In the comments section of my post "Why Traditional Logic Does Not Employ Truth Tables," David McPike takes issue with a couple things I said. I addressed some of these yesterday. On a related point, I had said:

Therefore, in the modern system, statements such as: "If the moon is made of green cheese, then ducks can swim" are considered true statements, since their antecedents (in this case, "the moon is made of green cheese") is false at the same time that the consequent ("ducks can swim") is false. In fact the antecedent is false and the consequent true, therefore (according to the modern logician) it is a true statement.

To which McPike responds:

This again seems misleading. In the modern system of "logic", statements such as "If P1 then P2" are considered formally, as being possibly true, possibly false. Insofar as propositions figure into actual reasoning about reality, what reason is there to think that modern and traditional logic are any different in viewing logic "as a linguistic and metaphysical art, not [merely!] a technical mathematical calculus"?

My response to the question of what reason I have for thinking that modern and traditional logic are different in their view of what kind of art they are engaging in is threefold: First, anyone versed in the particulars of the two systems in fact

*do*view them differently; secondly, they admit they treat them differently; and, third, they give the reasons why they, in fact, do treat them differently.
This characterization is less the case with modern logicians than with the traditionalists. Modern logicians are largely unfamiliar with the tradition of the traditional system and seem to be mostly unaware of the assumptions behind their own system since they are never called upon to have to explain them in an English academic world that still operates in the shadow of logical positivism (the ideological mileiu in which modern logic was birthed).

Traditional logicians, on the other hand, being in the minority, are in a position to have to explain why they are not doing the same thing as so many of their peers. Consequently, they seem to have a better grasp on the difference between the two systems.

Mr. McPike might want to consult several traditional logicians to see what I mean. The first would be Jacques Maritain, whose book

*Formal Logic*(1946) contains a discussion of some of these issues. Maritain considers the two systems so different that he even balks at calling modern logic "logic" at all. He refers to it as "logistics." There are other discussions too, such as that by Andrew Bachhuber in his*Introduction to Logic*(1957)*and in Daniel J. Sullivan's**Fundamentals of Logic*(1963). There is also a short discussion of this in Peter Kreeft's recent*Socratic Logic*. Anyone wanting something more in depth can go to the works of Henry Veach, who made a whole career out of examining the differences between the two systems and articulating and questioning the assumptions behind the modern system (*Aristotelian and Mathematical Logic*(1950),*In Defense of the Syllogism*(1952);*Intensional Logic*(1952);*Logic as a Human Instrument*(1959); and*Two Logics*(1969)).
And the differences between the two systems has not gone unacknowledged by the moderns, as evidenced by Bertrand Russell's summary dismissal of it (along with Aristotelianism in general, an indication that he understood that the difference between the two systems was rooted in the respective underlying metaphysical beliefs). Irving Copi too acknowledges it briefly in his text, and a good example of the some the issues can found online in Kelly Ross' "

*In Defense of Bramantip*," which is, ironically, a defense of at least one plank in the traditionalist platform by a modern analytic philosopher.
In regard specifically to conditional statements, I'm not sure it is accurate to say that modern logic treats them "as being possibly true, possibly false." If the modal qualifiers ("possibly") in this characterization simply mean that the statement may be true or false depending on the actual state of affairs in the world, then I have no problem with it. But once that state of affairs is taken into account, there is "possibly") about it: If the antecedent is true and the consequent false, then the statement is definitely false. In all other circumstances, the statement is definitely true.

Traditionalists agree with the first part of this, but categorically deny the second. In other words, practitioners of the two systems have contradictory understandings of three of the four possible truth value combinations involved in determining the truth of a conditional statement. This seems to me to constitute a rather marked difference. Moderns believe you can determine the truth of a conditional statement based solely on the truth value of its component statements and traditionalists do not (with the exception of the one case of the antecedent being true and the conclusion false).

On the matter of whether the disagreement between the two systems indicates a different believe about the kind of art logic is, I may need a bit more clarification from Mr. McPike on the import of his question. If it is a question about whether logic is, for both schools, a language art, I would argue that it could not be considered so by the moderns, since they view logic as a purely quantificational system (that's why they refer to logic as "quantification theory") and language is not purely quantitative. If the issue then becomes whether language is, in fact, purely quantitative, as I suppose a logical positive may very well believe (I haven't thought a lot about that), then the difference would go deeper than just logic.

If the question is whether the proponents of two systems of logic agree that logic is a metaphysical art, I would simply point to the fact that, first, most of those who championed it in the early twentieth century explicitly denied the existence of metaphysics since they were, in large part, logical positivists (see A. J. Ayer's

*Language, Truth, and Logic*for a good example, particularly the first chapter, which is entitled, "The Elimination of Metaphysics"); and, second, that the system itself betrays this belief, as I have explained several times.
I'll leave it at that for now.