p is not true.

This implies that "knowledge" is a product of judgement, not a product of "what is the case". And, when we recognize the following two premises, knowledge is a product of human judgement, and that human judgement is fallible, we can conclude logically that knowledge may consist of some faulty judgements.

Knowledge is a feature of one's attitude. There is nothing unusual or strange here, just a recognition of the fact that people can change their minds. At one time the person knows "p", and at a later time the person knows "not-p". This demonstrates the need for skepticism. We must always revisit our knowledge, and keep abreast of the need for change.

That is why we ought to define "true" in the way that I proposed, as related to honesty rather than "what is the case". Then we can accurately represent Knowledge as justified true belief, because "true" would then signify the position of the ideas which comprise "knowledge" as relative to an honest attitude, rather than some pie in the sky absolute, referred to as "what is the case".

So there is no need for us to enquire as to what does "what is the case" signify, just a need to enquire as to what does "honesty" signify. The modern trend is to completely ignore the importance of honesty in knowledge, and replace it with something which no one can understand, "what is the case". Then we can endless discuss the meaning of "what is the case" thereby avoiding the true issue which is honesty.

So, what does the paper say about factive verbs?

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

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. And the fact is that people often claim to know things, which turn out to be not the case. So the definitions which epistemologists prescribe as to what "knowledge" ought to mean, do not accurately reflect how "know" is truly used.

But this is all irrelevant, because the point was that without the premise being stated, the logic is invalid.

So let's state it:

     Kp ⊢ p     Kp ⊢ p

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

So here you have the premise stated. But in Srap's rendition of the propositional attitude, this is not stated as a premise, it is presented as a valid conclusion. Srap also extended this invalid logic to other attitudes, to conclude if it is remembered it is what is the case, if it is seen it is what is the case, and if it is regretted it is what is the case. The point is that one might state these as premises, as you have, to be judged for truth or falsity, but to present them as logically valid conclusions without providing the premises required to make the conclusion, is a mistake.

That knowledge entails truth means only that if someone does know X then X is the case. — Andrew M

You can state this as a premise, in which case I would reject the premise as unsound, because much knowledge ends up not properly representing what is the case, and therefore requiring revision, but you have not yet shown the premises required to make this ("if someone does know X then X is the case") a logically valid conclusion. That is the point I've been making.

The problem I believe is in how you relate "true" to "is the case". If "true" means what is the case, and if knowledge entails truth, then knowing X means that X is the case. However, as I explained above, in common usage knowing X does not mean X is the case. So there is a problem here. 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.

As Srap Tasmaner has pointed out, know is a factive [*] term while imagine is not. — Andrew M

The point is, that for the logic to be valid :"know" must be defined as a "factive" term as a premise. Other wise, this notion that knowing something logically implies the existence of the thing known is an unstated premise which is required for the claimed conclusion. Conclusions which require additional premises other than those stated are not valid conclusions.

The required premise (Kp ⊢ p) comes from observing how the term know is ordinarily used in language. — Andrew M

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. This is the problem, relying on unstated premises denies us the capacity to judge the soundness of the premise. Then the unsoundness of the unstated premise is allowed to contaminate the validity of the logic.

Also, there is very much ambiguity in the normal use of the term "know", so that premise, if stated ought to be judged as false (dishonest sophistry). Much more often than not, |know" is used in a fallible way, as I said much earlier. 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

Having no philosophy is not a disqualifier. — TonesInDeepFreeze

Your lack of training in philosophy really shows. And, it is very annoying for a philosopher, when a person without philosophy comes to a philosophy forum, and enters into a philosophy of math discussion, insisting that philosophers ought not discuss the metaphysical principles upon which mathematical axioms stand, if they have not first studied mathematics. Clearly, it is philosophy which is being discussed in the philosophy of mathematics, not mathematics.

I am reasonable in forums. — TonesInDeepFreeze

The above is unreasonable behaviour. And, you personally increase the degree of unreasonableness with the use of insult. When you do not understand the philosophical principles being discussed, because you have no philosophy, you simply hurl insults at the philosopher. Try some introspection, to reveal to yourself, your unreasonableness. You may find the way toward respect.

Srap is talking about knowing something that is not the case. — Luke

No, Srap is claiming that if someone "knows" something, "remembers" something, "sees" something, or "regrets" something, then without a formal definition of these words, it is logically implied that what the person knows, remembers, sees, or regrets, is necessarily the case. Of course this is clearly invalid logic. We cannot produce any deductive conclusions from a word or symbol without any defining propositions.

You mean if I wrote something like this?

