Come join us at this week’s Philosophy Club meeting Thursday, October 4th from 12:15 to 1:45 in 421 Auerbach Hall.
With the immense amount of work done on the analysis of deductive argument forms in the past century, it seems odd that we have not done something similar with inductive argument forms.
To be sure, much work has been done on the processes of induction itself, perhaps the pinnacle of such efforts being Ray Solomonoff’s Theory of Universal Inductive Inference, a mechanized approach to the recognition of patterns in data sets. But few scholars have ventured into studying inductive argument forms in a manner similar, say, to Aristotle’s study of syllogisms. This is even more odd because the key difference between deductive and inductive argument may amount to the types of quantifier used. The deductive inference of Aristotle’s logic and modern predicate logic relies on the universal (all) and existential (some) quantifiers in either their affirmative or negative occurrences (e.g. All A are B/Not all A are B; Some A are B/No A are B). Could we not obtain a similar analysis of inductive argument forms simply by changing the quantifiers and making all resulting necessary adjustments?
After all, it may be noted that ‘All A are B’ is just the upper limit of “most A are B’, while ‘No A are B’ is the lower limit of ‘Few (if any) A are B’. This could give us four quantifiers from which to fashion our inductive argument forms: Most, Not most, Few (by far, if any) and Not few, or Many.
In his article, “On the Logic of ‘Few’, ‘Many’, and ‘Most’” (Notre Dame Journal of Formal Logic, vol. XX, no. 1, January 1979), Philip Peterson shows how we might extend Aristotle’s Square of Opposition, his tool for defining the meanings and relationships between his four quantifiers: All/Not all/ Some/None, thereby suggesting that inductive forms might plausibly be studied in relation to deductive ones. Much later on, in fact quite recently, Corina Ströβner (“The Logic of ‘Most’ and ‘Mostly’”, in Axiomathes, April 28, 2017) has attempted something similar, this time seeking to incorporate, by inclusion of the same kind of inductive quantifiers we have been discussing, into modern predicate logic, creating as it were a sort of continuum between inductive and deductive logic.
My interest is distinguished from the interests of these authors in that I am seeking not so much to absorb inductive logic into deductive logic as to understand and develop our understanding inductive argument form on its own terms. Inductive argument forms are forms we hold in place to measure whether and to what extent the continually incoming evidence makes the conclusion more likely. Inductive reasoning is making inferences from incomplete evidence, with the extreme limit of complete evidence almost always beyond our reach. Yet our understanding of induction must acknowledge this link, that inductive forms at least in principle may become deductively valid at those extremes. Our evaluation of inductive argument forms, therefore, ought to include rating the dependability or at least plausibility of the growth of the probability of the conclusion as the evidence for the premises increases – an evaluation of these forms as moving targets rather than as static figures. By increasing evidence for the premises, I mean evidence that makes most proceed to all as a limit, few proceed to none as a limit, along with the corresponding permutations for the negations of these. (Full article attached.)
Dr. Skelly teaches Philosophy here at the University and locally.
The University of Hartford Philosophy Club has an informal, jovial atmosphere. It is a place where students, professors, and people from the community at large meet as peers. Sometimes presentations are given, followed by discussion. Other times, topics are hashed out by the whole group.
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