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I'm reading Wieland's: Infinite Regress Arguments. In here:

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I don't understand how the fail to settle all disputes implies that one couldn't settle many of them. The only possibility I see is using the meaning of "all" as "all disputes of a certain class" as such that this class does not contain all possible disputes.

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He doesn't say that from not being able to settle all disputes follows that one can settle many disputes. He merely notes that it allows for that.

His point is that ¬∀d∈D[S(d)] is weaker than ¬∃d∈D[S(d)], since the first allows for ∃d∈D[S(d)] (although this does not necessarily follow), while the second doesn't. (I use D for the set of all disputes, S(d) for 'it is possible to settle d').

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  • Does ¬∀d∈D[S(d)] means: ¬S(d1)∧¬S(d2)∧¬S(d3)∧...∧¬S(dn) or one to evaluate the value of ∀d∈D[S(d)] first and then apply the negation?
    – Red Banana
    Commented Jan 18, 2015 at 18:36
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    @Vÿska no, ¬∀d∈D[S(d)] means. It is not true that for all d in D holds that S(d). From De Morgan's laws follows then that there is at least one d in D for which S(d) does not hold.
    – user2953
    Commented Jan 18, 2015 at 20:59
  • Got it. It was more or less as I suggested in the second case. Although that view was kinda skewed.
    – Red Banana
    Commented Jan 18, 2015 at 23:00

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