Arguers should verify the Validity (at least, before Soundness) of each others' arguments. But are logicians and philosophers expected to do the following all mentally, in real life and real time?

Step 1: Translate the argument into Sentential Logic. This already can be difficult if the argument contains many propositions: P, Q, R, S, T. ...

Step 2: Determine Validity of the Symbolised Statement with a (Simplified) Truth Table. But can you do this mentally, for a complex Statement like the following (that I fabricated and whose Validity I have not checked)?
P ∧ [ Q ∨ (¬R ⟺ S) ]  ⟹  (P ∨ ¬S) ∧ (Q ⟺ R)

Hypothetically, an arguer can suspend the argument to take time to to determine Validity, by working on a sheet of paper or a computer program; but this appears strange and impractical, especially for a politician arguing in a deliberative assembly or a lawyer arguing in court.

  • Do you have a real-life example of a debate where this is done? Should I translate this into formal language and if so, is its intent clearer or not? – Mozibur Ullah Jul 31 '16 at 4:34
  • Ok, I hadn't understood it was an exercise which the author of the textbook thinks will be interesting for the student and gets them using the formalism. – Mozibur Ullah Jul 31 '16 at 4:48
  • @MoziburUllah I do not know of real-life footage of someone arguing a complex statement like that in my paragraph above. But because the Natural Language arguments (that exercises in Logic textbooks ask to be converted into Logical Symbolised Statements) are realistic and easily in real life, I question how arguers would resolve such tasks (i.e. perform these exercises for real) in public and in real life. – AYX.CLDR Jul 31 '16 at 5:01
  • @MoziburUllah I rewrote my comment above. – AYX.CLDR Jul 31 '16 at 5:01

The problem with your assumption is that formal checking is only that: formal checking. Someone could write gibberish and translate it into valid logic.

Say (in the style of Alice in Wonderland):

If a snark has carrots, then its father is a boojum.

I found your snark with carrots in its ears.

Hence your snark is a son of a boojum.

Real life is not a mathematical world (where you can have such a thing as "something is demonstrated", "something is impossible", etc.) but a physical world where we have educated guesses and at best quasi-certainties (and it is impossible to prove that something does not exist, which is a good reason why we have presumption of innocence, otherwise no one could ever be acquitted of an accusation).

In doing "scientific reasoning", we need to keep into account the applicability of axioms, as well as the soundness/demonstrability of the theorems. Futhermore, there are many subjects where there is no agreed-upon axioms or unambiguous laws (which is why we have debates, conciliations, arbitrations and courts).

You could have such a "logical checking" only when two parts in a debate are agreeing on axioms, definitions, theorems, logic rules and the procedure for verifying facts. But then, if that was the case, what would be the point of having a debate? We would just have to put our question into a computer program and get an unquestionable (or at least unquestioned) answer.

In real life, deduction is only one of two forms of reasoning, and it is usefully applicable to (alas) only a fraction of the phenomena we find around us. In the the immense, marshy, bushy or virgin territory that surrounds our human knowledge, we have only induction as our compass. And that is largely out of limits for computers, let alone logical notations. Which is why we have human researchers in mathematics, physics and other subjects (as well as forensic detectives), who are paid to make educated guesses that others can put to the test.

Sadly, education programs in mathematics are so engrossed with the (actual) wonders of deductive logic that they often forget to mention that, in the imperfect state of our knowledge, it is not always applicable to real life.

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  • This is such solid advice, sound both in theory and practice. I wish this were a FAQ on every site in SE. – Dan Bron Nov 29 '16 at 16:01

Of course the timing of political assemblies or court trials is incompatible with detailed formal analysis. By the time you end the formalisation and calculate the truth values and contradictions, you have lost the vote or the lawsuit.

You may prepare like this previously, imagining what arguments your opponents will rise, and searching for inconsistencies there. Or you can do it if an event is postponed, in which case you can analyse the arguments made in the previous meeting, in preparation for the next one. But during an actual discussion, you do not have the time for this. But a good debater (and a formal training in Logic won't harm one's ability to debate, and maybe will allow one to make simple formalisations and propositional calculus mentally) is able to detect inconsistencies (real or otherwise) in the discourse of an opponent, and to expose them in a short, cutting way, that leads the audience to dismiss the attacked argument ("Build a wall on the Mexican border? But there are not enough stonemasons in the US for a work like that; we would need Mexican immigrant stonemasons for the job, so your wall would increase immigration instead of reducing it"). But then this belongs more to the swampy territory of Rhetorics than to healthy mountains of Logic.

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