# How being unable to settle all disputes makes it possible to settle many disputes?

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

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.

## 1 Answer

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').

• 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? Commented Jan 18, 2015 at 18:36
• @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. Commented Jan 18, 2015 at 23:00