Exact(1)
The response, then, is that in any situation where the reductionist chance of heads really is 0.5, suitable outcome sequences in that situation or its nearest neighbours are in fact all unbiased with respect to outcome frequencies.
Similar(58)
(Hall 2004 develops a more limited version of this conclusion, arguing that reductionists about chance can't justify the PP).
Anti-reductionists about chance have generally found these arguments less persuasive (Popper 1992; Black 1998; Weiner and Belnap 2006).
According to reductionist theories of chance, discussed further below (§3), the values of the chances are fixed by the total history of occurring events.
Prospects look rather better on a reductionist view of chance (Supplement A.3).
Perhaps the most promising reductionist view about chance is Lewis' best system analysis of probabilistic laws (Lewis, 1994; Loewer, 2004).
If we adopt a non-reductionist account of chance, this line of resistance is quite implausible.
Non-reductionist views about chance, which take chances to be independent fundamental features of reality, can follow PP.
Joyce notes that an aspect of his principle NP is a commitment to the earlier principle Chance-Analyst, so adopting NP as one's conception of deference to chances allows the reductionist to block the problem of undermining in the way sketched above.
The key to the existence of undermining futures is the broadly Humean (or reductionist) principle that whatever the chances are, they should supervene on the total arrangement or pattern of occurrent events (see §A.3).
We hoped that our reductionist's approach would give us a chance to identify novel HIV Env regions capable of inducing nAbs in the absence of the otherwise overpowering influence of immunodominant regions.
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