Continuing with our thoughts from yesterday.... What are we saying when we say we know that 45 + 303 = 348? That depends on what we understand numbers, and arithmetic, to be. I think the sensible course is to adopt an operational/pragmatic view of mathematical knowledge according to which it is a shorthand for facts concerning the way the world works. In G.E. Moore's spirit, I might hold up a hand, "here is one hand." Then I might hold up another, :"Here, also, is a hand." Finally, with both of them in my field of sight, I can say, "there are two hands here." So we can take 1 + 1 = 2 as settled. But 45 + 303 might be tedious to prove in that way, with some object other than hands (marbles?). Further, there would be the threat of false refutations. I might lose track of the first marble before I collected the 348th. Then I'd count them all and declare that the real answer to the question must be 347! A naive empiricism about such matters becomes...
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One issue raised by the tracking theory of knowledge discussed in yesterday's post is "epistemic closure." Epistemic closure is a property of belief systems that is generally considered a good thing. Specifically, a belief system is said to be "closed" if and only if we can say that whenever a subject (S) knows a proposition (p), and S also knows that P implies q, then S knows q. If I know that today is Sunday, and I know that this implies that yesterday was Saturday, then I know that yesterday was Saturday. In examples like yesterday-was-Saturday, closure is strongly intuitive. But the standard view of the consequences of the tracking theory is that accepting it entails the abandonment of closure as a premise. Consider the "fake barns" scenario. I'm driving through a neighborhood where some of the locals delight in creating fake paper mache barns that look quite realistic from the road. I don't know about the local custom and, when I...
This will be the first item in a three part series about the tracking theory of knowledge. I'll be talking about it in the form given it by Robert Nozick, in Philosophical Explanations (1981) though Nozick owed a considerable debt to Fred Dretske. According to Robert Nozick's tracking theory of knowledge, I know p (some proposition) if: 1) p is true 2) I believe p 3) If p were not true I would not believe it, and 4) if p were true I would believe it. The fourth point seems oddly worded, because of course the first point already said that p IS true for purposes of our further discussion, so why the hypothetical language by the time we move to the fourth? Well, the awkward language is necessary to resolve certain hypotheticals that bothered Nozick, and because combining (3) and (4) helps fix in our minds the underlying metaphor of tracking. One common example: a lottery ticket. I don't remember if Nozick himself invoked lottery tickets or if I encountered this...
There is an old theory of knowledge known as the JTB view: the view, that is, that knowledge is "justified true belief." Edmund Gettier gets a lot of credit for weakening the hold of JTB upon conventional wisdom, in his brief article of 1963 in the journal ANALYSIS, arguing that there are cases in which all three circumstances are met, but which one wouldn't ordinarily speak of as "knowledge." Some people believe Gettier gets more credit than he deserves. Alvin Plantinga has written: According to the inherited lore of the epistemological tribe, the JTB [justified true belief] account enjoyed the status of epistemological orthodoxy until 1963, when it was shattered by Edmund Gettier... Of course there is an interesting historical irony here: it isn't easy to find many really explicit statements of a JTB analysis of knowledge prior to Gettier. It is almost as if a distinguished critic created a tradition in the very act of destroying it. ...
My personal view of the field, in ten questions. I'll work in traditional order, from Being through Knowledge, to Value. 1. Does the world consist of substances with attributes (that is, enduring things with various properties), or is that a misleading way of thinking? 2. If one accepts the substance/attributes dichotomy, what COUNTS as a substance? How many of them are there in the world? Are there an infinite number of substances, or could it all be boiled down to a smaller number? Three, as Descartes thought (mind, matter, God), or maybe just one? 3. In terms of the nature of a human being, are we each one substance with various attributes? Or are we two different substances that somehow interact? Or is a person an attribute of a trans-personal Substance? 4. If we end up with a view of the world in which humans consist of both mind and body: how DO they interact? 5. What do we mean by "truth" as a matter of common language. also, what SHOULD we take the ...