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

Question

_{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.

Answer 1

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.

Answer 2

In logic, if you have a chain of arguments to be evaluated, one only need to read the statements one at a time and determine their value. If any one item in the chain fails the entire chain can be thrown away as an invalid argument. This is the driving force for making concise and easy to understand direct statements instead of long winded arguments. Due to the limitations of human intellect the more complex your argument the more likely it is flawed when it comes to human generated arguments (which is what we actually care about).

From a practical perspective, anyone that tends to have a valid argument can usually simplify it into something intelligible for even novice logicians. Any time I see a convoluted series of statements arguing for something red flags go up immediately in my head. Even the most complex arguments tend to fall on simple grounds such as the new versions of the ontological argument for example.

This can be done through hard practice, diagrams, etc. but enough practice tends to hone your intuition of what to look for provided you are well acquainted with logical fallacies and cognitive biases (not logic, but helps you spot fallacies).