From a French point of view, influenced by Descartes, knowledge is strongly linked to certainty: strictly speaking says Descartes, I cannot know anything unless it is impossible for me to doubt it, that is, unless I am certain about it. In traditional French philosophy, knowledge is defined as " (1) connaissance [hard to translate: cognizance, acquaintance] (2) certaine"

However, I see that in the English-speaking philosophical world, certainty is so to say absent from discussions regarding language. I cannot see where certainty can be found in the standard definition of knowledge as true justified belief.

How to explain this?

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    For Descartes a belief is justified only if it is certain, so that’s where it is found. – Eliran Jul 3 '19 at 15:40
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    "Justified true belief" is Plato's formula, it is not an English speaking idea, and the certainty is supposed to be in the "justified", since Plato believed that we can achieve absolute justification via anamnesis. Emphasis on certainty is generally typical of epistemological foundationalists, who include Kant and Husserl, among others, so it is not specific to France. It is true that Anglophone philosophy always had a strong empiricist bent, and emphasized fallibility of knowledge, vs French/German rationalism. But I am not sure what would count as "explanation". Traditional practicality? – Conifold Jul 3 '19 at 16:48
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    Certainty as a psychological state is really no more than presumption. Logically justified certainty is the comprehension that the a conclusion is logically entailed by premises that are necessarily true. – polcott May 27 at 3:30
  • The most certainly true assertion is "existence exists". Any attempt to prove that existence does not exist would be self-refutational, (because it would form an example of a thing that exists thus a counter-example to the claim that "existence does not exist" ). This makes the assertion that "existence exists" is irrefutable. – polcott May 27 at 19:25

However, I see that in the english speaking philosophical world, certainty is so to say absent from discussions regarding language. I cannot see where certainty can be found in the standard definition of knowledge as true justified belief. How to explain this?

I think that the theory of knowledge as justified true belief is typical of analytical philosophy, which is hegemonic in English-speaking countries, and in particular in the United States.

Certainty, however, is a psychological condition and certainty that p doesn't imply p and therefore doesn't imply knowledge that p.

As I understand it, Descartes' idea is that doubt disproves knowledge, an idea he put to very effective use to arrive at the Cogito. However, as a psychological condition, certainty itself seems immune to analysis and therefore of little interest in particular to analytically-minded philosophers.

Is there an overlap?

Certainty applies to beliefs. We have beliefs, and we are certain of some of our beliefs while uncertain of others. Some of the beliefs we are certain of may be actual knowledge. Uncertainty, i.e. doubt, disproves knowledge, according to Descartes, but certainty doesn't prove knowledge.

So, there is perhaps an overlap.

Let's assume p is true. Let's assume further that subject A believes that p, and that A is somehow justified in believing that p. The theory of justified true belief says that, under those assumptions, subject A knows that p. However, what if A has some doubts about believing that p. Descartes would say that therefore A doesn't know that p (the slightest doubt is enough to disprove knowledge).

So, here it seems we have a clear contradiction between the two perspectives, one analytical philosophy, the other a typically "continental" philosophy.

The two perspectives are clearly very different but there is nonetheless a striking similarity in the difference...

According to the JTB theory, a justified true belief is equivalent to knowledge. However, it is unclear that we could ever know that we know p since there is no finite procedure to decide that we know that p is indeed true as required.

So, JTB is logically inconclusive since we don't know how to ascertain the truth of at least one of the premises theorised as necessary to the conclusion.

Descartes has also a problem, though. To disprove that you know p, you need to be able to doubt that p. However, how do you know that you doubt that p? Descartes doesn't offer any procedure to decide that you know something. His procedure is only effective in disproving that you know something. You can prove you don't know that p by being able to doubt that p is true. You cannot prove that you know that p. And, therefore, you cannot prove that it is true that you doubt that p is true.

So, at least as described by Descartes, his view was also logically inconclusive.

Perhaps Bertrand Russell bridged the gap. He made the distinction between propositional knowledge, i.e. subject A knows that p, and knowledge by acquaintance where subject A knows p.

For example, subject A knows that subject B is in pain: This is propositional knowledge. However, subject B is experiencing the pain: Subject B knows pain. This is knowledge by acquaintance, although only so while pain is being experienced. Knowledge by acquaintance reduces to propositional knowledge after the event.

Although I dispute the coherence of the theory of justified true belief, nonetheless it seems to me that its object is propositional knowledge, while Descartes' Cogito is typical of knowledge by acquaintance.

And perhaps the twain shall never meet.

