Knowledge-to-fact arguments can deliver knowledge

This paper examines Williamson's anti-KK arguments. We first investigate the epistemology assumption in Hintikka's epistemic logic, mainly based on his monograph Knowledge and Belief. We then compare it with Williamson's when he argues against KK principle. We discovered that the latter is not as neutral as he claimed, and these assumptions make his arguments very problematic, if not false. Williamson tried to construct a semantic that can be used to analyze the feature of knowledge, unlike Hintikka. But we find that there is a lot of hard work left unfinished.

Notices of the American Mathematical Society, 2010

We give a new proof for Godel's second incompleteness theorem, based on Kolmogorov complexity, Chaitin's incompleteness theorem, and an argument that resembles the surprise examination paradox. We then go the other way around and suggest that the second incompleteness theorem gives a possible resolution of the surprise examination paradox. Roughly speaking, we argue that the flaw in the derivation of the paradox is that it contains a hidden assumption that one can prove the consistency of the mathematical theory in which the derivation is done; which is impossible by the second incompleteness theorem.

2012

Polish Journal of Philosophy, 2014

A novel argument is offered against the following popular condition on inferential knowledge: a person inferentially knows a conclusion only if they know each of the claims from which they essentially inferred that conclusion. The epistemology of conditional proof reveals that we sometimes come to know conditionals by inferring them from assumptions rather than beliefs. Since knowledge requires belief, cases of knowing via conditional proof refute the popular knowledge from knowledge condition. It also suggests more radical cases against the condition and it brings to light the underrecognized category of inferential basic knowledge.

Journal of Philosophical Logic

The knower paradox states that the statement ‘We know that this statement is false’ leads to inconsistency. This article presents a fresh look at this paradox and some well-known solutions from the literature. Paul Égré discusses three possible solutions that modal provability logic provides for the paradox by surveying and comparing three different provability interpretations of modality, originally described by Skyrms, Anderson, and Solovay. In this article, some background is explained to clarify Égré’s solutions, all three of which hinge on intricacies of provability logic and its arithmetical interpretations. To check whether Égré’s solutions are satisfactory, we use the criteria for solutions to paradoxes defined by Susan Haack and we propose some refinements of them. This article aims to describe to what extent the knower paradox can be solved using provability logic and to what extent the solutions proposed in the literature satisfy Haack’s criteria. Finally, the article off...

How much can we turn the screw on counter-examples to the KK principle? The principle, also sometimes called “positive introspection”, says that if one knows that P, one knows that one knows that P. It is widely, although not universally, acknowledged that the KK principle is false, and not just for the boring reason that one can know that P without having formed the belief that one knows that P. One can know that P, and believe that one knows that P, without knowing that one knows that P, because one is not in a strong enough epistemic ...

Philosophia, 2024

Alter (The Matter of Consciousness: From the Knowledge Argument to Russellian Monism, GB: Oxford University Pres, 2023) argues for something surprising: despite being widely rejected by philosophers, including Frank Jackson himself, Jackson's knowledge argument succeeds. Alter's defense of Jackson's argument is not only surprising; it's also exciting: the knowledge argument, if it's sound, underscores the power of armchair philosophy, the power of pure thought to arrive at substantial conclusions about the world. In contrast, I aim to make a case for something unsurprising and unexciting: that the knowledge argument does not succeed, or, even less far-reaching, that Alter's defense of it is not persuasive. Mine is a classic file-drawer thesis, but what it has going for it is that it's true, or so I think, and hope to illustrate why you should too. Keywords Knowledge argument • Frank jackson • Consciousness • Reduction • A priori In The Matter of Consciousness: From the Knowledge Argument to Russellian Monism, Torin Alter argues for something surprising: despite being widely rejected by philosophers, including Frank Jackson himself (1994), Jackson's (1982, 1986) knowledge argument-in essence, that not all facts are physical facts because you cannot learn what the experience of seeing color is like from black and white information-succeeds. Alter's defense of Jackson's argument is not only surprising; it's also exciting: the knowledge argument, if it's sound, underscores the power of armchair philosophy, the power of pure thought to arrive at substantial conclusions about the world. In contrast, I aim to make a case for something unsurprising and unexciting: that the knowledge argument does not succeed, or, even less far-reaching, that

History and Philosophy of Logic, 2024

In his Knowledge and Belief (1962), Hintikka establishes his system of epistemic logic with the KK (Knowing that One Knows, in symbols, KpKKp) principle (KK for short). However, his system of epistemic logic and the KK principle are grounded upon his strong notion of knowledge, which requires that knowledge is infallible, that is, it makes further inquiry pointless, and becomes 'discussion-stopper'; knowledge implies truth, to wit, cognitive agents will not be mistaken in their knowledge; cognitive agents will be 'perfect logicians', i.e. they have infinitive capability of logical inference. Hintikka calls the argument for KK from the strong notion of knowledge as the