The Pervasiveness of Aristotle’s Logic

From the beginning, young men have been seeking to make a name for themselves. Caste, heritage, and ability were limitations on what an individual could obtain, but it has been consistent that most people strive for more than what they grew up with particularly with the lower classes. Coming from a place of privilege can lead to complacency because of blessing, yet this can be negated by proper parenting. There is a unique hurdle to overcome when one is in a field that already has a master at the top that has just revolutionized everything. Aristotle was raised in the Academy with Plato at the helm. Through the Socratic dialogues and Plato’s Forms, philosophy, politics, and religion were set upon a new path that these subjects were happy to go along with for seemingly ages to come. Aristotle was not content with the answers that he was given through this school of thought. He wanted a more concrete answer to the big questions of life. Instead of sitting and waiting for his teacher to help him, Aristotle developed his own system of thought and started to ask his own questions. Thankfully, he did not start from scratch. Rather he started to compile all the major theories that came before him and compared them to one another. This is helpful because instead of starting something new, Aristotle goes through what is right and wrong with all the other major systems. During the compiling stage, he worked to develop his system of logic. Having a clear system of logic is what vastly set him apart from all the other thinkers. His use of logic and the syllogism was his greatest contribution to academia. From there, he applied it to his physics and his metaphysics to build a system all its own, taking parts that fit and worked from those who had taught him. This can be seen in how his logic was different and the impact that it had upon his physics and metaphysics. 

Joining the Academy at 17 years old (Aristotle v), Aristotle was thrown into the reasoning of Socratic dialogues and inductive reasoning.  According to Merriam-Webster’s, induction is “inference of a generalized conclusion from particular instances”. This was used in order to clarify a situation by looking for examples through questions and answers. If one was trying to figure out if an apple was a fruit, one could compare it to an orange to see the similarities and differences between the two. This worked as long as it was known that an orange was a fruit. Because it was possible to question the validity of both fruits, real and true knowledge was shaky. Socrates and Plato would both look at the particular and compare them to the ideal Form. Aristotle was not satisfied in this. He wanted more concrete answers. 

This led him to go about things in the complete opposite, though complementary, direction. Instead of asking if an apple was a fruit and then questioning what made a fruit a fruit, Aristotle looked at all growing things, saw similarities between them, and then labeled them as fruit. He introduced what became known as deductive reasoning. To quote Merriam-Webster’s again, deduction is “inference in which the conclusion about particulars follows necessarily from general or universal premises.” Looking at the particulars and drawing conclusions from them is the basis of the deductive reasoning that became known as Aristotelian logic. 

The main tenant of Aristotelian logic is the use of the syllogism. The syllogism has two main components: two premises and a conclusion. “A premise then is a sentence affirming or denying one thing of another. This is either universal or particular or indefinite” (39). “All dogs are canines” would be an example of a universal, while “some dogs are German Shepherds” would be a particular. The conclusion that follows from these two premises is that “all German Shepherds are canines.” To give this syllogism in the correct format as Aristotle would appreciate, it would look like this:

“All M is P.

Some M is S.

All S is P.”

This is what has become known as standard categorical form. “P” is the major term, is in the first and major premise, and is at the end of the conclusion. “S” is the minor term, is in the second and minor premise, and is at the beginning of the conclusion. “M” is the middle term that connects the major and minor premise together. The conclusion is always in some form of “S is P” as the minor term is being assumed into the major term. As Aristotle put it, “I call that a perfect syllogism which needs nothing other than what has been stated to make plain what necessarily follows” (39). 

Aristotle did have some warnings and advice when it came to thinking through things using syllogisms. An important part of the job is that “Syllogism should be discussed before demonstration, because syllogism is the more general: the demonstration is a sort of syllogism, but not every syllogism is a demonstration” (40). What he meant by this is that syllogism were merely a scaffolding to hang truths. One had to check to make sure that the scaffolding was sound before hanging terms upon it. Otherwise, one could be setting up an invalid syllogism, leading to more misunderstanding or false thinking. Aristotle spent more time showing how to misuse syllogisms and the pitfalls of them than he did showing how to use them correctly. The reason for this is that while there are only 24 valid syllogisms, there are a total of 256 permutations of the forms and moods. For a logic student, it would be imperative to memorize the 24 valid forms, so that one could simply check the form and mood to see if the argument follows from the syllogism. 

