Aristotle's logic enjoyed early success and maintained its dominant influence in the philosophical world from the Middle Ages until the 19th century (Groarke, n.d.). However, everything changed rapidly when modern logicians adopted a new, more mathematical form of logic, casting aside what they deemed an obsolete and clumsy method of syllogisms. Groarke (n.d.) notes that while Aristotle's detailed and rich explanation of logic differs from current approaches, it is not merely a historical curiosity. Instead, it provides an alternative for addressing logic and continues to offer critical perspectives on contemporary issues.
The Subject of Logic: Syllogisms
Aristotle focuses on a central idea: deduction (Smith, 2020). This is essentially reasoning where, by assuming certain things, something different inevitably results from those assumptions. His most well-known contribution is the theory of inference, commonly referred to as syllogistics. This theory deals with inferences with two premises, each being a categorical sentence, sharing a common term and leading to a categorical conclusion that includes only those two terms not shared by the premise (Smith, 2020). In short, according to Hintikka & Spade (2020), Aristotle confines himself to arguments with two premises and one conclusion, all being categorical propositions.
In this way, Aristotle designates the term shared by the premises as the "middle term," the term that is the predicate of the conclusion he calls the "major term," and the term that is the subject of the conclusion he calls the "minor term" (Smith, 2020). The middle term must appear as the subject or predicate in each premise, and this can happen 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 (Smith, 2020). In short, according to Hintikka & Spade (2020), the subject and predicate of the conclusion are present in each of the premises, along with a third term, the middle, which is in both premises but not in the conclusion.
From Words to Propositions
Aristotle believed that not all reasoning centered on words (Groarke, n.d.). However, words are a good starting point for studying his logic, which focuses on how arguments are evaluated, composed of statements that, in turn, are made up of words. In Aristotelian logic, the most basic statement is a proposition, a complete sentence that asserts something. Ideally, according to Groarke (n.d.), a proposition consists of at least three words: a subject (a word that names a substance), a predicate (a word that names a property), and a connecting verb, which logicians call the copula.
Paradigmatically, the subject would be considered a secondary substance, a natural division of primary substances, and the predicate would be a necessary or essential property (Groarke, n.d.). However, a too restrictive metaphysical idea about the terms of a proposition seems to limit intelligent discourse. For example, someone claims that "anger is not ethical." But anger is not a substance; it is a property of a substance, that is, an organism. Still, qualities can be attributed to anger, such as being unethical, difficult to control, and quite familiar. Of course, producing propositions is not enough; what is sought are true propositions. According to Groarke (n.d.), Aristotle believed that only propositions are true or false, at least concerning linguistic expression, as they involve combining words into complete propositions that intend to assert something about the world.
Aristotle suggests that a proposition must be either an affirmation or a negation; not both (Groarke, n.d.). Therefore, he does not recognize sentence compounds, such as conjunctions and disjunctions, as single affirmations (Smith, 2020). He points out that propositions can make claims about the necessary, the possible, or the impossible (Groarke, n.d.). An illustrative example is the hypothetical naval battle, where the necessary truth of the proposition does not guarantee the certainty of future events. For instance, the existence of a naval battle tomorrow does not determine the truth of any of the alternatives. So, the necessity attached to the proposition "there will or will not be a naval battle tomorrow" does not transfer to the assertion "there will be a naval battle tomorrow" or the assertion "there will not be a naval battle tomorrow." In summary, according to Groarke (n.d.), Aristotle emphasizes that personal beliefs about the future do not determine the truth of individual propositions.
Having established the proper logical form of a proposition, Aristotle proceeds to classify different types of propositions (Groarke, n.d.). He begins by differentiating between particular terms, which refer to individual things, and universal terms, which refer to a group of things. For example, the name "Socrates" is a particular term because it refers to a single human being, while the word "spiders" is a universal term, applying to all members of the group "spiders." Therefore, Aristotle realizes that universal terms can refer to both parts and entire groups. For example, it can be asserted that all spiders have eight legs or that only some have book lungs. According to Groarke (n.d.), in the first case, a property applies to the entire group referred to by the universal term; in the second case, the property applies only to a part of the group.
