Knowledge and deductive closure

Synthese ◽  
1991 ◽  
Vol 86 (3) ◽  
pp. 409-423 ◽  
Author(s):  
James L. White
Keyword(s):  
Deductive Closure

Against Deductive Closure

Theoria ◽  
2016 ◽  
Vol 83 (2) ◽  
pp. 103-119 ◽  
Author(s):  
Paul D. Thorn
Keyword(s):  
Deductive Closure

scholarly journals On modal logic of deductive closure

2006 ◽  
Vol 141 (1-2) ◽  
pp. 218-224 ◽  
Author(s):  
Pavel Naumov
Keyword(s):  
Modal Logic ◽  
Deductive Closure

Deductive closure principle

2018 ◽  
Author(s):  
Kelly Becker
Keyword(s):  
General Principle ◽  
External World ◽  
Theory Of Knowledge ◽  
Closure Principle ◽  
Rhetorical Device ◽  
Deductive Closure ◽  
Brain In A Vat ◽  
Philosophical Questions

The deductive closure principle is based on the thought that one straightforward way to extend one’s knowledge is to competently deduce some proposition from one or more propositions that one already knows. G.E. Moore (1939) appears to presume this in his proof of an external world. Updating Moore’s proof to incorporate the more recent rhetorical device of a brain-in-a-vat (BIV), from his putative knowledge that he has hands and his knowledge that his having hands entails that he is not merely a BIV being fed experiences, through electrodes, of having hands, Moore deduces and therefore claims to know that he is not a BIV. A natural sceptical reply also exploits the idea that one can extend one’s knowledge through deduction. The sceptic will say, for example, that Moore does not know that he is not a brain-in-a-vat (BIV), for if he were his experience would be no different to what it actually is. Moore does know, however, that if he has hands then he is not (just) a BIV. Therefore, Moore does not even know that he has hands, for if he did, he could deduce and come to know that he is not a BIV, but that is not something he can know because, again, his vat experiences would be indistinguishable from normal ones. The idea that knowledge can always be extended through competent deduction from known premises – which implies that knowledge is deductively closed under known entailment – raises at least three philosophical questions. First, what general principle best captures this phenomenon? Due primarily to risk arising from the fallibility of belief-forming processes including deduction, there is reason to question even the most plausible formulations of closure. Second, are there any counterexamples to the principle or constraints on its application? Some philosophers claim that a properly formulated closure principle admits of exceptions, even if deduction is assumed to be infallible. Third, how might a theory of knowledge that upholds a robust (exceptionless) closure principle achieve anti-sceptical results?.

Deductive closure principle

2018 ◽  
Author(s):  
Anthony Brueckner
Keyword(s):  
External World ◽  
Sense Experience ◽  
Closure Principle ◽  
Logical Implication ◽  
Logic Of Knowledge ◽  
Body Of Knowledge ◽  
Sensory Evidence ◽  
Deductive Closure ◽  
Brain In A Vat ◽  
Sceptical Hypothesis

It seems that one can expand one’s body of knowledge by making deductive inferences from propositions one knows. The ‘deductive closure principle’ captures this idea: if S knows that P, and S correctly deduces Q from P, then S knows that Q. A closely related principle is that knowledge is closed under known logical implication: if S knows that P and S knows that P logically implies Q, then S knows that Q. These principles, if they hold, are guaranteed by general features of the concept of knowledge. They would form part of a logic of knowledge. An influential argument for scepticism about knowledge of the external world employs the deductive closure principle. The sceptic begins by sketching a logically possible hypothesis, or counter-possibility (for example, that one is a brain in a vat, with computer-induced sense experience) which is logically incompatible with various things one claims to know (such as that one has hands). The proposition that one has hands logically implies the falsity of the sceptical hypothesis. Supposing that one is aware of this implication, the deductive closure principle yields the consequence that if one knows that one has hands, then one knows that one is not a brain in a vat. The sceptic argues that one does not know this: if one were in a vat, then one would have just the sensory evidence one actually has. It follows that one does not know that one has hands. Some philosophers have sought to block this argument by denying the deductive closure principle.

Deductive closure

Synthese ◽  
2011 ◽  
Vol 186 (2) ◽  
pp. 493-499
Author(s):  
Isaac Levi
Keyword(s):  
Deductive Closure

No Justification for Smith’s Incidentally True Beliefs

2021 ◽  
pp. 1-20
Author(s):  
Alfred Schramm
Keyword(s):  
True Belief ◽  
False Beliefs ◽  
Evidential Support ◽  
Deductive Closure ◽  
Proportionality Principle

Abstract Edmund Gettier (1963) argued that there can be justified true belief (JTB) that is not knowledge. The correctness of Gettier’s argument is questioned by showing that Smith of his famous examples does not earn justification for his incidentally true beliefs, while a doxastically more conscientious person S would come to hold justified but false beliefs. So, Gettier’s (and analogous) cases do not result in justified and true belief. This is due to a tension between deductive closure of justification and evidential support. For being justified, any believing, disbelieving, or withholding of deductively inferred propositions must be distributed proportionally to given evidential support. This proportionality principle has primacy over deductive closure in case of conflict. Although the author’s argument does not save the JTB-account, it explains why subjects in Gettier situations do not earn knowledge.

Justification, Deductive Closure and Reasons to Believe

Dialogue ◽  
1991 ◽  
Vol 30 (1-2) ◽  
pp. 77-84 ◽  
Author(s):  
Robert Audi
Keyword(s):  
Justified Belief ◽  
Closure Principles ◽  
Deductive Closure

By deduction, we often extend both our knowledge and our justified belief. Moreover, in achieving knowledge or justified belief of some proposition, we commonly acquire justification for believing many of its entailed consequences, such as at least some of those that self-evidently follow from it. These and related facts have led some philosophers to endorse strong closure principles, for instance: If a person, S, is justified in believing a proposition, p, and p entails q, then S is justified in believing q. Others have denied such principles, whether for justification or, with the appropriate additions, for knowledge. The debate continues. There is, however, this much consensus: there are difficult problems about the scope of closure, and epistemology should develop theories that can resolve them.

scholarly journals Partial Deductive Closure: Logical Simulation and Management Science

1997 ◽  
Vol 43 (9) ◽  
pp. 1229-1245 ◽  
Author(s):  
Jaap Kamps ◽  
Michael Masuch
Keyword(s):  
Management Science ◽  
Deductive Closure
Sign in / Sign up

Export Citation Format

Share Document