# Without computers, how can you conjecture the (in)validity of a long convoluted argument in Predicate Logic?

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), each exercise on deductions (e.g. the following) divulges the (in)validity of the argument, and so enables you to know instantly what to do. But without computers, for arguments with > 10 long, convoluted premises: what if the (in)validity were concealed or tacit?

Per the above, I already know that a Valid Argument can be proven only with Deduction, and an Invalid Argument disproven with a Counterexample. But before 1. writing a Deduction or 2. finding a counterexample, you must have conjectured the argument, respectively, 1. valid and 2. invalid (Otherwise, how would you know to write a Deduction or find a counterexample?!?) So how would you conjecture (in)validity before doing the work?

• I merged your other question that seemed to be a duplicate - if the questions are significantly different, can you show how? – user2953 Aug 15 '16 at 11:42
• @Keelan To me, they do differ because the other asks about how to conjecture the conclusion, but the one above asks about how to conjecture the (in)validity. These are 2 different steps, the former preceding the latter. What do you think? – Greek - Area 51 Proposal Aug 15 '16 at 20:16
• I agree with @Timere, the other question was different. I also deleted my comment that was moved here from that question since it doesn't make sense in this context. – Eliran Aug 15 '16 at 20:26
• Apologies, you are quite right. I was too quick with this. Could you ask the other question again, and then delete this one? It seems that a merge cannot be undone. Sorry for the inconvenience. – user2953 Aug 16 '16 at 14:17
• @Keelan Please ignore my previous comment, because I deleted my question at Meta SE that proved a duplicate. Instead, please tell me if you wish to try the last paragraph at meta.stackexchange.com/a/136168/226001 (to avert two copies (even deleted)), or if I should delete the merged question and repost it. – Greek - Area 51 Proposal Aug 17 '16 at 5:24