Our Trouble With Conditionals
Please join us at our next meeting of the University of Hartford Philosophy Club this Wednesday, Oct. 27 from 1 p.m. to 2 p.m. in Room 420 Auerbach Hall at the University of Hartford. You can also join the meeting online by clicking on the WebEx link:
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This week, Brian Skelly will present the topic:
Our Trouble with Conditionals –
How Logical Illusion Can Disable Our Thinking on Vital Matters
Whether we have studied it formally or not, many of us recognize the importance of the academic study of logic and its relevance to human knowledge and thought. But we tend to underestimate the toll logical illusion takes on our own thinking and the decisions we make.
What I refer to here as ‘logical illusion’ is not simply sloppy or lax thinking, but errant, even fallacious thought carried out under the guise of logical rigor.
Logical illusion festers in areas of ambiguous interpretation of logical connectives. One famous case is the notorious confusion of exclusive with inclusive disjunction. The bulk of the mess we make for ourselves is with the misuse of the conditional. Here I aim both to explain our confusion are by an analysis of several examples, before moving on to my main case in point: our horrid mis-framing of the issue of economic management resulting in the fruitless centuries-long polemic between capitalist theory and socialist theory.
The case of ambiguity with respect to disjunction is easy enough to explain. It is that we utilize two disjunctive connectives with different truth conditions: exclusive-or and inclusive-or. As long as we are reflectively cognizant of this fact, it does not harm us. To be sure, formal logical system must decide which to consider primary, and do. Modern propositional logic considers inclusive disjunction to be primary and expresses exclusive-or in its terms as follows: p exclusive-or q is equivalent to (p inclusive-or q) and not-(p and q). Conversely, Boolean logic chooses exclusive-or to be its basic disjunctive operator and thus translates inclusive-or in its terms as: (p exclusive-or q) exclusive-or (p and q).
The main trouble that arises is that in spoken language we typically express disjunction ambiguously. Unlike in Latin, in which punctilious authors made sure to use ‘aut’ for exclusive-or and ‘vel’ for inclusive, most modern languages don’t have such convenient resources typically at hand. So it is left up to us to determine by context which sense of disjunction is intended.
For example, when mom tells us we can have the pie or the brownie for dessert, we can count on the intended sense to be exclusive. Just try to take both and see what happens! Conversely, if, as a child I don’t know what to do on a rainy day, it can be suggested to me that I can read a book or play piano, I shouldn’t expect flak for doing both, but might well get some for moping around doing neither.
The trouble here doesn’t seem to be much, and most of that which we might have is covered by correct interpretation of context. But the conditional is another matter.
My daughter Teresa and I have had this ongoing query about a pair of related scriptural quotes. It all started when I once remarked that I was relieved by Jesus saying that (NAF) whoever is not against him is for him (Luke 9:50; Mark 9:40), since it appears to offer an easy standard of belonging. Teresa, however, ruffled my feathers by pointing out that Jesus had also said that (NFA) whoever is not for him is against him (Matthew 12:30), which appears on its face to suggest a rather more rigid standard of membership. Others have noted this apparent conflict, some even suggesting it amounts to a contradiction. In fact and quite surprisingly - it amounts to no difference at all according to standard logical analysis. (See attached for full document and references).
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Brian D. Skelly, Philosophy
413-273-2273