No Justification for Smith’s Incidentally True Beliefs

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.

No Justification for Smith’s Incidentally True Beliefs

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.

Deductive closure principle

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

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.

The principle of deductive closure of knowledge and contextualism

The hypotheses of radical skeptics are so conceived to put the attributor of knowledge in such position that she can?t ascribe knowledge to anyone, because the subject can?t get proper evidence to exclude skeptical alternatives. There are several versions of the skeptical arguments by which she tries to point out the impossibility of knowledge ascriptions as direct consequence of the impossibility to rule out skeptical alternatives. All of those arguments are based on a very intuitive epistemological principle: if we know p, and if we know that p implies q, then we know q as well. This principle is called the principle of deductive closure of knowledge (or simply closure). In this paper, the author analyzes the most important contextualist solutions to the skeptic paradox, those that accept the closure principle, and those that reject it as well.

On Some Objections to The Deductive Closure of Legal Systems

I criticize an argument presented by Pablo Navarro and Jorge Rodríguez (2014) against the conception of legal systems as sets of statements closed under logical consequence. First, I show that the example on which they ground their argument incurs in a fallacy of equivocation. Then, I recognize that the authors are right about the fact that two different normative bases can react differently to changes, but I claim that that is not a decisive reason for choosing always the expressly enacted norms as the system’s basis, that the selection of the best basis should be guided by methodological considerations and that, to that purpose, it is necessary to consider the whole set of logical consequences as part of the system.

Epistemic Justification and Deductive Closure

Epistemic Justification and Deductive Closure