[4.12.3] Robert Kilwardby on Syllogistic Form and Matter

Robert Kilwardby (ca. 1215–1279 AD), in his commentary to Aristotle’s “Prior Analytics commentary,” enriches the Arostotelian logic (see [1.3.9]) with a few new perspectives:

  • He applies the theory of four causes (see [1.3.4]) on syllogism and concludes that syllogisms, like any other objects, have material, formal, efficient, and final causes.
  • Syllogisms have matter (the premises and terms) and form (the mood and figure), thus presenting a hylomorphic structure (see [1.3.5])

The following  OntoUML diagram presents the main elements of Kilwarby’s hylomorphic syllogism:

Kilwardby on syllogistic matter and form
ClassDescriptionRelations
Syllogism“A syllogism is composed of form as well as matter.23 In elaborating
on this idea, Kilwardby applies the Aristotelian doctrine of causes to the syllogism.” (Thom, 2013)
A syllogism is an “inference with two premises, each of which is a categorical sentence, having exactly one term in common, and having as conclusion a categorical sentence the terms of which are just those two terms not shared by the premises”. (Smith, 2018)
Not all the triplets of two premises and one conclusion of the required structure are syllogisms, only just those who lead to a valid inference, listed in the moods.
E.g. P1: All man are mortal. P2: Socrates is man, C: Socrates is mortal.
has Form; has Matter; relates 2 Premises with 1 Conclusion; produces KnowledgeOrBelief
PropositionPropositions (assertion, apophanseis) are sentences with a specific structure: “every such sentence must have the same structure: it must contain a subject and a predicate and must either affirm or deny the predicate of the subject.” (Smith, 2018)
Term“Subjects and predicates of assertions are terms (horos) which can be either individual, e.g. Socrates, or universal, e.g. human. Subjects may be individual or universal, but predicates can only be universals.”(Smith, 2018)shared part of Proposition
PremiseA possible role of an Proposition, relative to a Syllogism is Premise (protasis).
E.g. P1: All man are mortal. P2: Socrates is man.
in material relation with Conclusion; role of Proposition
MajorPremise“The major premise occupies a determining role, since it is ‘contracted’ by the minor premise to produce the conclusion. Because of this relation between major and minor premise, Kilwardby reasons, the minor should not be counted along with the major; and so, he says, the Aristotelian definition of the syllogism rightly names oratio (in the singular) as its genus, not orationes.” (Thom, 2013)
E.g. P1: All man are mortal.
subkind of Premise
MinorPremise“The major premise occupies a determining role, since it is ‘contracted’ by the minor premise to produce the conclusion. (Thom, 2013)
E.g. P2: Socrates is man.
subkind of Premise
ConclusionA possible role of an Proposition, relative to an Syllogism is Conclusion (sumperasma).
E.g. C: Socrates is mortal.
role of Proposition
Figure“The middle term must be either subject or predicate of each premise, and this can occur in three ways: the middle term can be the subject of one premise and the predicate of the other, the predicate of both premises, or the subject of both premises. Aristotle refers to these term arrangements as figures (schêmata)”. (Smith, 2018)
There are 3 Figures.
characterizes Syllogism
MoodMood characterizes a syllogism, and is prooved with a Proof. There are 14 Moods, 4 for the First figure, 4 for the Second figure, and 6 fot the Third figure.characterizes Syllogism
MatterThe matter of the syllogism “consists of two propositions (the
major and minor premises) and three terms. It is worth noting that on Kilwardby’s account, the syllogism is materially constituted by two propositions, not three. The conclusion is not part of the syllogism; therefore, the syllogism is not a type of consequence. The syllogism’s two premises, however, possessa unity thanks to the fact that they aim at a single conclusion.” (Thom, 2013)
E.g. matter in this example:
Major premise: All man are mortal.
Minor PremiseSocrates is man
Terms: man, mortal, Socrates
is MaterialCause; generalizes Premise and Term
Form“A syllogism’s form is the figure and mood as shown respectively by the relative position of the terms in the premises and by the premises’ quality and quantity; this is indicated by Aristotle when he says that in the syllogism certain things are posited (positis).”is FormalCause; generalizes Mood and Figure
Knowledge
OrBelief
“The demonstrative and dialectical syllogism also have a final cause, namely, the production respectively of knowledge or belief.” (Thom, 2013)is FinalCause
HumanHumanproduces Syllogism; is EfficientCause
Cause“Aristotle places the following crucial condition on proper knowledge: we think we have knowledge of a thing only when we have grasped its cause (aitia).” (Falcon, 2019)
MaterialCause“The material cause: ‘that out of which’, e.g., the bronze of a statue. […]
The bronze enters in the explanation of the production of the statue as the material cause. Note that the bronze is not only the material out of which the statue is made; it is also the subject of change, that is, the thing that undergoes the change and results in a statue. The bronze is melted and poured in order to acquire a new shape, the shape of the statue.” (Falcon, 2019)
subkind of Cause
FinalCause“The final cause: ‘the end, that for the sake of which a thing is done’, e.g., health is the end of walking, losing weight, purging, drugs, and surgical tools.” (Falcon, 2019)subkind of Cause
EfficientCause“the actual syllogisms that people produce have efficient causes.” (Thom, 2013))
“The efficient cause: ‘the primary source of the change or rest’, e.g., the artisan, the art of bronze-casting the statue, the man who gives advice, the father of the child.” (Falcon, 2019)
subkind of Cause
FormalCauseFormal cause, or the expression of what it is”, e.g., the shape of a statue. […]
The bronze is melted and poured in order to acquire a new shape, the shape of the statue. This shape enters in the explanation of the production of the statue as the formal cause.” (Falcon, 2019)
subkind of Cause

