Aristotle's Logic: General Survey and Introductory Readings

Selected Bibliography on the Logic of Aristotle: General and Introductory Readings

INTRODUCTION: LOGIC AS FORMAL ONTOLOGY

"There are several different conceptions of the nature of logic. Here I want to contrast an ontic conception with an epistemic conception. On one ontic conception logic investigates certain general aspects of 'reality', of 'being as such', in itself and without regard to how (or even whether) it may be known by thinking agents: in this connection logic has been called formal ontology. On one epistemic conception, logic amounts to an investigation of deductive reasoning per se without regard to what it is reasoning about; it investigates what has been called formal reasoning. On this view, logic is part of epistemology, viz. the part that studies the operational knowledge known as deduction. It has been said that one of the main goals of epistemically-oriented logic is to explicate the expression 'by logical reasoning' as it occurs in sentences such as: a deduction shows how its conclusion can be obtained by logical reasoning from its premise-set.

Relevant to the axiomatic method there would be two branches of epistemology: one to account for knowledge of the axioms and one to account for how knowledge of the theorems is obtained from knowledge of the axioms, in other words, one investigating induction and one investigating deduction. The latter is logic according to the epistemic conception.

On the ontic view of logic, on the other hand, logic is an attempt to gain knowledge of the truth of propositions expressible using only generic nouns (individual, property, relation, etc.) and other 'logical' expressions. In the framework of Principia Mathematica those are propositions expressible using only variables and logical constants. Principia Mathematica is an excellent example of an axiomatic presentation of logic as formal ontology. Below are some typical laws of formal ontology.

Excluded middle: Given any individual and any property either the property belongs to the individual or the property does not belong tothe individual.

Noncontradiction: Given any individual and any property it is not the case that the property both belongs to the individual and does not belong to the individual.

Identity: Given any individual and any property, if the property belongs to the individual then the individual has the property.

Dictum de omni: Every property A belonging to everything having a given property B which in turn belongs to everything having another property C likewise belongs to everything having that other property C.

Dictum de nullo: Every property A belonging to nothing having a given property B which in turn belongs to everything having another property C likewise belongs to nothing having that other property C.

Commutation of Complementation with Conversion: Given any relation R the complement of the converse of R is the converse of the complement of R.

From this sample of logic as ontic science we can see how the focus is on ontology, or, as has been said by others, on the most general features of reality itself and not on methods of gaining knowledge. According to Russell Introduction to mathematical philosophy, 1919, 169, 'logic is concerned with the real world just as truly as zoology, though with its more abstract and general features.' These six laws are purely ontic in that they involve no concepts concerning a knowing agent or concerning an epistemic faculty such as perception, judgement, or deduction. This is not to deny that there is an epistemic dimension to logic as ontic science but only to affirm that the focus if ontic. Every science in so far as it is science has an epistemic dimension. The epistemic differs from the ontic more as size differs from shape than as, say, animal differs from plant.

Logic as ontic science was referred to above as formal ontology. Logic as epistemic metascience may in like manner be called formal epistemology. It is important and interesting to note that both are called formal logic but for very different reasons. Some formal onticists justify the adjective formal by reference to the fact that its propositions are expressed exclusively in general logical terms without the use of names denoting particular objects, particular properties, etc. cf. Russell 1919, 197. Some formal epistemicists justify the adjective formal by reference to the fact that the cogency of an argumentation is subject to a principle of form and in particular to the following principles: (l) every two argumentations in the same form are either both cogent or both non-cogent, (2) every argumentation in the same form as a deduction is itself a deduction. In fact, some formal epistemicists such as Boole claimed, with some justification, that they were dealing with the forms of thought, i.e. with the forms of cogent argumentations. For more on cogency of argumentations and the principles of form see Corcoran 1989.

Formal onticists are often easy to recognize because of their tendency to emphasize the fact that formal ontology does not study reasoning per se. In fact, the formal onticists often think that the study of reasoning belongs to psychology and not to logic. For example, Łukasiewicz in his famous book on Aristotle's syllogistic makes the following two revealing remarks. Łukasiewicz 1957 pages 12 and 73, respectively. 'Logic has no more to do with thinking than mathematics. "[Aristotle's] system is not a theory of the forms of thought nor is it dependent on psychology; it is similar to a mathematical theory...'

There are significant differences among formal onticists. For example, even among those that emphasize the truth-preserving character of deduction some accept the view that it is consequences-conservative as well and some reject this view. For example, Łukasiewicz 1929, 16 explicitly rejects the view that deduction is a process of information extraction. He says that in deductive inference '...we may obtain quite new results, not contained in the premises'." pp. 17-19

From: John Corcoran: The founding of logic. Modern interpretations of Aristotle's logic - Ancient Philosophy, 14, 1994 pp. 9-24

(to be continued...)