Logic of Aristotle

Logic of Aristotle The greatest of Aristotle's influence, while it was felt in many other areas, was in logic. Aristotle was the acknowledged expert in logic in late antiquity, at the time when Plato remained the greatest metaphysical thinker, and he stayed in this role into the Middle Ages. Christian philosophers did not acknowledge him as the foremost authority in the subject of metaphysics until the thirteenth century. His dominance in logic persisted even after the Renaissance, although this superiority was mainly lost. All Catholic philosophers and many others stubbornly deny the findings of contemporary reasoning, clinging to a theory that is as unquestionably ancient as Ptolemaic astronomy, even in the modern era. It is challenging to honor Aristotle's legacy historically because of this. His influence today is so detrimental to rational thought that it is difficult to recall the enormous strides he made over all of his predecessors, including Plato, or how admirable his logical work would still seem if it had been a step toward continuous progress rather than (as it was) a dead end that was followed by more than two millennia of stagnation. It is not necessary to remind the reader that Aristotle's predecessors were not inspired orally; as a result, one may commend them for their accomplishments without feeling obligated to accept all of their beliefs. On the other hand, Aristotle remains a battlefield, particularly when it comes to logic, and cannot be approached just from a historical perspective. The syllogism concept is Aristotle's most significant contribution to logic. An argument that has three components—a main premise, a minor premise, and a conclusion—is called a syllogism. There are several types of syllogisms, and the scholastics have given names to each of them. The most well-known kind is referred to as "Barbara" and states that all men are mortal (Main Premise). A man is Socrates (Minor premiss). Socrates is mortal as a result (Conclusion). Or: Humans are all mortal. Greeks are guys all. Consequently, every Greek is mortal. Additional types include: No fish are rational, all sharks are fish, so no sharks are rational (Aristotle does not differentiate between these two forms; this is incorrect, as we shall show later). (This is referred to as "Celarent.") Since all men are rational beings, certain animals must also be rational. (This is known as "Darii.") Since some males are Greek and not all Greeks are Black, some men are not Black. These four comprise the "first figure" (this is termed "Ferio"). Aristotle adds a second and third figure, and the schoolmen add a fourth. It is demonstrated how several methods can reduce the three later numbers to the first. From a single premiss, certain conclusions can be drawn. Apart from such inferences as the above, Aristotle and his followers believed that all deductive inference, when strictly stated, is syllogistic. From "some men are mortal," we can infer that "some mortals are men." According to Aristotle, this can also be inferred from "all men are mortal." From "no gods are mortal," we can infer that "no mortals are gods," but from "some men are not Greeks," it does not follow that "some Greeks are not men." It should thus be able to avoid all fallacies by outlining all legitimate forms of syllogism and presenting each proposed argument in syllogistic form. This system was significant and commendable since it marked the beginning of formal logic. It is subject to three types of criticism, nevertheless, as it is seen as the conclusion rather than the beginning of formal logic: (1) Formal flaws in the system itself. (2) The syllogism is overestimated in comparison to other deductive reasoning techniques. (3) Exaggerating deductions as a means of support. There has to be something stated about each of these three. Formal flaws. Let's start with the two claims: "Socrates is a man" and "all Greeks are men." Aristotelian logic does not clearly distinguish between these two, so let's start there. Certain of Aristotle's syllogisms are invalid without the prevalent interpretation that the sentence "all Greeks are men" implies the existence of Greeks. For example, the statement "All Greeks are men, all Greeks are white, therefore some men are white" is true only in the case that there are Greeks. My conclusion would be incorrect even if my premises would be somewhat accurate if I were to state: "All golden mountains are mountains, all golden mountains are golden, therefore some mountains are golden." The first assertion, "there are Greeks," and the second, "if anything is a Greek, it is a man," must be separated if we are to be precise. The second statement is simply hypothetical and does not indicate that there are Greeks. With "Socrates" as its subject, the statement "all Greeks are men" is much more complex in form than the statement "Socrates is a man." On the other hand, "all Greeks are men" does not have "all Greeks" as its subject because "there are Greeks" and "if anything is a Greek, it is a man" do not mention "all Greeks." This purely formal error was the source of errors in metaphysics and theory of knowledge. The majority of us are content to rely on testimony in order to determine the truth of the proposition "Socrates is mortal," but for testimony to be considered reliable, it must trace back to a person who knew Socrates and witnessed his death. Let us examine the current state of our knowledge regarding these two propositions. We were reassured of Socrates' mortality by the one apparent fact—the dead corpse of Socrates—as well as the fact that he was known by this name. However, things are different when it comes to the statement "all men are mortal." It is really