Sources

  • Thom, Paul, “Robert Kilwardby on the Syllogistic Form”, A Companion to the Philosophy of Robert Kilwardby, Christopher Henrik Lagerlund and Paul Thom (ed), Brill, 2013
  • Falcon, Andrea, “Aristotle on Causality“, The Stanford Encyclopedia of Philosophy (Spring 2019 Edition), Edward N. Zalta (ed.)
  • Smith, Robin, “Aristotle’s Logic“, The Stanford Encyclopedia of Philosophy (Winter 2018 Edition), Edward N. Zalta (ed.)
  • Silva, José Filipe, “Robert Kilwardby“, The Stanford Encyclopedia of Philosophy (Winter 2016 Edition), Edward N. Zalta (ed.)

First published: 11/2/2021

[4.11] Albert the Great on Universals

Albert the Great (Albertus Magnus, 1200?-1280 AD), in his paraphrase of Aristotle’s Organon, took the position that the universal’s mode of being should be analyzed based on its function. It may be considered in itself, or relative to understanding, or as existing in one individual. This way, he concluded, that both the nominalist and realist solutions to Porphyry’s questions are too simplistic.
He harmonized “Plato’s realism in which universals existed as separate forms with Aristotle’s more nominalistic theory of immanent forms”.

Porphyry’s questionsUniversals according to Albert
(a) whether genera and species [universals] are real or are situated in bare thoughts alonethey are real
(b) whether as real they are bodies or incorporealsthey are incorporeals
(c) whether they are separated or in sensibles and have their reality in connection with themthey are separated, but also in sensibles and have their reality in connection with them, based on the point of view of the analysis.

Albert’s model of universals is presented in the following OntoUML diagram:

Albert on universals
ClassDescriptionRelations
UniversalAlbert “defined the term universal as referring to ‘ … that which, although it exists in one, is apt by nature to exist in many.’ Because it is apt to be in many, it is predicable of them. (De praed., tract II, c. 1) He then distinguished three kinds of universals, those that pre-exist the things that exemplify them (universale ante rem), those that exist in individual things (universale in re), and those that exist in the mind when abstracted from individual things (universale post rem). […]
Albert appealed to his three-fold distinction, noting that a universal’s mode of being is differentiated according to which function is being considered. It may be considered in itself, or in respect to understanding, or as existing in one particular or another. Both the nominalist and realist solutions to Porphyry’s problem are thus too simplistic and lack proper distinction. Albert’s distinction thus allowed him to harmonize Plato’s realism in which universals existed as separate forms with Aristotle’s more nominalistic theory of immanent forms.”
Pre-existingUniversalPre-existing universals (universale ante rem): “For universals when considered in themselves (secudum quod in seipso) truly exist and are free from generation, corruption, and change”is role of Universal
UniversalInIndividualUniversals in individal (universale in re): “But when they are considered in particulars (secundum quod est in isto vel in illo) their existence is exterior to as well as beyond the mind, yet existing in things as individuated.”is role of Universal; exclusive part of Individual
UniversalInMindUniversal in mind (universale post rem) ar abstracted from individuals: “If, however, they are taken in reference to the mind (refertur ad intelligentiam) they exist in two modes, depending on whether they are considered with respect to the intellect that is their cause or the intellect that knows them by abstraction.”is role of Universal; shared part of Mind
Minda human mindknows Individual
Individualan individual (or particular)exemplifies Pre-existingUniversal
AnalysisViewpointThe viewpoint form which we consider analize the Universal.
RelativeItself; RelativeIndividual; RelativeUnderstanding“Albert appealed to his three-fold distinction, noting that a universal’s mode of being is differentiated according to which function is being considered. It may be considered in itself, or in respect to understanding, or as existing in one particular or another.”subkinds of AnalysisViewpoint; relates to (in order) Pre-existingUniversal; UniversalInIndividual; UniversalInMind

Related posts in theory of Universals: [1.2.2][1.3.1][1.3.2][2.5][2.7.3][4.3.1][4.3.2][4.4.1][4.5.2], [4.9.8]

Sources

  • All citations from: Führer, Markus, “Albert the Great”The Stanford Encyclopedia of Philosophy (Summer 2020 Edition), Edward N. Zalta (ed.)

First published: 21/1/2021
Updated: 7/3/2021 added AnalysisViewpoint and its subkinds