21 research outputs found
The logic of knowledge and demonstratives
The thesis aims to demonstrate how an epistemic operator K can be added
to the Logic of Demonstratives. I started with a description of Kaplanâs LD. First
off, I showed two reasons motivated Kaplan to create the formal system LD. There
are several contingent logical truths in LD but one of them ÏâAÏ played a crucial
role in my further reasoning. In the second section of the thesis, I tried to add the
epistemic operator K to the LD using its standard definition. As a result, I got a
formula (K+A) that leads to a number of weird results. For example, If it is known
that ÏâAÏ then every truth is known. I argue that LD is inconsistent with the
standard interpretation for K. However, Rabinowicz and Segerberg(1994) provide
the non-standard interpretation of epistemic operator K. They consider necessity
and actuality operators as ones with a fixed perspective and allow K to have a
variable perspective. As a result, their definition of K might be directly added to
LD without creating the troublesome formula (K+A). It helps to avoid all the
problems from the second section Thatâs why I conclude that we can have the Logic
for Knowledge and demonstratives (LD+K) and treat it like a possible extension
of LD. This conclusion equips us with a formal tool to analyze sentences like âIt is
known that I am here nowâ that was unanalyzable in the original formal system.https://www.ester.ee/record=b538086
Church-Fitchs argument Àn en gÄng, eller: vem Àr rÀdd för vetbarhetsparadoxen?
Enligt ett realistiskt synsÀtt kan ett pÄstÄende vara sant trots att det inte ens i princip Àr möjligt att veta att det Àr sant. En sanningsteoretisk antirealist kan inte godta denna möjlighet utan accepterar en eller annan version av Dummetts vetbarhetsprincip:
(K) Om ett pÄstÄende Àr sant, sÄ mÄste det i princip vara möjligt att veta att det Àr sant.
Det kan dock förefalla rimligt, Ă€ven för en antirealist, att gĂ„Ì med pĂ„Ì att det kan finnas sanningar som ingen faktiskt vet (har vetat, eller kommer att veta) Ă€r sanna. Man kan dĂ€rför tĂ€nka sig att en antirealist skulle acceptera principen (K) utan att dĂ€rför gĂ„ med pĂ„ den till synes starkare principen:
(SK) Om ett pÄstÄende Àr sant, sÄ mÄste det faktiskt finnas nÄgon som vet att det Àr sant.
Ett mycket omdiskuterat argument â som ytterst gĂ„r tillbaka till Alonzo Church, men som först publicerades i en uppsats av Frederic Fitch i Journal of Symbolic Logic 1963 â tycks emellertid visa att principen (K) implicerar principen (SK). Anta nĂ€mligen att (K) Ă€r sann, medan (SK) inte Ă€r det. Men om (SK) Ă€r falsk, sĂ„ finns det ett pĂ„stĂ„ende som Ă€r sant men som ingen faktiskt vet Ă€r sant. Anta nu att p Ă€r ett sĂ„dant pĂ„stĂ„ende. LĂ„t Kp betyda att nĂ„gon vet att p Ă€r sant. Det galler alltsĂ„Ì att p Ă€r sant samtidigt som Kp inte Ă€r det. Betrakta nu pĂ„stĂ„endet (p ⧠âKp). Enligt antagandet Ă€r detta pĂ„stĂ„ende sant. Enligt (K) mĂ„ste det dĂ„ vara möjligt att nĂ„gon vet att (p ⧠âKp). D.v.s., det mĂ„ste vara möjligt att pĂ„stĂ„endet K(p ⧠âKp) Ă€r sant. Men i sĂ„ fall Ă€r det ocksĂ„Ì möjligt att pĂ„stĂ„endet Kp ⧠KâKp Ă€r sant, vilket i sin tur implicerar att det Ă€r möjligt att Kp ⧠âKp Ă€r sant, vilket ju Ă€r absurt. SĂ„ledes kan inte (K) vara sann samtidigt som (SK) Ă€r falsk. Vi tycks sĂ„ledes kunna sluta oss till att (K) implicerar (SK).
I uppsatsen diskuterar jag nĂ„gra olika sĂ€tt att undgĂ„Ì Church-Fitch paradoxala slutsats. Ett tillvĂ€gagĂ„ngssĂ€tt Ă€r att ersĂ€tta kunskapsoperatorn med en hierarki av kunskapspredikat. Ett annat Ă€r baserat pĂ„ distinktionen mellan faktisk och potentiell kunskap och ett förkastande av den vanliga modallogiska formaliseringen av principen (K). Den senare typen av lösning betraktas bĂ„de frĂ„n ett realistiskt och ett icke-realistiskt perspektiv. UtifrĂ„n denna analys kommer jag fram till slutsatsen att vi, vare sig vi Ă€r realister eller antirealister rörande sanning, kan sluta oroa oss för vetbarhetsparadoxen och Ă€ndĂ„ uppskatta Church-Fitchs argument
Vagueness and Introspection
Version of March 05, 2007. An extended abstract of the paper appeared in the Proceedings of the 2006 Prague Colloquium on "Reasoning about Vagueness and Uncertainty".We compare three strategies to model the notion of vague knowledge in epistemic logic. Williamson's margin for error semantics typically uses non-transitive Kripke structures, but invalidates the principle of positive introspection. On the contrary, Halpern's two-dimensional semantics preserves the introspection principle, but using more complex uncertainty relations that are transitive. We present a modification of the standard epistemic semantics, which validates introspection over one-dimensional non-transitive structures, and study its correspondence with Halpern's approach. While the semantics can be seen as the diagonalization of an explicit two-dimensional semantics, it affords a more intuitive representation of the uncertainty characteristic of vague knowledge. We examine the implications of the semantics concerning higher-order vagueness and the status of the non-transitivity of perceptual indiscriminability. We respond to a potential objection against our approach by giving a dynamic model of the way subjects with inexact knowledge make successive approximations of their margin of error
Counterfactual theories of knowledge and the notion of actuality
The central question of this article is how to combine counterfactual theories of knowledge with the notion of actuality. It is argued that the straightforward combination of these two elements leads to problems, viz. the problem of easy knowledge and the problem of missing knowledge. In other words, there is overgeneration of knowledge and there is undergeneration of knowledge. The combination of these problems cannot be solved by appealing to methods by which beliefs are formed. An alternative solution is put forward. The key is to rethink the closeness relation that is at the heart of counterfactual theories of knowledg
Modal Epistemology
Some central epistemological notions are expressed by sentential operators O that entail the possibility of knowledge in the sense that 'Op' entails 'It is possible to know that p'. We call these modal-epistemological notions. Using apriority and being in a position to know as case studies, we argue that the logics of modal epistemological notions are extremely weak. In particular, their logics are not normal and do not include any closure principles
On a New Tentative Solution to Fitchâs Paradox
In a recent paper, Alexander argues that relaxing the requirement that sound knowers know their own soundness might provide a solution to Fitchâs paradox and introduces a suitable axiomatic system where the paradox is avoided. In this paper an analysis of this solution is proposed according to which the effective move for solving the paradox depends on the axiomatic treatment of the ontic modality rather than the limitations imposed on the epistemic one. It is then shown that, once the ontic modality is standardly introduced, the paradox still follows and, in addition, some puzzling consequences arise