challenging to determine what such broad assertions are that we know. Sometimes they are only verbal: "Every Greek is a man" is well-known as only men are referred to as "Greeks." These kinds of broad assertions are easily found in dictionaries; they reveal nothing about the outside world other than the usage of words. However, the statement "all men are mortal" is not of this type; an immortal man cannot be rationally contradicted. Since there isn't a single well- documented instance of a man surviving for more than, say, 150 years, we accept the argument based on induction; yet, this just makes it plausible, not certain. As long as there are live males, it cannot be assured. Assuming that "all men" is the subject of "all men are mortal" in the same way that "Socrates" is the subject of "Socrates is mortal" led to philosophical errors because it allowed one to hold that "all men" in some sense denotes an entity of the same sort as that denoted by "Socrates," which in turn led Aristotle to assert that a species is a substance. He takes pains to modify this, but his adherents—Porphyry in particular—lacked prudence. Aristotle also makes the fallacy of believing that a predicate of a predicate can also be a predicate of the original subject. It is clear that "human" is a predicate of "Socrates" and that "Greek" is a predicate of "Socrates," but Aristotle believes that "human" is a predicate of "Greek," even though "human" is not a predicate of "Greek." This blurring of the distinction between names and predicates—or, in metaphysical language, between particulars and universals—has disastrous consequences for philosophy. As a result, there was some misconceptions, one of which was the idea that a class consisting of only one member is the same as that class. This prevented the development of a valid explanation of the number one and gave rise to countless flawed conceptions of unity in metaphysics. (2) The syllogism is overestimated. A syllogism is only one type of logical reasoning. Since mathematics is entirely deductive, syllogisms are rare in the field. Mathematical arguments may, of course, be rewritten in syllogistic style, but this would make them seem extremely unnatural and less persuasive. Consider arithmetic as an example. How much change do I get if I offer a $5 bill as payment for products costing $4.63? It would be ridiculous to present this straightforward total as a syllogism, as this would tend to hide the true character of the argument. Again, non-syllogistic conclusions exist within logic, such as the following: "A horse is an animal, therefore a horse's head is an animal's head." In actuality, valid syllogisms are only a subset of valid deductions; they do not logically supersede other types of deductions. The endeavor to elevate the syllogism above other reasoning methods in deduction confused philosophers about the essence of mathematical reasoning. Kant concluded that mathematics relies on extra-logical principles since he did not believe it to be syllogistic. Nevertheless, he believed these principles to be just as definite as those found in logic. Respect for Aristotle led him, like his predecessors, but in a different way. (3) Excessive deduction estimates. Compared to current philosophers, the Greeks often valued deduction as a source of knowledge. Compared to Plato, Aristotle was less flawed in this regard as he always acknowledged the value of induction and gave careful thought to the topic of how to determine the first premises that deduction must begin from. However, in his idea of knowing, he, like other Greeks, overemphasized deduction. We'll accept that Mr. Smith (say) is mortal, and we may obliquely argue that we know this because we are aware of the mortality of all people. We believe that Mr. Smith will pass away because, in reality, what we actually know is not that "all men are mortal," but rather that "all men born more than one hundred and fifty years ago are mortal, and so are almost all men born more than one hundred years ago." However, this is not a deduction; rather, it is an induction. While it produces merely a likelihood rather than a certainty and lacks the cogency of a deduction, it does provide fresh information. The few areas where conclusions outside of logic and pure mathematics are deductive, namely law and religion, are all inductive, not deductive, with the initial principles of each drawing from an indisputable source, i.e. the texts or the code of laws. In addition to The Prior Analytics, which addresses the syllogism, Aristotle wrote additional works that are very significant in the annals of philosophy. The brief study on The Categories is one of these. Porphyry, the Neoplatonist, penned a commentary on this work that had a significant impact on medieval philosophy. However, for the purposes of this discussion, let's disregard Porphyry and stick to Aristotle. I have to admit that I have never been able to comprehend exactly what is meant by the word "category," whether it comes from Aristotle, Kant, or Hegel. Personally, I don't think the word "category" has any value in philosophy as it doesn't convey any distinct concepts. Aristotle classified things into ten categories: affection, action, place, time, position, substance, amount, and quality. "Expressions which are in no way composite signify" is the sole definition provided for the term "category," and it is followed by the list above. This seems to imply that any word that has a meaning that is distinct from that of other words denotes a material, a number, etc. The list of 10 categories has not been developed based on any proposed principles. The main definition of "substance" is that which cannot be predicted from or found in a subject. When something