Valid forms, moods, and syllogisms are all well and good, but they are all built upon premises. If our forms and mood are valid, but the premises that we put into our syllogism are false, we prove nothing. Syllogisms were a way to learn new things and to also check to see if what one was learning was true. They did it in a very particular way. Aristotle opens Posterior Analytics with “All instruction given or received by way of argument proceeds from pre-existent knowledge” (97). This means that one goes from what they know into what they do not know. One starts with a true premise, connects it to another true premise, to lead to a new discovery in the conclusion. Aristotle spends much of his time going from premise to premise, building these immense systems of syllogisms and logic. He proves one thing and then moves on to the next, always building his body of knowledge through his logic. Knowledge is built upon a keystone so to speak, and from that keystone, all other knowledge is stacked and set. This is a vastly different system of knowledge than his teacher, Plato, had. This is seen from Aristotle’s summary of Meno from Posterior Analytics, “If this distinction is not drawn, we are faced with the dilemma in the Meno: either a man will learn nothing or what he already knows; for we cannot accept the solution which some people offer” (97). Instead of saying that all of life is simply relearning of things from prior lives, Aristotle does say that we learn new things by building upon prior knowledge. Humans start off with sensory knowledge then should switch to knowledge derived logically through the use of syllogisms to make sure our knowledge is sound and valid. 

From his observations of the world, Aristotle took his prior knowledge and applied his logic to his physics. This is made obvious by the opening lines of Physics, “When the objects of an inquiry, in any department, have principles, conditions, or elements, it is through acquaintance with these that knowledge, that is to say scientific knowledge, is attained. For we do not think that we know a thing until we are acquainted with its primary conditions or first principles, and have carried our analysis as far as its simplest elements” (259). Through this work, he seeks to establish to major ideas of what “being” is by way of what motion is. This will naturally lead Aristotle to wrestle with his idea of the “Unmoved Mover” as he has to process the fact that something must have started the first movement. 

Physics is meant to be a study of nature, and Aristotle says that “Nature has been defined as a ‘principle of motion and change’” (278). This is at the beginning of Book III which starts his discourse on motion. He breaks motion into 3 separate things: “(1) what exists in a state of fulfilment only, (2) what exists as potential, (3) what exists as potential and also in fulfilment” (278). He is talking about motion in the past, in the future, and ongoing. He is not just talking about movement as we tend to think of movement as one can see by this quote: 

Now each of these belongs to all its subjects in either of two ways: namely (1) substance—the one is positive form, the other privation; [5] (2) in quality, white and black; (3) in quantity, complete and incomplete; (4) in respect of locomotion, upwards and downwards or light and heavy. Hence there are as many types of motion or change as there are meanings of the word ‘is’ (278). 

This is a very complete view of motion, even in today’s sense. In most respects, number 4 is the only one talked about when motion is referred to, but by including the other 3, he really does take into account the full spectrum of motion. 

From here, Aristotle gets into one of his stickiest situations: his struggles with infinity and how to make sense of it. 

The science of nature is concerned with spatial magnitudes and motion and time, and each of these at least is necessarily infinite or finite, even if some things dealt with by the science are not, e.g. a quality or a point—it is not necessary perhaps that such things should be put under either head. Hence it is incumbent on the person who specializes in physics [35] to discuss the infinite and to inquire whether there is such a thing or not, and, if there is, what it is. (280)

Time has to be factored into the equation of motion because that is how we measure and reference motion. It is change over time. Motion had to be quantified in some way, which means it had to be measured. Counting and arithmetic were not foreign to him, so doing these calculations were not hard or troubling. Seeing the sun, moon, and planets move about him, he could measure time in daily life to some accuracy. He could continue to add day upon day or split the days into however many hours or minutes. Both of these ideas of infinity worked for him. He put it this way: “everything that is infinite may be so in respect of addition or division or both” (282). He could grasp things going into the future forever, changing along the way. He could understand dividing things in half forever as well. These were known principles to him. The one notion that he could not get around with infinity is infinity by subtraction. Negative numbers did not exist to Aristotle yet. They would not come to Western Mathematics for several hundred years. 

Looking at the world around him, he saw that it was spinning and swirling around him. This is the one type of motion that he saw as being infinite. “Let us now proceed to maintain that it is possible that there should be an infinite motion that is single and continuous, and that this motion is rotatory motion” (348). This rotational movement would still be infinite by addition though as it does have to be started. This led Aristotle to say this statement:

We have argued that there always was motion and always will be motion throughout all time, and we have explained what is the first principle of this eternal motion: we have explained further which is the primary motion and which is the only motion that can be eternal: and we have pronounced the first movent to be unmoved.

This is in reference to his “unmoved Mover,” the one who started the first thing spinning. He gave no name to this being, but it does lead us to our discussion on his metaphysics. 

