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In Chance , Love and Logic, Peirce defines reasoning into two categories: analytic and non-analytic. All forms of reasoning have three fundamental components: rule, case, result.

Analytic reasoning is deduction, and is the specific structure of components: rule and case, therefore result.

Non-analytic reasoning splits into induction and abduction, which are explained as case and result therefore rule, and rule and result therefore case, respectively.

My understanding of logic was formed around deductive and inductive reasoning, and they were always explained to me in a "premises, conclusion" paradigm. Deductive logic is when the conclusions of arguments follow necessarily from the premises. Inductive logic is when the conclusions of arguments are "supported" by the premises, but do not follow necessarily.

My question is: in Peirce's paradigm, what is the justification for dividing the premises of arguments into the categories of "rule" and "case"? There seems to be a way in which all premises are not "equal", but I am not clear on how.

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First, Pierce's rule, case, and result are equivalent to syllogistic logic's major premise, minor premise, and conclusion. If we look at the classic syllogism example:

All men are mortal
Socrates is a man
Socrates is mortal
  • The first sentence (the major premise) establishes the rule that all members of the category 'men' have the property 'mortal.'
  • The second sentence (minor premise) establishes that the object 'Socrates' is a member (or case) of the category 'men.'
  • The last sentence is the conclusion (the result of combining the first two sentences).

There's nothing mysterious here. Pierce is merely shifting the language of deductive reasoning for his own purposes. His language, if nothing else, is more concrete and focused than the standard usage.

Inductive reasoning and abductive reasoning in Pierce's logic are forms of reasoning we use when we are trying to infer the premises we should start from, given a particular outcome. We use inductive reasoning — case, result, thus rule — to establish what properties a general category has. In other words, if we know that Socrates is a man, and we know that Socrates died, we can (through induction) claim that all objects in the category 'men' have the property that they die. By contrast, we use abductive reasoning — rule, result, thus case — when we are trying to figure out whether a particular object belongs in a given category. In other words, if we know that all men are mortal, and we know that Socrates has died, we can (through abduction) claim that Socrates is a member (case) of the category 'men.'

Deduction is always correct, assuming the premises are true and the deductive chain is valid. However, there are no validity rules for induction or abduction, so there is always a measure of doubt. The fact that Socrates died does not necessarily mean that all men will die (finding an immortal man would nix that induction); the fact that all men die and Socrates died does not necessarily imply that Socrates was a man (things other then men die: I could have named my pet hamster 'Socrates,' nixing that abduction). This is why we generally prefer multiple cases to form an induction, and why we prefer to evaluate cases on multiple properties to create as unique a member-inclusion signature as possible.

  • +1. But I would separate out abduction. Abduction is a mix of induction and deduction, not a form of logic in itself. Peirce calls it 'inference to the best explanation' and this would be a process of induction and deduction, and anything else that helps. . . . . – user20253 Dec 22 '19 at 18:04
  • I'm going to have to go back and reread Pierce to get his exact take on it; it's been a while. But I'll look into it. – Ted Wrigley Dec 23 '19 at 3:16
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I would argue that the difference in how the deductive-inductive dichotomy is framed in terms of premises and conclusions and how Pierce's characterization function is a result of the differences in how both topics relate to logic and epistemology and the two senses of argument. In the narrow sense, an argument is an inference from two or three sentences, where as in the broad sense, an argument is a structure of narrow arguments as well as other objects that attempts to achieve some end. To prove Socrates is mortal because he is a man is an example of the first, to argue that human consciousness resembles a Turing machine would exemplify the second. This is mirrored in the fact that logic as the ancient Greeks saw it was more epistemological and less ontic in nature.

Deductive reason which started with very simple systems like Aristotelian syllogism has always been of limited scope with the focus being on the certainty of statements in regard to each other; here the focus is on almost grammatical-level examination of what constitutes truth about simple entities and their properties. How do Socrates, man, and mortality relate? This would the analytic distinction you mention.

Yet, in informal argumentation, where the emphasis is generally not argumentation for the sake of understanding inference and argumentation, but rather interested in the messy, informal, and complicated business of reality, the emphasis is on producing an argument through inference that works. This would be the non-analytic distinction you cite.

From the perspective of someone who is more interested in the epistemic aspect of argumentation rather than the logical aspect, it would be natural to place an emphasis not on the level of statement and proposition which are one level of meaning-bearer, but rather on a higher, more holistic level: cases and the rules that can be derived from them. Ray Jackendoff proposes in his Foundations of Language that meaning occurs at multiple levels: the phonological, syntactic, semantic, and spatial levels, so that the argument to prove Socrates mortality is essentially grammatical, whereas the argument concerned with the adequate characterization of mind would be at the highest level possible. A concrete example may serve to illustrate.

In analogical argumentation such as that used in legal reasoning by case, one is not about the nuts and bolts of the grammar generally. Certainly, disputes may over occur in regards to the meaning of statements by parties, but the overall concern is how to rule in regards to the conflict, let us say in civil law. A trier of fact must resolve by deciding what to do, and in the Anglo-American tradition of law, this creates a precedent or rule for future judges. So, the distinction in paradigms reflects the notion that there are two subtly different definitions of argument, one in the narrow technical sense, and one in the broader practical sense.

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