     Kp ⊢ p     Kp ⊢ p

Like stating that kind of premise? Or would you prefer something like this?

     ∀p(∃xKxp → p) — Srap Tasmaner

Sorry, I don't understand the language. Try English, please.

But then, honestly, I'm not sure what there is to talk about if your position is that one can know things that are not so, see things that are not there, remember things that did not happen, and regret doing things you did not do. — Srap Tasmaner

It's very common, I claim to know, see, remember, or regret something, which turns out not to be so. Remember, logic deals with propositions, and a proposition is what is claimed, it is not what is so. And you agreed that human beings are fallible. So the proposition "I know X" does not mean that X is the case. "Jack knows X. Therefore X is what is the case." Wait, something is missing. Can't you see that we are missing a premise, the one which says "if someone knows something then it is what is the case"? And as I said, you might state such, as a proposition, or premise, but it would be rejected as false, because of that fallibility; especially with the other terms, see, remember, and regret.

It's only sophistry, your claim that knowing something, seeing something, remembering something, or regretting something, implies that what is known, seen, remembered, or regretted is what is the case. Just like in my examples of feeling something, or intuiting something, these do not imply that what is intuited or felt, is the case. Since you still don't seem to get it, let me add "imagining something". 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?

Yes, we're a wicked bunch intent on the corruption of the intellects of youth in order to bring them to the alter of our Satan, Paul Erdos RIP. All bow. — jgill

Not all mathematicians are the same, just like not all theists are the same. It's just that some are fanatics with a cultlike attitude, who are inclined toward professing absurd ontologies to support their beliefs.

I had to look up Paul Erdos, to see that he is famous for his work on Ramsey theory. Seems like Erdos was very socially active. Is he responsible for the famous notion "six degrees of separation"? Or was he just paranoid about aliens? I see you can still earn money by solving Erdos' problems. Have you ever managed to get any reward?

You cannot know what is not so. You cannot see what is not there. You cannot remember what did not happen. You cannot regret doing what you did not do. — Srap Tasmaner

All of these examples, "know", "see", "remember", and "regret", require another premise establishing a relationship between each one of them, and "what is", in order to produce a valid conclusion.

There is no premise which states that if you "know" it, it is. No premise which states that if you "see" it, it is, nor for "remember", or "regret".

I could just as easily say, "if I feel like it's going to rain this afternoon, then it is going to rain", or, "intuition tells me so". What makes "regret", "remember", "see", or "know" produce a more valid conclusion than "feel" or "intuit"? Or, we could take the example from . If I say "pass me the kettle" does this imply that there actually is a kettle? Validity requirements do not allow us to make such conclusions. That's why a definition of sorts is a required part of the premises.

Logic doesn't guarantee the truth of what you say, but connects one truth to another. — Srap Tasmaner

Logic guarantees that properly derived conclusions are valid. Your conclusions for the attitudinal propositions are not valid, because they depend on unstated definitions for terms like "know", "see", etc.. Valid logic uses premises which state something necessary, or essential about a term ('man is mortal' for example), and then it proceeds to utilize that necessity stated, to produce a valid conclusion.

You have not stated the necessary premises concerning the terms, "know", "see", etc;, to produce a valid conclusion. And, if you did state those premises, "if you know it then it is true", "if you see it then it is true", they would just be rejected as false propositions. So it's as if you believe that by not stating the required premises you can avoid having them rejected as false, and simply proceed to produce a valid conclusion without the required premises through some sort of sophistry. But you cannot, because the premises are required to produce a valid conclusion.

In modus ponens, the conclusion follows necessarily from the premises. The conclusion, that today is Joe's birthday does not follow necessarily from the premise "I remember that today is Joe's birthday", because there is no premise to relate "I remember", to what "is".

Now the nature of infinity is an interesting topic to explore! — Real Gone Cat

I stated earlier in the thread, what I believe to be the reason for the concept of infinite:

What I think, is that we allow "infinite" so that we will always be able to measure anything. If our numbers were limited to the biggest thing we've come across as of yet, or largest quantity we've come across, then if we came a cross a bigger one we would not be able to measure it. So we always allow that our numbers can go higher, to ensure that we will always be able to measure anything that we ever come across. In that way, "infinite" is a very practical principle. — Metaphysician Undercover

But it may surprise you to know that many mathematicians today believe that actual infinite sets exist in math! — Real Gone Cat

That doesn't surprise me at all. I've had numerous discussions in this forum with mathematicians, and I've already been well exposed to the absurd ontology which seems to be exclusive to that cult.