What is Logic? Plato and Aristotle

Logic emerged in the history of the West as a method of true thought and without contradictions through the Platonic dialectic. The word logoswhich can be translated by language-speech and thought-knowledge, was the starting point for Greek philosophers to question whether the logos obeyed rules or not, whether or not it had rules, principles and criteria for its use and functioning (CHAUÍ, 2000).

The problem of logic begins with Parmenides and Heraclitus. Heraclitus claims that the logos and the truth is found in the changing of things – and these things are found in Becoming. Change takes place in the form of contradiction, that is, all things change into their opposites. Struggle is the harmony of opposites and is responsible for the rational order of the universe. O logos – orderer of Becoming – is change, is contradiction. However, the centrality of his thinking is the idea of the profound unity that constitutes multiplicity.

However, Parmenides’ statement was opposed to that of Heraclitus. According to the Parmenidian doctrine, reason must be guided according to the principles of non-contradiction and identity in order to know the Truth. It is according to these same principles that one must understand the conception of Being proposed by Parmenides: the Being has to be identical with itself to exist. Therefore, the Being is immutable, it cannot transform itself into its opposite. At this point, the principle of non-contradiction and identity emerges in the history of Western philosophy because, from Parmenides, thought and language require identity.

In order to escape the problems encountered in Parmenides and Heraclitus, Plato and Aristotle offer two different solutions. The questions refer to contradiction – change and identity-permanence of beings. In the present work, we aim to discuss Aristotelian analytics, that is, about logic as proposed by Aristotle – considering that he aimed to solve the problems mentioned above.

Platonic dialectic is the direct exercise of thought and language. In the dialectical method, division takes place – diaeresis – of the entity or concept on opposite sides in order to arrive at something indivisible. The last division manifests the essence of what is investigated. Aristotle criticizes his master for discrediting the dialectical method as a legitimately logical process. Estagirita was innovative in seeking to show the right path for the investigation of sensible reality through demonstration. Aristotle thinks of logic as an instrument that precedes the exercise of thought and speech, that is, logic offers the means for thought and speech to take place. Thus, Platonic dialectics is a way of knowing and Aristotelian logic is an instrument for knowing it: “Aristotelian logic offers procedures that must be employed in those reasonings that refer to all things of which we can have a universal and necessary knowledge, and its starting point are not contrary opinions, but principles, rules and necessary and universal laws of thought” (CHAUÍ, 2000, p. 230).

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The object of logic is the proposition and this expresses, through language, the judgments formulated by thought. A proposition is the attribution of a predicate to a subject (“S is P”). Logic studies the constituent elements of the proposition (which are the categories), the types of propositions, the types of syllogisms and the principles that are necessary for every proposition and every syllogism to be true: principle of identity, of non-contradiction and the excluded third. Propositions claim to be objective, and this means that statements always refer to phenomena present in the world. It is also worth noting the following statement by Reale when speaking of categories, within the scope of Aristotelian metaphysics, so that we can, at the end of this work, establish a relationship between ontology and logic: “Sensible being is unthinkable without categories; and that means that, as such, they are necessary” (REALE, 2001, p. 81).

The categories, in turn, have the function of designating something and indicate how the thing is or does, or how it is. Moreover, they are captured by our thinking and our perception. In the proposition, the categories are the predicates attributed to a subject. The predication or attribution takes place through the linking verb “to be” and its basic form is “S is P”. And yet, “the doctrine of categories is primarily interested in establishing the general conditions that make it possible to understand the predication and the structure of the world that the predication intends to express” (ANGIONI, 2009, p. 32).

Predication has a basic structure: a compound formed by a subject term and a predicate term. This formation takes place through the copulative operators “é” and “não é”. The copulative operators indicate the value of truth or falsity present in the proposition and the correspondence with what exists united or separate in the world. However, Aristotle claims De Interpretationeare nothing in themselves as they depend on a composition which is only understandable if the items are connected.

