in this formulation is taken to refer to assent by the putative knower to a word ‘belief’ proposition and is conventionally regarded as being stronger than mere ungrounded p, opinion but weaker than knowledge. To upgrade a true belief into the knowledge class, a justification must exist, which may or may not be internally accessible to the knower: internalism requires this accessibility, while externalism allows it not to be available to him. Under the tripartite definition, the three conditions, individually necessary and jointly sufficient, for subject having knowledge of a true proposition are as follows: s p p believes that s p is justified in believing that s p Condition (3) is arguably the most interesting epistemologically, and the various schools of epistemology treat the notion of justification in different ways. For example, internalists, as we have already seen, require to have access to the justifying s knowledge while externalists do not. However, the starting point for all camps is the assertion that has knowledge if and only if is true, believes that and s p’ p s p, s’s ‘that belief in proposition is in some way justified. Using the list of symbols defined p above, we can re-write this as follows: Ks . Bs . JBs p p p p ↔ Two traditions pose a threat to this, or, indeed, to any conception of knowledge. The first, in which Descartes is a prominent figure, involves proposing a radical sceptical hypothesis the existence of a or more recent, or genium malignum, Matrix – others’, in a which undermines claims to knowledge. The arguments ‘Brain Vat’ scenarios – for this first tradition, in outline, begin from the premiss that having knowledge certain of proposition requires that knows sceptical hypothesis to be false. Since cannot p s h s know that is false, because may be subject to (the trickery of the h s h genium for example), without being aware of it, cannot be certain of Again, this malignum, s p. can be transliterated into the symbolic conventions defined a moment ago, to enable propositional logic to provide a handrail through the argument: Ks Ks [~h] p →
word ‘belief’ in this formulation is taken to refer to assent by the putative knower to a proposition p, and is conventionally regarded as being stronger than mere ungrounded opinion but weaker than knowledge. To upgrade a true belief into the knowledge class, a justification must exist, which may or may not be internally accessible to the knower: internalism requires this accessibility, while externalism allows it not to be available to him. Under the tripartite definition, the three conditions, individually necessary and jointly sufficient, for subject s having knowledge of a true proposition p are as follows: p s believes that p s is justified in believing that p Condition (3) is arguably the most interesting epistemologically, and the various schools of epistemology treat the notion of justification in different ways. For example, internalists, as we have already seen, require s to have access to the justifying knowledge while externalists do not. However, the starting point for all camps is the assertion that s has knowledge ‘that p’ if and only if p is true, s believes that p, and s’s belief in proposition p is in some way justified. Using the list of symbols defined above, we can re-write this as follows: Ks p ↔ p . Bs p . JBs p Two traditions pose a threat to this, or, indeed, to any conception of knowledge. The first, in which Descartes is a prominent figure, involves proposing a radical sceptical hypothesis – the existence of a genium malignum, or others’, more recent, Matrix or ‘Brain in a Vat’ scenarios – which undermines claims to knowledge. The arguments for this first tradition, in outline, begin from the premiss that having certain knowledge of proposition p requires that s knows sceptical hypothesis h to be false. Since s cannot know that h is false, because s may be subject to h (the trickery of the genium malignum, for example), without being aware of it, s cannot be certain of p. Again, this can be transliterated into the symbolic conventions defined a moment ago, to enable propositional logic to provide a handrail through the argument: Ks p → Ks [~h]
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