Islamic

[3.3.5] Ontological Structure of Ibn Sina’s Logic

A. L. Komáromi3 Comments

Ibn Sina (Avicenna, 980-1037 AD) was the most crucial logician in the Arabic tradition. He synthesized, re-framed and extended the problems and solutions inherited from Aristotle and the Peripatetic tradition, e.g.:

  • enriched Aristotelian term logic [3.3.9] with the systematical and detailed consideration of modality and reading (see Categorical Propositions),
  • introduced propositional logic different from the Stoic one [3.5.4] (see Hypothetical Propositions).

Here is a very high level OntoUML representation of Avicenna’s logic:

Avicenna on logic
ClassDescriptionRelations
PropositionProposition (qaḍiyya) according to Avicenna can be (1) categoricals, and (2) hypotheticals. 
Categorical
Proposition 		“Categorical (ḥamliyyāt) propositions are subject (mawḍūʿ)-predicate (maḥmūl) propositions expressing a relation (nisba) or judgment (ḥukm) between terms.”
E.g.: “Avicenna is man.”
“All man are mortal.”		is Proposition
Hypothetical
Proposition		“Hypotheticals (šarṭiyyāt) comprise two main sub-types, depending on whether the component sentences are in connection (ittiṣāl) or in conflict (ʿinād)… The resulting propositional types are conditionals (muttaṣilāt) and disjunctions (munfaṣilāt)…”is Proposition
Conditional
Proposition		The Conditional proposition is formulating a relation of following (ittibāʿ) between and two propositions, an antecedent (muqaddam) and a consequent (tālin).
E.g. “If [the sun rises], then [it is day].”		is Hypothetical Proposition
Disjunctive
Proposition 		The Disjunctive Proposition expresses a conflict in terms of a disjunction of propositions (or parts, ağzāʾ).
E.g. “Either [this number is even] or [<this number> is odd].” 		is Hypothetical Proposition
AntecedentAntecedent is a possible role of a Categorical Proposition in a Conditional Proposition, where designates a condition.
E.g. “[the sun rises]”		is shared part of Conditional proposition; is Categorical Proposition
ConsequentConsequent is a possible role of a Categorical Proposition in a Conditional Proposition, where designates a consequence of the Antecedent.
E.g. “[it is day].” 		is shared part of Conditional proposition; is Categorical Proposition
FollowingThe relation of following between antecedent and consequent in conditional propositions.Relates Antecedent with Consequent
ModalityModality: “every categorical proposition is modalized, either implicitly or explicitly. The modality may be either temporal […], alethic […], or a combination of both.”Characterizes Categorical Proposition
Temporal
Modality		Temporal Modality can be e.g.: sometime, always, never etc.inherits from Modality
Alethic
Modality		Alethic Modality can be e.g.: necessarily, possibly, impossibly etc. inherits from Modality
Reading“every categorical proposition is subject to an additional reading, depending on whether the proposition is taken to express a relation between the predicate and what is picked out by the subject:”
(a) referential/substantial (ḏātī): “as long as what is picked out by the subject exists (mā dāma mawğūd aḏ-ḏāt) or
(b) descriptional (waṣfī): “as long as it is qualified—or ‘described’ (mā dāma mawṣūf)—by the subject. This move amounts to adding a temporal parameter that identifies”		is related to Categorical Proposition
SyllogismSillogism is an inference with two ore more premises, and having as conclusion a proposition. the terms of which are just those two terms not shared by the premises.
E.g. P1: “All man are mortal.” P2: “Avicenna is man,” C: “Avicenna is mortal.” 		relates 2 or more premises and 1 conclusion;
Connective
Syllogism		“Connective syllogisms are divided into two main types: (1) categorical (ḥamlī) and (2) hypothetical (šarṭī) syllogisms.” is Syllogism
Repetitive
Syllogism 		“The repetitive (istiṯnāʾī) syllogistic covers inference patterns such as modus ponens and modus tollens (in their conditional and disjunctive variants)…
Repetitive syllogisms consist of (i) a hypothetical premise (conditional or disjunctive) containing the conclusion or its negation as one of its parts, and (ii) another premise which asserts or denies (and thereby “repeats”) part of the hypothetical premise.”		is Syllogism
ReductioAd
Absurdum		“A reductio [ad absurdum] is a compound syllogism (qiyās murakkab)—i.e., a concatenation of syllogisms—consisting of a connective hypothetical syllogism and of a repetitive syllogism. Both categorical and hypothetical propositions may be proved by reductio.”is Syllogism
Categorical
Syllogism		“Categorical syllogisms are those whose premises and conclusions are all and only categorical propositions.”is Connective Syllogism
Hypothetical
Syllogism 		“The hypothetical syllogistic investigates arguments in which at least one of the premises is a hypothetical proposition (of type (i), namely one whose parts are themselves categoricals. Purely hypothetical syllogisms are those in which the combination of the premises involve only hypotheticals (conditional-conditional; conditional-disjunction; disjunction-disjunction). Mixed hypothetical syllogisms are those in which the combination of the premises involves a hypothetical (conditional or disjunction) and a categorical.”is Connective Syllogism
MoodMoods are formalized templates of valid (productive) syllogismsCharacterizes syllogism

Sources

  • All citations from:  Strobino, Riccardo, “Ibn Sina’s Logic”, The Stanford Encyclopedia of Philosophy (Fall 2018 Edition), Edward N. Zalta (ed.)