The essential function of predication is to refer to real situations that occur in this world: “it intends to refer to facts given in the world, and thus, it presents itself as a pretense of finding or recording these facts” (ANGIONI, 2009 p. 17) . By applying the copulative operator “is” to a set of terms, there is the pretense of asserting that the state of affairs, expressed through language, objectively exists in the world. In this way, it is understood that the terms subject and predicate are united in reality because “it is” indicates composition – synthesis – between the terms of the sentence and, as it intends to refer to data in the world, what is presented in reality is united. By using the copulative operator “is not”, a separation is established – diaeresis – between the two terms of the sentence. Therefore, the terms separated in the sentence – subject and predicate – are also separated in reality.

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For the Stagirite, as noted earlier, predication is something beyond the combination of signs – a combination subject to the rules of syntax – as it is conceived as a claim to truth with regard to the things reported by the terms involved in the sentence. As truth is taken as objectivity, predication is taken as a claim to objectivity. Truth is established in predication when the things, of which the predication purports to speak, are presented as intended.

It can be noted that there is a concern, on the part of the Stagirite, regarding the relationship between discourse and truth. This means that the utterance must refer to reality and is called a “declarative utterance” – apophantikoi. They are called this way because they intend to declare or show a state of affairs, that is, they are statements defined essentially by the objective of verifying a given situation in the world. Its characteristic is the pretense of truth. Therefore, a statement is true when its proposal is presented in the world and:

Thus, the theory of predication involves a semantic theory, which seeks to delimit the rules and conditions by which the terms, combined in propositions, can objectively refer to verifiable situations in the world and, therefore, precisely, we can say that it presents itself, at the at the same time, as an ontology: the theory of predication is a theory about the correlations between, on the one hand, the objective structures through which things occur in the world and, on the other, the logical-linguistic structures through which we intend to verify them. them and refer to them ( ANGIONI, 2009, p. 20).

As exposed by Angioni (but not clearly by Stagirita), the Aristotelian theory of statements is composed by the logical and ontological doctrine, since the classification of predicates is dominated by logical criteria while the classification of categories is linked to semantic problems and these, in turn, involve ontological problems. The problem related to the classification of categories, as involving ontological problems, was also noted by Wolff, as can be seen through the following question: “How, more particularly, to solve the problem of attributive discourse – how to explain that a single thing can be other than what it is, a man, for example, to be white without ceasing to be what he is, a man? Here also by the theory of categories” (WOLFF, 1996, p. 185). According to Wolff, “being” is said in many senses, and these senses correspond to categories. Or better: “Being has many meanings. In fact, being means, on the one hand, the essence and something determined, on the other, quality or quantity and each of the other categories” (Arist., Met., Z 1, 1028 to 10-13).

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The composition between subject and predicate seeks objectivity, truth. The entity refers to the existence of states of affairs. The science that deals with the being as a being must determine the types of complex facts that exist in the world – which in the field of language result in different types of composition between subject and predicate. At this point, the link between ontology and logic becomes evident. Due to this articulation, the Stagirita did not stick only to the logical rules that strictly stated the coordination between the linguistic elements involved in the proposition. Aristotle also paid attention to the nature of the things to which the predicates refer, as it is this nature of things that determines the types of possible combinations, that is, separation or union between them. Angioni states that the world presents itself through the coexistence of two structures – a being by concomitance and a being in itself.

It is up to metaphysics to scrutinize the principles through which this coherent coexistence takes place: “The theory of predication – of which the “doctrine of categories” is only a part – is precisely a part of metaphysics thus understood” (ANGIONI, 2009, p. 36). Through Aristotelian thought and through the pertinent analysis made by Angioni, the relationship between ontology and logic is evident: both have the entity as one of their objects of investigation, however, the method to analyze this object is different since Metaphysics it is considered a science and logic is only an instrument for the sciences. But this does not mean that the problems and reflections of both do not intersect at some point in Aristotle’s theory.