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2015-04-12
Contra Searle on Rules
John Searle is one of my favorite philosophers, but I fear remarks he makes in Rationality in Action about the role of rules in logic qualify as veritable "howlers".  He writes:

The correct thing is to say that the rules of logic play no role whatever in the validity of valid inferences.  The arguments, if valid, have to be valid as they stand.  (20).

But how is it that we determine when arguments are "valid as they stand"?  That is, how do we tell whether they have that all-important truth-preserving character?  I know I use rules of logic, rules like modus ponens, viz. "protasis, conditional, apodosis" (conveniently representable symbolically as "(p&(p->q))->q").

Is there some other useful way of determining validity in an argument?  Surely there is no way of identifying validity apart from identifying truth-preservingness, and how do you identify truth-preservingness without alluding to some kind of rule?  In particular, how would you show that a mathematical proof is valid without talking about permissible rules of inference?

Pace Dodgson's Tortoise, rules of logic like modus ponens are not premises from which one might infer whether an argument is valid, but are rather part of the very measure of that validity.  And, I submit, the public availability of such rules is intrinsic to the very objectivity of logic.  So instead of playing no role, the rules of logic play the role in determining validity.  Am I wrong?


2015-04-14
Contra Searle on Rules
Reply to Gerald Hull
I'm not a logician, but my two cents anyway:

There is Wittgenstein's Tractarian view which seems to deny any justificatory role to rules of logic, eg., 5.132.

You seem to be using "determine" in two different senses, first in the sense of identifying when arguments are valid, secondly in the sense of constituting validity. It's not clear to me how you move from the first sense to the second.

If I use the truth-table method to determine truth-preservingness or validity, do I need to know rules like modus ponens or disjunctive syllogism?

2015-04-14
Contra Searle on Rules
Reply to Gerald Hull
Your confusion is common. Inference vs deduction.

We can deduce logically within any tautology (in any axiomatic system), because the information is complete.

We can identify contradictions logically (in both axiomatic and rational systems), where information is sufficient to do so.

We cannot *infer* logically, we can only *theorize* logically.  That is the limit of what logic can do for us: assist us in the test of internal consistency and non-contradiction (an act of criticism or falsification), and assist us in the formation of theories.

In addition, once we construct a theory, we can test a theory:
- We can test for external correspondence (empiricism)
- We can attempt to falsify by external correspondence. (parsimony)
- We can test for existential possibility. (Operational Definitions, Operationalism, Operationism, Intuitionism) and that we are not substituting imaginary information.
- We can test for morality (the absence of involuntary transfer, Propertarianism)

And even then, when we have done our due diligence in internal consistency, external correspondence, attempts at falsification (parsimony), existential possibility free of imaginary substitution, 

There are no non-tautological, non-trivial, and therefore certain premises.  As such, the limit of logic (and why people like me criticize formal logic when used for other than the its narrow utility)  is in either falsification of statements, or the construction of theories that can be further tested. But you cannot determine truth propositions of non-tautological non-trivial propositions by logical means.

The function of logic is criticism, not truth.  Once exhaustively criticized, you can say an argument or proposition is valid in the sense that it is well constructed. But this says nothing about the truth of the argument or proposition. It says only that it is well constructed.  

Curt Doolittle 
The Propertarian Institute 
Kiev, Ukraine.


2015-04-14
Contra Searle on Rules
Reply to Gerald Hull
I would interpret Searle so that logical rules may describe valid inferences, but the validity of those inferences is not (in some strong sense) based on those rules. That leaves place for us to use rules to determine whether some inference is valid or rather explicate why it is not valid. He writes:

I am not saying that there could not be any rules to help us in rational decision making. On the contrary there are many famous such rules and even maxims. (22)

(Though not explicitely referring to logical rules, but I see no reason why it should not contain also them.)

Perhaps this is also connected to the Brandom's stress on the role of material infenrence in rationality? Similarily Searle points to the semantic content of inferences (in human rational action).

2015-04-15
Contra Searle on Rules
Reply to Gerald Hull

Thanks for a number of helpful comments!  Let me clarify my claim that Searle has committed a "howler" in spurning the relevance of rules of logic for everyday argumentation.

He asserts it's a mistake to ascribe modus ponens "any role whatever" (his emphasis, RiA 19) in the validity of arguments with that pattern, because of the Lewis Carroll paradox.  This implies that mp neither constitutes the validity of such an argument, nor can be relied upon to tell whether it is valid.  The latter is how I used "determine" above, and in that sense Searle's claim is obviously false; hence "howler".

A more conciliatory interpretation suggests Searle might allow the use of mp to identify validity but deny that it constitutes that validity.  And in the propositional calculus, at least, one can also use truth tables to determine logical consequence (this might be the sense of Tr. 5.132).  But note that one is still depending upon "rules of logic", albeit in tabular form.  Searle claims that validity depends instead upon "the meanings of the words", but since "if" is one of those words, this again leads to truth tables or something equivalent.

More significantly, in neither role does reliance upon mp lead to paradox.  Dodgson's (Carroll's) "What Achilles said to the Tortoise" trades on the ambiguity in claiming mp "justifies the conclusion".  But mp does not support the apodosis!  It is completely consistent with the argument (when unsound) having a false conclusion.  Mp rather supports inferring the apodosis from the given premises.  There are two possibilities:  either mp does not always identify valid inferences, or it does.  If it doesn't, what is needed is not a rule for applying mp but a better rule for identifying validity (and the burden is on the Tortoise to explain what's at fault with mp); and if it does, no further rule is relevant.

At times the crux of Searle's complaint seems to turn on his familiar distinction between syntax and semantics, and is the claim that mp as a syntactic rule is irrelevant to common argumentation.  He is 100% right on that, of course, but I have taken mp to identify a semantic pattern (protasis, conditional, apodosis), and as a semantic claim involving truth dependencies in conditionals it is hardly less a rule of logic.



2015-04-15
Contra Searle on Rules
Reply to Gerald Hull
Oops.  Should be "What the Tortoise said to Achilles".  Curiously (or curiouser), Searle makes the same mistake (18n).

2015-04-23
Contra Searle on Rules
Reply to Gerald Hull

Jerry! Thanks for opening this very interesting and important discussion (at least for me).

I mainly agree with you and I think that Searle is here on the right track but goes too far.

I would call logical rules like mp tools that logicians use like scientists use their instruments.

When a chemist determines that water is salty by measuring its salt concentration, we could say (if we were radical constructivists) that the use of the meter makes the water salty. But this would be clearly wrong because everyone could do similar determination just by tasting the water. (Further it could be said that the measuring only describes the situation and it does not explain it.)

Determining the validity of an inference is very similar, because a logician can do it explicitly by using their tool (rules, tables), but in many cases a lay person can also see correctly the validity even if not ever heard about truth tables and logical rules. In these cases I think in everyday life the validity is based on the meanings of the words (and true: “if” is a word!) and this kind of inference Brandom calls material.

Let’s take the classical syllogism: Soctrates is human; humans are mortal; and thus Socrates is mortal. This is a valid inference and its validity can be described many ways.

MP: x(human); x(human) -> x(mortal); and thus x(mortal)

The material inference here would mean that if someone knows what the words “human” and “mortal” mean, then she would know that every human must be mortal even though she would not know what “if” means.

(I hope I did not go too far from the topic.)