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A.V. Ravishankar asked:
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What is the major difference between material, strict and causal and counterfactual implications?
Which one captures the "common sense reasoning" involved in our daily discourse?
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============
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(1) Material implication is truth-functional implication. This means that P materially implies Q is true
when either P is false or Q is true, but when P is true and Q is false, P materially implies Q is false.
There need be no connection between P and Q so that we can determine the truth of the implication
between P and Q solely by the truth values of P and of Q. So, for instance, "If Dogs are reptiles, then
The Earth is spherical" is true because "Dogs are reptiles" is false.
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(2) Strict implication or entailment is not truth-functional implication. P strictly implies Q when it is
impossible for P to be true and for Q to be false. That is, when P, but not Q would be a contradiction.
Thus, "This figure is a triangle" strictly implies "This figure has three sides".
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(3) Causal implication would state a causal connection between P and Q. Thus, If this piece of copper
is heated, then this piece of copper will expand.
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(4) Counter-factual implication (often called a "counterfactual conditional") states an implication
between P and Q where the antecedent, P, is contrary to fact. An instance would be, "If this piece of
metal were being heated now, then it would expand." Note that the proposition, "This piece of metal is
being heated now" is false. Of course, that counter-factual is true. Here is another instance: "If this
stone dropped from my hand, then it would fly upward." This counterfactual is, of course, false. The
problem is to determine the truth-conditions for counterfactual conditionals.
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Your second question has no clear answer. It involves the interpretation of formal systems which is
very complex. None of these different kinds of implication replicates "common-sense," but it might be
that a formal system might actually improve on common-sense implication by refining it.
Commonsense need no more be the touchstone of truth in logic than it is in physical science. An
interesting book on the relation of logic to ordinary language (and to that extent, commonsense) is
Logical Formsby Mark Sainsbury.
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Kenneth Stern
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