[3.3.5] Ontological Structure of Ibn Sina’s Logic

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
Readingevery 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

[3.2.5] Al-Farabi on Happiness

Al-Farabi’s (872-950 AD) views on the human happiness are spread through some of its works: The Political Regime (Kitāb al-siyāsa al-madaniyya), The Principles and Opinions of the People of the Virtuous City (Mabādi’ ārā’ ahl al-madīnah al-fāḍilah), and Attainment [of Happiness]. In these works:

  • He upholds the Aristotelian theory that each human person has a goal of living (telos), which is the ultimate felicity. This state can be reached just in the afterlife when the soul is separated from the body.
  • Ultimate felicity is the attainment of the actual phase of intellect (essentially the act of thinking – see [3.2.4]), not virtuous action (see [1.3.17]), virtue (see [2.2.7]), pleasure (see [2.1.3]), or love of God (see [2.5.5]), as for different other philosophers and schools.
  • Ultimate felicity is possible for all humans in the afterlife, if the person meets some preconditions, like exercising virtuous actions and having the right knowledge and opinions.

This structure is presented in the following OntoUML diagram:

ClassDescriptionRelations
Person“Prior to death, human beings [persons] are hybrids—corporeal entities, on the one hand, yet also immaterial, on the other, due to their intellects, that is, the rational faculty of their souls which survives death—and as such exposed to two sets of powers. Just like every other inhabitant of the sublunary world, human beings are subject to the natural laws determining corporeal substances. In contrast, however, to all the other species belonging to the sphere of generation and corruption, human beings moreover experience a certain influence by the so-called ‘active intellect’, an immaterial, incorruptible, supralunary entity whose existence is pure thinking. This active intellect does not affect the body of a human being, but rather her intellect and imagination, i.e., those psychic faculties involved in thinking. The most fundamental influence which the active intellect exerts on the human soul consists in, first, the provision and, second, the basic ‘formatting’ of the rational faculty:
… [the active intellect] gives the human being a faculty and a principle by which to strive, or by which the human being is able to strive on his own for the rest of the perfections that remain for him. That principle is the primary sciences and the primary intelligibles attained in the rational part of the soul. (Political Regime B, 1, 68: 62)” (Germann)
has GoalOfLiving; has HumanIntellect; pursuits EarthlyFelicity
GoalOfLiving“In line with Aristotle, al-Farabi leaves no doubt whatsoever that there is one kind of happiness which constitutes the telos [goal of living] of every human being.”(Germann)is UltimateFelicity
Happinessal-Farabi “distinguishes between ‘earthly’ and ‘ultimate felicity’ [happiness]“. (Germann)
EarthlyFelicityEarthly felicity is a subkind of Happiness, not relevant for the goal of living.subkind of Happiness
UltimateFelicity“from the majority of his writings it is clear that happiness in the strict sense of the word, that is, as the concomitant of the highest human perfection, is ultimate felicity.” (Germann)subkind of Happiness; is attainment of ActualIntellect; has Precondition
Precondition“As the last citation from the Perfect State conveys, when discussing the preconditions of felicity, al-Farabi distinguishes between (a) common and (b) specific duties of the citizens, as well as between (i) knowledge and (ii) activities.” (Germann)
Knowledge/
Opinion
Al-Farabi thinks that the people in the virtuous city should have virtuous knowledge or at least virtuous opinions: “The things in common which all the people of the excellent city ought to know are: (1) In the first place to know the First Cause and all its qualities; (2) then the immaterial existents [including the above mentioned active intellect] …; (3) the celestial substances …; (4) [without number in Walzer’s translation] then the natural bodies which are beneath them, and how they come to be and pass away …; (5) then the generation of man; (6) then the first ruler …; (7) then the rulers who have to take his place …; (8) then the excellent city and its people and the felicity which their souls ultimately reach …” (Perfect State V, 17, 1: 277–9)subkind of Precondition
KnowledgeOfObjectThe knowledge of the objects necessary for ultimate felicity “presupposes a quite profound knowledge of cosmology, physics, anthropology, and philosophy of society.” (Germann)
This knowledge is attainable just for a handful of people, who are intellectually gifted enough to do science.
subkind of Knowledge/
Opinion
KnowledgeOf
Symbolic
Representation
The knowledge of symbolic representations of objects necessary for ultimate felicity is attainable for every person, even modest intellectual capacity:
“according to al-Farabi, the requirement of knowing these common objects does not exclude anyone from attaining happiness, because they
‘… can be known in two ways, either by being impressed on [the people’s] souls as they really are or by being impressed on them through affinity and symbolic representation.‘ (Perfect State V, 17, 2: 279)” (Germann)
subkind of Knowledge/
Opinion
Action“There are some indications regarding the common activities […]. It appears that, once again in unison with Aristotle, these embrace all sorts of exercises suited to purify one’s soul while it is still unified with ‘its’ body, as al-Farabi’s references to the soul’s disposition as well as his recurrent comparisons with arts and crafts suggest. Thus, he intimates, in connection with the last quoted passage:
‘When each of [the people of the excellent city] acts in this way [i.e., according to the citizens’ common duties], these actions of his make him acquire a good and excellent disposition of the soul, and the more steadily he applies himself to them, the stronger and better becomes that disposition of this and increases in strength and excellence—just as steadily applying himself to performing the actions of writing well make a man acquire proficiency in the art of writing’ …. (Perfect State V, 16, 2: 261)” (Germann)
subkind of Precondition
ActualIntellect“And precisely in the realization of this activity, i.e., thinking, and its perfection—ideally, the attainment of its most sublime level, i.e., science—consists humanity’s telos. Human beings, hence, are born with the natural obligation to perfect their rational faculty. While they are equipped by the active intellect with this faculty and the principles of thought, their task consists in actualizing this potential, i.e., their intellects, “by which a human being is a human being” (Political Regime A, 2, 8: 32). Becoming an intellect in actuality, just like the active intellect and the other separate intelligences, therefore, constitutes humanity’s perfection. Once a human being reaches this level of perfection, she acquires the state of ultimate happiness:
‘When the rational faculty attains to being an intellect in actuality [actual intellect], that intellect it now is in actuality also becomes similar to the separate things and it intellects its essence that is [now] intellect in actuality. …. Through this, it becomes such as to be in the rank of the active intellect. And when a human being obtains this rank, his happiness is perfected. (Political Regime A, 2, 8: 33; square brackets thus in the translation)
Across al-Farabi’s various writings, it remains unclear whether this stage of ultimate felicity can already be reached during one’s lifetime, when the soul is still linked with the human body, or only in the hereafter, once the soul has separated from the body due to this latter’s death.
Happiness, consequently, consists in the as-perfect-as-possible assimilation of the human soul to the active intellect, whose unique activity is thinking.” (Germann)
phase of HumanIntellect
HumanIntellectHuman intellect (arabic: aql, greek: νοῦς) “is understood as a faculty of the soul by means of which certainty about necessary, true, and universal premises is attained. Premises of this kind are not arrived at by means of syllogisms, but are present in the subject in a prior way, either by nature or without one being aware of how these premises were acquired. Hence, this faculty is some part of the soul by which humans have access to the first principles of the theoretical sciences.” (López-Farjeat)  

Sources

First published: 27/07/2019