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Question: I'm under the impression that material logic is very close to the concept of soundness, is material logic an outdated concept?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
    Commented Mar 9, 2015 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
    Commented Mar 9, 2015 at 14:20
  • It should be noted the accepted answer seems to omit some important references to sources that do define material logic.
    – J D
    Commented Mar 13, 2023 at 22:48

5 Answers 5


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).


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.


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.


Excellent dictionary definition...

material logic logic that is valid within a certain universe of discourse or field of application because of certain peculiar properties of that universe or field


And that applies immediately to the properties of our own universe.

There is, however, only one logic and so it is a profound mistake to see material logic as somehow different from formal logic. The name itself, "material logic" is likely to be misunderstood as signalling a different kind of logic.


Each concerns itself with a different type of inference. Formal logic is concerned with formal inferences. For formal inferences, the meanings of terms are defined by the logic you're using, then that meaning determines validity. Material logic is concerned with material inferences. For material inferences, the meaning of terms is determined outside the logical system (for example, by ordinary language), and this 'extra-logical' meaning determines validity.

Formal inference:

Socrates is a man. If Socrates is a man, then Socrates is mortal. So, Socrates is mortal.

The meaning of 'If...then' is determined within a logical system. We just need to know the meaning of 'If...then' to know whether the argument is valid (though not sound).

Material Inference:

Sydney is North-West of Canberra. So, Canberra is South-West of Sydney.

The meaning of 'North-West' is determined by ordinary language use, not by the logical system. We need to know the meaning of 'North-West' to know that 'South-West' is its converse. We just need to know the meaning of 'North-West', to know whether the argument is valid (though not sound).

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