First published: 29/08/2019
Updated: 6/3/2021 added Following

[3.3.4] Ibn Sina on the Phases of Intellect

A. L. Komáromi2 Comments

Ibn Sina (Avicenna, 980-1037 AD) thinks that the human Intellect goes through a series of four phases – starting from the empty potentiality of a newborn to the fully actualized intellectual faculty containing Forms acquired from the Active Intellect (see also [3.3.2], [3.3.3] and al-Farabi’s similar structure [3.2.4]).

The following OntoUML diagram shows the four phases of the Intellect:

Ibn Sina on Stages of Intellect
ClassDescriptionRelations
HumanIntellectIntellect is acquiring concepts/forms through actualization from Active Intellect.
Material
Intellect		“‘Material intellect‘ is the wholly ‘unqualified potentiality’ for thought which belongs to ‘every member of the species.’ It is a ‘disposition’ (isticdad) inhering in the incorporeal human soul from birth.”
E.g. “The newborn infant has the potentiality for writing only in the sense that it may eventually learn to write.”		phase of Intellect
Intellect
InHabitu		“‘Intellect in habitu‘ (bil-malaka) is the ‘possible potentiality’ in which the human subject possesses the ‘first intelligible thoughts.’ These are attained through cogitation.
E.g. “Later, the ‘boy matures’ and comes to ‘know the inkwell, the pen, and the letters.’ Inasmuch as he controls the rudiments and can go on to master the art with ‘no intermediate’ step, he is said to have a ‘possible potentiality’ for writing.”		phase of Intellect; posesses FirstInteligible
Actual
Intellect		“‘Actual intellect,‘ despite the name, is a further stage of potentiality— the stage of fully actualized potentiality. It is the ‘complete [kamdliyya] potentiality’ that is attained when both ‘second intelligibles'[derivative scientific
propositions] and ‘intelligible forms’—that is to say, derivative propositions and concepts—have been added to the ‘first intelligibles,’ with the proviso that the human subject is not thinking the propositions and concepts. At the stage of actual intellect, the human subject does not ‘actually … attend to’ his knowledge, yet can do so ‘whenever he wishes.'”. These are attaied also with the help of cogitation.		phase of Intellect; posesses FirstInteligible and SecondIntelligible
Acquired
Intellect		“‘acquired [mustafdd] intellect,’ which alone is an ‘unqualified actuality.’ At the level of acquired intellect, ‘intelligible forms’ are actually ‘present’ to the man, and he ‘actually attends’ to them. Avicenna’s acquired intellect is, literally, acquired from the active intellect. The unqualified actuality of thought is ‘called. . . acquired, because it will be shown . . . that potential intellect passes to actuality’ by establishing contact with the active intellect and having ‘forms acquired from without imprinted’ in man’s intellect.”
E.g. “At a still higher level stands the ‘scribe,’ who is adept with the [writing] implement,’ is ‘accomplished in his art,’ and can apply the art ‘at will.’ When he is not exercising his skill, the scribe has a ‘perfect’ potentiality for writing.”		phase of Intellect; posesses FirstInteligible , SecondIntelligible and Form
Active
Intellect		“The active intellect is (1) the emanating cause of the matter of the sublunar world, (2) the emanating cause of natural forms appearing in matter, including the souls of plants, animals, and man, and (3) the cause of the actualization of the human intellect.”actualize Acquired
Intellect; emanates Form
Formnatural form of the lower worldexclusive part of ActiveIntellect; characterizes Intellect
FirstIntelligiblefirst intelligibles: “are theoretical propositions of the sort man affirms without being able to ‘suppose that they might ever not be affirmed’; examples are the propositions that ‘the whole is greater than the part’ and ‘things equal to the same thing are equal to each other.'”
SecondIntelligibleSecond intelligibles are derivative propositions and concepts.
IntelligibleFirst intelligibles, second intelligibles and forms are intelligibles.

Sources

  • All citations from:  Herbert A. Davidson, “Alfarabi, Avicenna, and Averroes, on Intellect”, Oxford University Press 1992

First published: 22/08/2019
Updated: added first and second intelligible on 22/11/2020