Mackie’s objection to miracles:
Suppose the following formula be a law: if P & - I, then G. Now we observe P&-G. The theist may think that what we observe is a miracle. But what is rational for us to believe is that the given formula is not a law. So anytime there is claimed to be a miracle, the rational thing to believe is that there is no miracle and the law that’s supposedly broken is not actually a law.
Objection to Mackie: P&-G is not evidence against the identity of the given formula as a law, because P&-G is not contradictory against the given formula. Furthermore, P&I&-G is not contradictory against the given formula either. (As a matter of fact, it confirms it if we take the conditional in issue to allow for contraposition and exportation.) To sum up this objection, when P&-G occurs, the rational thing to believe is not that the given formula is not a law. So Mackie is wrong about this.
Thursday, March 19, 2009
Monday, March 2, 2009
Divine knowledge and indicative conditionals
I've rarely seen this question being raised.
Does 'God knows that P' entail that 'God is certain that P'?
This question occurred to me when I was thinking about God's knowledge of indicative conditionals. According to the Equation (Bennett's term), the probability of P→Q equals the probability of Q given P. But there is the Bombshell (Edgington's term). The Bombshell shows that one cannot at the same time accept the Equation and the claim that indicative conditionals have truth value. This is exactly true...of humans, since it happens so often (or, always?) that we are not 100 percent certain about something. But things might be different with God, as long as we accept the claim that God is always certain about things: i.e. about any proposition p, either God is certain that P or God is certain that not P (I'm assuming that God has exhaustive knowledge about everything). Retaining this claim as an assumption, we can safely accept the claim that indicative conditionals have truth value and the Equation is correct. The reason is simple: the arguments for the so-called Bombshell all assume that one's degree of belief in something can be anywhere within the range [0, 1] (inclusive at both ends). But our assumption is that God's degree of belief can only have two possible values: 0, 1. So the conclusion is that the Bombshell does not apply to God under certain assumption.
This does look great. Is there any problem with this scenario?
Does 'God knows that P' entail that 'God is certain that P'?
This question occurred to me when I was thinking about God's knowledge of indicative conditionals. According to the Equation (Bennett's term), the probability of P→Q equals the probability of Q given P. But there is the Bombshell (Edgington's term). The Bombshell shows that one cannot at the same time accept the Equation and the claim that indicative conditionals have truth value. This is exactly true...of humans, since it happens so often (or, always?) that we are not 100 percent certain about something. But things might be different with God, as long as we accept the claim that God is always certain about things: i.e. about any proposition p, either God is certain that P or God is certain that not P (I'm assuming that God has exhaustive knowledge about everything). Retaining this claim as an assumption, we can safely accept the claim that indicative conditionals have truth value and the Equation is correct. The reason is simple: the arguments for the so-called Bombshell all assume that one's degree of belief in something can be anywhere within the range [0, 1] (inclusive at both ends). But our assumption is that God's degree of belief can only have two possible values: 0, 1. So the conclusion is that the Bombshell does not apply to God under certain assumption.
This does look great. Is there any problem with this scenario?
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