Philosophy Optional :- Explanation of Alonzo Church's logic for refutation of Weak Verification of Ayer

Recall what Ayer means by direct and indirect verification:

S is directly verifiable iff either S is an observation sentence or else S, perhaps in conjunction with other observation sentences A, B, C,…, logically implies an observation sentence that is not implied by A, B, C….

S is indirectly verifiable if and only if S, perhaps in conjunction with other sentences P, Q, R,… logically implies a directly verifiable sentence D that is not implied by P, Q, R,…. Furthermore, these sentences P, Q, R are each either analytic or directly verifiable.

Now, take this proposition, lets call it (1):

 (¬O1&O2) v (O3&¬S)    ( ¬ means Not, v means Or, & means And)

O1, O2, O3 are some observation statements, S is any statement. 

Now take (1) and O1:

Premise 1: (¬O1&O2) v (O3&¬S)

Premise 2: O1

Conclusion: (O3&¬S) 

Hence (1) and O1 together imply O3. Hence (1) must be directly verifiable. 

Now take S and (1)

Premise 1: (¬O1&O2) v (O3&¬S)

Premise 2: S

Conclusion: (¬O1&O2)

Hence S and (1) together imply O2. Therefore now S is indirectly verifiable. 
But S will not be indirectly verifiable if O2 is implied only by (1) alone.

But if that is the case, O2 must follow from (O3&¬S) (since O2 is already implied in (¬O1&O2))

If this is the case, then ¬S becomes directly verifiable.

Hence, you can take any statement S and show that it is either indirectly or its negation is directly verifiable. 

On a side note, there is no point remembering such complicated criticisms. There won't be much time and space in the exam for writing them.

Regarding discussion, i do not know of any groups as such. But I am willing to discuss doubts, questions etc. here on forum itself.