gerard.caseyProposition 1: Absence of evidence is evidence of absence
Subject: Absence of evidence—S
Predicate: evidence of absence—P
Copula: affirmative, either universal, particular or singular
Giving us either SAP, SIP or SA’P
Proposition 2: Absence of evidence is not evidence of absence
Subject: Absence of evidence—S
Predicate: evidence of absence—P
Copula: negative, either universal, particular or singular
Giving us either SEP, SOP or SO’P
The most plausible interpretation of these propositions is as universals and that’s how I’ll take them from now on. If they are taken particularly then it is possible for both to be true simultaneously. If, for example, the propositions ‘students are intelligent’ and ‘students are not intelligent’ are taken universally, then both propositions cannot be simultaneously true; if taken particularly, both can be simultaneously true.
Both of our propositions have exactly the same subject and exactly the same predicate and so are comparable and so can be plotted on the Square of Opposition. They differ in quality—one is affirmative and the other is negative.
We than have SAP vs SEP
Let’s take your second paragraph and amend it slightly[material within []]
If absence of evidence is evidence of absence then there is evidence [of absence].
If absence of evidence is not evidence of absence then there is no evidence [of absence].
Absence of evidence can not be both evidence [of absence] and no[t] evidence [of absence].
True
Therefore, absence of evidence in premiss 1 is not the same as absence of evidence in premiss 2.
Yes, they have different properties, as given by the predicate in their respective propositions but just as a term, ‘absence of evidence’ signifies exactly the same thing.
If the meaning of absence of evidence in premiss 1 [as given by the attachment of the predicate] is used in 2 then premiss 2 is self-contradictory and vice versa.
Well, yes, for this would be to assert SAP and SEP simultaneously.
I hope this helps a little.
Best wishes,
Gerard Casey