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I would like to know how material logic differs from formal logic.

From the little that I'm aware of, it is apparently the case that material logic concerns itself with the truth of the content of an argument, whilst formal logic only concerns itself with the validity of an argument form.

Question: I'm under the impression that material logic is very close to the concept of soundness, is material logic an outdated concept?

I would appreciate any elucidations.

  • Are you talking about reasoning with material conditionals? That's a very well documented logical notion that is recognised as philosophically distinct to the formal logical consequence relation, but considering the breadth and scope of material implications as a "logic" is something I've not encountered in the literature. – Paul Ross Mar 9 '15 at 13:02
  • Hi Paul. As far as I know, material logic is distinct from the material implication. Nonetheless, I have now accepted an answer for my question. – Five σ Mar 9 '15 at 14:20
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Neither SEP nor Wikipedia has heard of "material logic". In the writings of Jacques Maritain, it apparently means "applied logic" or thereabout; he goes into an elaborate argument why "material logic is the "Greater Logic".

According to Granström, which has a historical [re]view of the topic, "material logic" is a notion that was central in the scholastic period; John of St. Thomas defined it to be more or less what today is called epistemology. With the turn to formal logic in the 18th century, "material logic" has faded from modern treatments (of logic).

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Sir David Ross, in Aristotle’s Prior and Posterior Analytics - Oxford UP, 1949 - distinguishes between the formal logic of the Prior Analytics and the material logic of the Posterior Analytics.

Formal logic pertains to the structure of deduction and proof, with little-to-no reference to content.

Material logic pertains to the metaphysical background, scientific content, and scientific conditions of proof. For Aristotle, the metaphysical background is one of substance and accident; the scientific content consists in the species of a given genus and their necessary accidents; the conditions apply to, e.g., the terms (subject and predicate) of each of the premises of the demonstration (= proof). See Mure, Aristotle, for a discussion.

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Formal logic is logic as concerned with the pattern of valid inference which makes any proof a proof regardless of subject matter. For example, the subject of formal logic of the first operation of the mind (i.e. simple apprehension) is the term (i.e. "A sign out of which a simple proposition is constructed"), but formal logic does not investigate the intension of the term, simply its relation to other terms. Formal logic doesn't ask what X means in the statement, "All X are Y". This is logic as we understand it today, a study of the formal correctness and consistency of our reasoning.

Material logic is logic as concerned with proofs within a specific subject matter, so yes it has to do with soundness because the truth of premises are examined. Material logic is focused on the truth in knowing the intension of X in "All X are Y." For example, the subject of material logic of the first operation of the mind is the disposition of the universal (signified by the term), so material logic asks what are the conditions necessary for the universal.

W.D. Ross introduces the beginning of Aristotle's Posterior Analytics with this distinction between formal and material logic and shows the need for material logic:

Syllogistic inference involves, no doubt, some scientific knowledge, viz. the knowledge that premisses of a certain form entail a conclusion of a certain form. But while formal logic aims simply at knowing the conditions of such entailment, a logic that aims at being a theory of scientific knowledge must do more than this; for the sciences themselves aim at knowing not only relations between propositions but also relations between things, and if the conclusions of inference are to give us such knowledge as this, they must fulfil further conditions than that of following from certain premisses. To this material logic, as we might call it in opposition to formal logic, Aristotle now turns (Aristotle's Prior and Posterior Analytics, 51).

See John of Poinsot, Tractatus de Signis, ed. John Deely, p. 24/10-13. Also, John Deely, Four Ages of Understanding, 601.

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