is not a part of the subject but nevertheless needs the subject to exist, it is said to be "present in a subject." Two examples are provided: one is a piece of grammatical information that exists in the mind, and the other is a potential physical whiteness. In the first notion described above, a substance is a singular object, person, or animal. However, in a broader sense, a species or genus—such as "man" or "animal"—may be referred to as a material. This secondary sense appears indisputable and allowed for a lot of flawed metaphysics in the works of later authors. A issue which should be bothering every deductive theory is the main focus of The Posterior Analytics: How are initial premisses obtained? Since deduction must begin somewhere, it must be with an unproven hypothesis that can be learned by sources other than demonstration. Since Aristotle's thesis relies on the concept of essence, I won't go into depth about it here. He defines a definition as an assertion of something's fundamental characteristics. Up to the present era, the concept of essence has been a fundamental component of all philosophy that followed Aristotle. Though I think it's a fatally confused idea, we have to address it because of its historical significance. Socrates may be happy, sad, well, or ill at different times; the "essence" of a thing seems to have meant "those of its properties which it cannot change without losing its identity." They are not part of his nature, as he may alter these attributes without losing his identity as Socrates. However, it is said to be fundamental to Socrates' being a man, even though a Pythagorean, who believes in reincarnation, will not acknowledge this. Actually, the subject of "essence" has to do with how words are used. We refer to relatively diverse events that we see as expressions of a single "thing" or "person" under the same name on multiple occasions, but in reality, this is only a linguistic convenience. This means that the "essence" of Socrates is made up of such qualities that, without them, we shouldn't call him "Socrates." The issue is essentially linguistic: an object cannot have an essence; a word can. Similar to the idea of "essence," "substance" is only a language convenience that has been transferred to metaphysics. When explaining the universe, we find it easier to label certain events as occurring in the life of "Socrates" and others as occurring in the life of "Mr." Smith," which makes us consider "Socrates" or "Mr. Smith" as signifying anything that endures for a specific amount of years and is, in some sense, more "solid" and "real" than the things that happen to him. In contrast, disease necessitates that someone be unwell; if Socrates is ill, we believe that he is healthy at other times and that his existence is consequently independent of his illness. Socrates need not be sick, but for him to be taken seriously, something has to be happening to him. Therefore, he is not actually any more “solid” than the experiences that he has. When considered seriously, "substance" is an idea that will always have challenges. It is intended for a material to have properties and to be something separate from all of its properties. However, when stripping away the qualities and attempting to see the substance in its purest form, we discover that nothing remains. Stated otherwise, what makes one material different from another? Not a difference in attributes, as that would imply a numerical diversity between the substances in question, in accordance with the logic of substance. Thus, two substances must be just that—two—without having the ability to be distinguished from one another in any manner. So how will we ever discover that they are two? In actuality, "substance" is only an easy way to group occurrences together. Can you tell us anything about Mr. Smith? We see a pattern of colors when we look at him, and we hear a variety of sounds when we listen to him talk. We think he has thoughts and feelings just like the rest of us. However, what distinguishes Mr. Smith from all of these incidents? An fictitious hook, if you will, from which the events are meant to hang. Actually, they don't require a hook any more than the planet requires an elephant to sit on. In the equivalent instance of a geographical region, anybody can understand that the term "France" (for example) is only a linguistic convenience and that "France" itself does not exist outside of its many sections. The same is true for "Mr. Smith" is a collective term for several instances. Should we interpret it as anything more, it would signify something wholly unknown and so unnecessary for the articulation of what we do know. Simply put, the term "substance" refers to a philosophical error caused by transference to the world-structure of sentences that consist of a subject and a predicate. I come to the conclusion that all of the Aristotelian ideas that we have been discussing in this chapter are untrue, with the minor exception of the formal theory of the syllogism. Reading Aristotle or any of his students would be a waste of time for anyone hoping to master reasoning in the modern day. Nevertheless, Aristotle demonstrates remarkable aptitude in his logical writings, which would have benefited humanity had they been published at a period of intellectual innovation. Regretfully, they emerged at the very close of Greek thought's creative era, and as such, they gained credibility. It had taken two millennia for Aristotle to gain power, so it was extremely difficult to unseat him by the time logical primordiality returned. Almost all of the scientific, logical, and philosophical advancements made in the contemporary era have had to overcome resistance from Aristotle's adherents.