So, using Aristotelian language, a universal term can predicate a property universally or non-universally in relation to the group it refers to (Groarke, n.d.). This gives rise to four types of categorical propositions that establish relationships between two categories or types. Each categorical proposition has a quantity representing whether it is a universal or particular predication, as well as a quality that affirms or denies the specific predication. Consequently, contemporary logicians distinguish between four logical possibilities: universal affirmation, universal negation, particular affirmation, and particular negation. However, it is worth noting that these possibilities are not always mutually exclusive. Therefore, according to Groarke (n.d.), Aristotle explored how these propositions relate to each other.
The first states that contradictory propositions have opposite values; if one is true, the other is false, and vice versa (Groarke, n.d.). For example, if it is true that all birds lay eggs, then it is false that some birds do not. The second indicates that contrary propositions cannot both be true but can both be false. For example, the statements "all politicians tell lies" and "no politician tells lies" cannot both be true, but both can be false. The third implies that the truth of a universal proposition requires the truth of another particular proposition. For example, if all cheetahs are fast, then at least one must be fast; that is, "some cheetahs are fast" is true. The fourth points out that subcontrary propositions cannot both be false (Groarke, n.d.). For example, "some men have beards" and "some men do not have beards" are both true.
Finally, traditional logicians, inspired by Aristotle, identified immediate inferences to derive new propositions by rearranging terms (Groarke, n.d.). Firstly, subalternation is a clear example of immediate inference, where terms are exchanged to obtain a new affirmation. For example, once it is known that no circle is a triangle, it is known that no triangle is a circle. In obversion, the predicate term is denied while being replaced with the opposite term. For example, once it is known that some students are happy, it is known that some students are unhappy. Finally, in contraposition, both terms are denied, and their order is reversed. For example, according to Groarke (n.d.), once it is known that all voters are adults, it is known that all children cannot vote.
Definition
Aristotle left a significant mark on Western thought, especially with his theory of syllogism (Smith, 2020). It is interesting to note that, even though Aristotle did not use the term "logic," this concept emerged later in the time of Cicero, initially with the meaning of dialectic (López, 2017). Aristotle referred to this branch of knowledge as "analytic," conceiving it as an integral part of disciplined inquiry, not as an independent and self-sufficient subject (Groarke, n.d.; López, 2017). According to Navarro & Pardo (2009), logic, later recognized as the specific knowledge of the formal rules of correct reasoning, had its beginnings with the classification of Aristotle's writings on this subject under the name Órganon, establishing the consideration of logic as an independent science, essential for all other disciplines.
Logic in Aristotle's writings is not considered as a science, but rather as a set of observations about logos (Navarro & Pardo, 2009). In simple terms, logos refers to expressing something about something, understood not as the arbitrary action of a subject choosing words to make a judgment, but as the way things manifest in their truth and appear in their being. According to Navarro & Pardo (2009), this implies that for Aristotle, there is no separation between the organization of thought and the order of things, as logos refers jointly and inseparably to both spheres, whose separation could only be falsehood itself.
In short, Aristotle did not see logic as a way to prove that humans can have knowledge, thus dismissing excessive skepticism (Groarke, n.d.). His perspective was that logic should develop a coherent system to investigate, classify, and evaluate correct and incorrect forms of reasoning (Groarke, n.d.). Therefore, he did not see a difference between logic, the organization of thought, and ontology, the order of things, as he considered logic itself to be ontological (Navarro & Pardo, 2009). According to Hintikka & Spade (2020), this background helps understand why logical inferences are psychologically necessary for Aristotle.