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    @Speakpigeon.Thanks for this detailed and inspiring analysis! – user37859 Jul 4 '19 at 15:42
  • "Certainty, however, is a psychological condition and certainty that p doesn't imply p and therefore doesn't imply knowledge that p." Logically justified certainty is not psychological and is always based in semantic tautology. – polcott May 25 at 18:42
  • @polcott (1) I don't understand the concept of "logically justified certainty" unless it be psychological in nature. Maybe you could give a convincing example. - (2) Semantic tautology, I would assume, requires a lot of psychological huffing and puffing over what logical system is correct. Where's the proof that any system is correct? – Speakpigeon May 26 at 17:04
  • Successor(Successor(Successor(0))) = 3 We know that Successor(Successor(Successor(0))) equals 3 is true on the basis that the symbol: "3" on the RHS is stipulated to correspond to the (Peano axiom) algorithm on the LHS. – polcott May 26 at 17:52
  • "a tautology is a formula whose negation is unsatisfiable." A semantic tautology carries this same idea a little further. An expression of language that is necessarily true entirely based on its meaning: "Dogs are not cats" is impossibly false within the conventional meanings of those terms. – polcott May 27 at 3:28

A very rough explanation is that French philosophy has historically been inclined to various forms of rationalism which stress the power of a priori reason to deliver substantive and even fundamental truths about the world. On the model of mathematics, such truths are - or have been widely taken to be - demonstrable, immune from error, and certain - 'certain' in the sense (not psychological but epistemological) of 'certainly true'.

In equally broad terms, the English-speaking tradition has inclined towards empiricism and a reliance on sense-based knowledge, which is clearly liable to error. The senses are untrustworthy if it is certainty that one is seeking.

None of this does justice to the present state of French or of English-speaking philosophy and historically it neglects finesse, ignoring innumerable different streams of philosophical thought that have marked both French and English-speaking philosophy. But the broad historical contrast is correct or at least plausible.

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The only fully justified certainty that could possibly exist would be stipulated relations between ideas.

This most often happens when a new idea is created and this new idea is assigned to a new term. Whenever any new combination of ideas is assigned to a new term this assignment is stipulating the meaning of this new term. This stipulative definition process becomes the ultimate foundational basis of the meaning of this new term.

A stipulative definition is a type of definition in which a new or currently-existing term is given a new specific meaning for the purposes of argument or discussion in a given context. https://en.wikipedia.org/wiki/Stipulative_definition

Semantic Tautology
A Semantic Tautology occurs whenever any combination of semantic meanings is assigned to a word or phrase. This most often occurs whenever new combinations of ideas are created or discovered and they are assigned to a new term.

The only reason that we know that "3 > 2" is true is that the relation ">" has been stipulated between "3" and "2" when the ordered set of natural numbers has been defined.

If we construe the definitions of the meaning of words as a stipulated relations between words and their meaning then when we assess that an expression of language is true we would only be asking whether or not the relations that comprise it have been stipulated by its words.

Because we can verify that relations between words and ideas have been stipulated in the present moment it seems that none of the skeptical objections to fully justified certainty can be applied to this case.

Even if the entire universe including all of our memories were created just five minutes ago and the only existence of "cats" and "animals" is in our newly created memory of them the relation that: "a cat is an animal" would never-the-less still exist. This also applies to the brain-in-a-vat (Matrix film trilogy) thought experiment.

Analytic–synthetic distinction
(1) analytic proposition: a proposition whose truth depends solely on the meaning of its terms
(2) analytic proposition: a proposition that is true (or false) by definition
(3) analytic proposition: a proposition that is made true (or false) solely by the conventions of language --- https://en.wikipedia.org/wiki/Analytic%E2%80%93synthetic_distinction

Münchhausen trilemma
In epistemology, the Münchhausen trilemma is a thought experiment used to demonstrate the impossibility of proving any truth, even in the fields of logic and mathematics. If it is asked how any given proposition is known to be true, proof may be provided. Yet that same question can be asked of the proof, and any subsequent proof.

The axiomatic argument, which rests on accepted precepts which are merely asserted rather than defended. https://en.wikipedia.org/wiki/M%C3%BCnchhausen_trilemma

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  • What if we create new terms and ideas? Or if old ideas change meaning because new discoverings? Then perhaps the old truths become false... There is no rest in this world. All always changing... – framontb Jun 3 at 22:09
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    @framontb This is a very important question. It is very likely that errors would be easily introduced as words gradually evolve their meaning over time. The whole purpose of my answer is to show there are are at least some examples of fully justified certainty. The Münchhausen trilemma denies that there are any such examples at all. – polcott Jun 3 at 22:28
  • What about incorrigible beliefs, such as certainty regarding what seems to me to be the case? (ex: "I am certain that it seems to me that I am commenting on your answer", or "I am certain that I believe I am commenting on your answer".) These don't seem like tautologies and they could have even been false. – Adam Sharpe Jun 5 at 15:58
  • @AdamSharpe When I am explaining the one way that certainty is fully justified I am sticking with things that are true by definition (See Semantic Tautology above) and those things derived by valid deduction from premises that are guaranteed to be true because they are true by definition. – polcott Jun 5 at 16:42
  • @AdamSharpe That "you" are commenting on my answer is a semantic tautology when we leave open the exact definition of the term {you}. You may be a separate individual person, a computer program, or an aspect of my own subconscious mind. All that we really know about "you" is that you are the source of the message within the communication process. liarparadox.org/CommunicationProcess.png – polcott Jun 5 at 16:42

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