Aristotle starts off Metaphysics with a similar note as Physics, drawing from what one knows in order to figure out what they do not know. He goes a step farther when he gets into knowledge by experience and art, “And in general it is a sign of the man who knows and of the man who does not know, that the former can teach, and therefore we think art more truly knowledge than experience is; for artists can teach, and men of mere experience cannot” (499). He is contrasting art and experience, saying that an artist has an understanding about how and why he does what he does; while a man of experience merely knows how to do a task, not having the understanding of the why or how to pass along his knowledge to the next generation. This is to set up the scope of knowledge upon logic, in order to have the same keystone throughout his work. 

Book V in Metaphysics is perhaps the greatest difference between Socrates, Plato, and Aristotle. In Book V, he goes through and gives a clear, logical definitions for over 30 different terms that he would then use throughout the rest of his book. It is a division in his work that would make a rhetoric teacher proud. Socrates and Plato spent so much time arguing over what half of these terms mean that they barely got anything else done. Aristotle deals with what the main teachers of his time meant by these terms, he said what he understood about them, then he moved on to the subject at hand. While boring to read, it was definitely a breath of fresh air to be able to have something concrete to build the argument. 

From here, he moved on, trying to figure out the world around him beyond simply what he could see by observation. He spends more time in On Sense and Sensibility talking about the senses and observations that will shine light on this topic. While he does deal with substance, he does move beyond the physical into the spiritual. He tries to logically look at creation through his understanding of motion. “Therefore there is no other cause here unless there is something which caused the movement from potency into actuality. And all things which have no matter are without qualification essentially unities” (570). Potency here are things that could come into being. He understands that it does not matter what the thing is, it must have something to bring it into actuality. This follows logically from Aristotle’s world of cause and effect. There had to be something that set the first thing spinning. This paragraph helps to explain further, “Obviously, therefore, the substance or form is actuality. According to this argument, then, it is obvious that actuality is prior in substantial being to potency; and as we have said, one actuality always precedes another in time right back to the actuality of the eternal prime mover” (576). There are substances that have to be in place in order for something to go from potency to actuality. Because of this, he can negate the potency and just look at the actuality. The actuality retrogrades back to the beginning, bringing Aristotle to the prime mover. He then moves to disprove the Forms. “But those who say the Forms exist, in one respect are right, in giving the Forms separate existence, if they are substances; but in another respect they are not right, because they say the one over many is a Form” (564-565). By making the Forms a substance, he is making them secondary things to the created order. Substance had to come from somewhere, so the Forms were not first things. By doing this, he allowed his old teacher to still be mostly true, but under and in his own system. There had to be something that set things spinning first. He must spin back to the beginning in order to know logically how the present and future are to continue on. This is why Metaphysics led him back to the beginning of time. 

Aristotle was a man who observed the world thoroughly through his senses. He understood the limits of this as can be seen in Chapter 6 in On Sense and Sensibility. Through what he observed and learned from those who came before him, he was able to apply his logic in a way that could unite the knowledge of the world into one coherent system. He was able to make heads and tails of many of the tenants of the natural, physical, and spiritual world that confused most people. He had plenty of questions at the end of his life, but he hit on things that would be proved true, at least tangentially, in molecular physics, chemistry, and biology. He did this by consistently using simplistic logic. By using his syllogism, building upon a starting premise, he was able to structure the world in a logical way, taking into account the physical and spiritual aspects that he saw in the world. Looking at one more quote at the end of Metaphysics, book XI, chapter 7, one can see how he ties these things together himself: “Evidently, then, there are three kinds of theoretical sciences—physics, mathematics, theology. The class of theoretical sciences is the best, and of these themselves the last named is best; for it deals with the highest of existing things, and each science is called better or worse in virtue of its proper object” (592). He saw the importance of figuring out how the higher things worked and knew that they were the premises that the system had to be built upon. He seemed to be fine with not knowing all the answers, for he hoped that one would come along after him to figure it out. One could argue that is what the human race has been doing since to some degree or another: to fit all the pieces of the puzzle together. 

Works Cited

Aristotle. The Works of AristotleGreat Books of the Western World. Ed. Mortimer J. Adler and Philip W. Goetz. Trans. W. D. Ross. Second Edition. Vol. 7. Chicago: Robert P. Gwinn; Encyclopædia Britannica, Inc., 1990. Print. 

“Deduction (2a).” Merriam-Webster’s Collegiate Dictionary, 11th ed., Merriam-Webster, 2020, p. 324.

“Induction (2a).” Merriam-Webster’s Collegiate Dictionary, 11th ed., Merriam-Webster, 2020, p. 637.

Plato. The Dialogues of Plato; The Seventh LetterGreat Books of the Western World. Ed. Mortimer J. Adler and Philip W. Goetz. Trans. Benjamin Jowett and J. Harward. Second Edition. Vol. 6. Chicago: Robert P. Gwinn; Encyclopædia Britannica, Inc., 1990. Print.