Axioms
During the 18th, 19th, and early 20th centuries, scholars who saw themselves as followers of the Aristotelian and medieval tradition in logic often emphasized the laws of thought as the foundation of all logic (Groarke, n.d.). It would be unfair to say that these ideas solely originate from Aristotle or that he consciously presented a theory based only on these laws. Instead, Aristotle's theory assumes these principles and discusses or alludes to them in his work. According to Groarke (n.d.), traditional logicians considered these principles obvious, necessary for logical discourse to be possible.
The common list of logical laws includes three axioms (Groarke, n.d.). The law of identity means that things are identical to themselves. For example, something cannot be both white and not white simultaneously. The law of non-contradiction states that logically correct propositions cannot assert and deny the same thing (Groarke, n.d.). An example is that contradictory statements cannot be true simultaneously (Groarke, n.d.). Finally, the law of excluded middle holds that every proposition must be true or false, not both or neither. In line with Groarke (n.d.), since every proposition must be true or false, it does not necessarily follow that we can actually know whether a particular proposition is true or false.
Categories
According to Aristotle in his "Categories," the world is composed of substances, meaning individual things separated with different characteristics or properties (Groarke, n.d.). Aristotle identifies two types of primary substances, like a human or a trout, which are independent objects composed of matter and characterized by their form; and secondary substances, which are larger groups, species, or genera to which these individual organisms belong. For Aristotle, as per Groarke (n.d.), attributing correct properties to secondary substances indirectly involves attributing those properties to primary substances or individual things.
In the same line of thought, Aristotle lists ten different ways of describing something (Groarke, n.d.). These categories include substance, quantity, quality, relation, where, when, being in a position, owning, doing, or undergoing or being affected by something (Groarke, n.d.). Substance refers to the real and existing thing perceived through the senses (Montague, 2019), while the other categories are considered accidents that describe the substantive (Montague, 2019). According to Groarke (n.d.), in "Topics," he includes the same list but replaces substance with essence.
Fallacies
In a brief text titled "Sophistical Refutations," Aristotle introduces a theory on logical fallacies that has had a significant impact (Groarke, n.d.). While his approach is concise and somewhat obscure, there is some disagreement among scholars about the exact interpretation. Aristotle views fallacies as examples of deceptive reasoning; they are not merely errors but hidden mistakes. In other words, according to Groarke (n.d.), a fallacy is an incorrect reasoning strategy that gives the illusion of being solid or somehow conceals the underlying problem.
Aristotle categorizes fallacies into two main types: those that depend on language or verbal fallacies, and those that are independent of language or material fallacies (Groarke, n.d.). Language-dependent fallacies include: homonymy or verbal equivocation; ambiguity (amphiboly or grammatical equivocation); composition (confusing parts with a whole); division (confusing a whole with parts); accent or error due to mispronunciation; and figure of speech (ambiguity resulting from the form of an expression). Additionally, according to Groarke (n.d.), language-independent fallacies include: accident (overlooking exceptions); reverse accident (hasty generalization or inadequate qualification); irrelevant conclusion; affirmation of the consequent (assuming that an effect guarantees the presence of a possible cause); begging the question; false cause; and complex question (disguising two or more questions as one).
References
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Hintikka, J. (2020). History of Logic | Ancient, Medieval, Modern, & Contemporary Logic. Encyclopedia Britannica. Recuperado 14 June 2021, a partir de https://www.britannica.com/topic/history-of-logic
López, L. (2017). Dialéctica 101: Aristóteles. Luis Felip. Recuperado 31 May 2021, a partir de https://luisfelip.net/2017/11/28/dialectica-101-aristoteles/
Montague, B. (2019). The nature of Aristotle's logic. The Ecologist. Recuperado 3 June 2021, a partir de https://theecologist.org/2019/jul/18/nature-aristotles-logic
Navarro, J., & Pardo, J. (2009). Aristóteles. Lógica y ontología. Filosofia.net. Recuperado 3 June 2021, a partir de https://www.filosofia.net/materiales/sofiafilia/hf/soff_28.html
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