# From given premises, how can you conjecture the conclusion before attempting any (dis)proof?

Source: p 287, Sweet Reason: A Field Guide to Modern Logic (2010 2 ed) by Henle, Garfield, Tymoczko.

Predicate is the reason we started on deductions. In Sentential, remember, we can verify that an argument is valid by using truth tables or the short-cut method. With Predicate, we have no such tool. We can show that an argument is invalid if we exhibit a universe in which the premises are true and the conclusion is false, but (until now) we have had no means of showing that an argument in Predicate is valid.

In the 2 Logic textbooks read (the above and Hurley's), from the given premises, no exercise will ask you to determine the conclusion yourself; instead the textbook divulges the conclusion and then asks you to deduce it. But this is irrealistic; real life, one must determine conclusions oneself.

So without computers, from given premises (that may be long and convoluted), how can you conjecture, before deducing, the conclusion yourself? One must at least conjecture a conclusion before attempting any deduction or (dis)proof.

I think there's some confusion in your question. Correct me if I'm wrong.

Any line in a deduction (so long as it's not in a sub-proof) is also a conclusion. You have to know what conclusion you're aiming at, otherwise you just wouldn't know where to stop. It's somewhat like asking where to go without knowing your destination.

Example:

``````1. p->q        premise
2. q->r        premise
3. r->s        premise
4. p           premise
5. q           1,4
6. r           2,5
7. s           3,6
``````

Any one of 5,6,7 is a conclusion of the given premises. And it needn't stop here; you can go on: `p->p` is also a conclusion, and so are `p->r`, `p->s`, `q->q`, `r->r`, and so on. There are infinitely many conclusions for any given set of premises.

• Thanks. I comprehend all that you wrote above, but may I ask a follow-up question to confirm my comprehension: Are not there any situations where you are given the premises and you are never told what conclusion is desired, but you must still find some conclusion that proves longer and more convoluted than the premises?
– user8572
Nov 13, 2016 at 13:24