A History of Western Philosophy

Aristotelian logic

One of the most important elements of our lectures in searching for the roots of prejudice and inequality in western thinking will be the shape of traditional logic. We take logic for granted most of the time. No matter how unconsciously we do so, we all use it to structure things we say, and we all use to make sense of what other people say, and of the world in general. It underpins things that we are prepared to believe and things we are ready to reject. If someone contradicts themselves we are likely to say that they are being illogical and demand that they resolve the contradiction if they are to make sense. Even when we might get suspicious of logic, and prefer to follow emotions or feelings, we might still judge the justifications and the outcomes of our choices logically. 

But have you ever considered what makes logic logical?  

There is a clear answer to this, and it comes from Aristotle. It is what we will now explore in this lecture. But this is only the beginning of our critical thinking about logic. It will return in almost every lecture after this one, for reasons that will become clear in due course. But let’s put in a spoiler about some of the most important insights into the roots of prejudice and inequality. It might be the case that logic is so structured as to carry prejudice and inequality within it. It might be the case that prejudice and inequality are built into the very structure of logic. If so, then the three traditional first principles that come from logic, those of truth, nature and freedom, might also carry this structural prejudice and inequality within them. This sounds as challenging as perhaps it seems counter-intuitive. It just doesn’t seem to be right. How could truth be prejudiced, or how could freedom be unequal? Suspend your disbelief for a while if this seems incredible, or if it doesn’t seem ‘logical’.  We have some way to go yet to see how logic might be guilty as charged.  

Let us start with trying to define Aristotelian logic.[1]

In Aristotelian logic, the most basic statement is a proposition, a complete sentence that asserts something. A proposition is ideally composed of at least three words: a subject (a word naming a substance), a predicate (a word naming a property), and a connecting verb, what logicians call a copula (Latin, for “bond” or “connection”).  Consider the simple statement: “Socrates is wise.”  Socrates is the subject; the property of being wise is the predicate, and the verb “is” (the copula) links Socrates and wisdom together in a single affirmation.

In the Metaphysics, Aristotle provides his own definition of true and false: “to say of what is that it is, and of what is not that it is not, is true”; and “to say of what is that it is not, or of what is not that it is, is false.” (IV.7.1011b25, Ross.)  In other words, a true proposition corresponds to way things are.

The usual list of logical laws (or logical first principles) includes three axioms: the law of identity, the law of non-contradiction, and the law of excluded middle.

The law of identity could be summarized as the patently unremarkable but seemingly inescapable notion that things must be, of course, identical with themselves.  Expressed symbolically: “A is A,” where A is an individual, a species, or a genus.  Although Aristotle never explicitly enunciates this law, he does observe, in the Metaphysics, that “the fact that a thing is itself is [the only] answer to all such questions as why the man is man, or the musician musical.” (VII.17.1041a16-18, Ross.) 

Aristotle provides several formulations of the law of non-contradiction, the idea that logically correct propositions cannot affirm and deny the same thing:

“It is impossible for anyone to believe the same thing to be and not be.” [2]

“The same attribute cannot at the same time belong and not belong to the same subject in the same respect.”[3]

“The most indisputable of all beliefs is that contradictory statements are not at the same time true.”[4]

Symbolically, the law of non-contradiction is sometimes represented as “not (A and not A).”

The law of excluded middle can be summarized as the idea that every proposition must be either true or false, not both and not neither.  In Aristotle’s words, “It is necessary for the affirmation or the negation to be true or false.”[5]  Symbolically, we can represent the law of excluded middle as an exclusive disjunction: “A is true or A is false,” where only one alternative holds.  Because every proposition must be true or false, it does not follow, of course, that we can know if a particular proposition is true or false.[6]

At this point we reach an important moment for all of the lectures.

This logic can be characterized as a logic of mastery.

Mastery here means the masterful independence of a complete identity, one that it is uncompromised by any dependence upon anything outside itself for its own truth. Logic is based in the idea of this mastery. Why it is so based in mastery we will return to much later. The implications of the logic of mastery for how we live and how we think, and how we make some of our most important judgements will accompany us in most of our lectures. The implications of this mastery for prejudice and inequality will, I hope, become clear, showing how logic is at the root of prejudice and inequality. For now, we will see how this logic lends itself to establishing the three key notions of truth, nature and freedom. I am going to do this by way of a dialogue involving Socrates and a few people he is in conversation with. This is a version of Book 9 of Socrates On Trial (Bloomsbury, 2022).[7]

S: We will explore truth first. In the old city what was the most fundamental expression of necessity as truth?
X: Harmony was the old definition of truth―that which sang its own tune. 
S: And truth was the harmony of necessity and the necessity of harmony. The perfection of the circle. Could this truth be changeable?
X: No. If it changed, it ceased to be its own harmony.
S: Then it could not be different from itself.
X: No.   
S: And this defined something as a first principle.
X: Of course. A first principle was a truth in-itself, whole, complete, harmonious, necessary, and unchangeable. It could not be reduced to any simpler form or existence. 
S: And this necessity belonged to the logic of non-contradiction. 
X: Yes. The unchangeable is true because it is what it is and cannot be otherwise.
S: Which means that the logic of non-contradiction is also the logic of identity. Identity defines truth.
X: Which makes truth and this logic the one necessity. The term ‘in-itself’ captures this. Something true is something wholly, completely, and perfectly in-itself, with no potential left unrealized. 
S: Let us turn now to the ancient idea of nature.
X: Nature was the name given to the harmony and order of the cosmos, or of the stars and the planets. The term cosmos originally meant the beauty of order and arrangement. 
S: Was this the same harmony that defined truth as something in-itself?
X: It was. But some firmly believed that this natural harmony could also be found in the souls of human beings. People would have a life close to perfection if they could establish a natural tranquillity in their lives. They would see and understand the laws of nature, of life and death, of order and harmony, and would therefore be at peace with all that life could throw at them. This stoical life was the microcosm of the natural order and harmony of the macrocosm.
S: What was the first principle of nature in-itself?
X: The prime or unmoved mover. The law of nature was harmonious movement, and the prime mover was the self-necessity or in-itself of such movement. It was unmoved by anything else, and hence was its own cause, and was the principle by which everything else moved. 
S: Clearly. It was independent and suffered no negation and no risk to itself.
Y: Its perfection as a circle made it impossible for there to be a beginning of the cosmos. If it was caused to begin by something else, it would not be perfect. And if that cause also had a cause and so on to infinite regression, then there would never be a first cause at all, never a first principle of movement. So, they reasoned that because there is movement, there must be a first principle of nature, and because it cannot be made to begin either by itself or anything else then it must be eternal. 
X: An eternal yet still first cause.
Y: Yes. Moving yet unmoved. 
S: And still within the truth, the necessity, of the logic of non-contradiction. So far, then, we have explored truth and nature as shapes of logic and identity. But how did the ancients define freedom?
Y: They believed that the free man was the man of leisure. As with truth and nature, so the free man had to be his own first principle. He had to be his own harmony. 
X: So this meant that, like the prime mover, he could not have his freedom or his self-principle compromised by anything external to him? If so, he wasn’t dependent for this principle upon anyone else. He was self-sufficient. 
Y: Yes. He was the independent life that kept death at a safe distance. He was his own truth. And he was his own nature. This was his freedom. 
X: And he was also free of any dependence upon external objects and the work required to produce them. His freedom included freedom from any kind of physical work. The highest value was given to leisured thinking and the lowest value to any kind of manual work. The needs of the body were seen as inferior to the needs of the mind. The free man, having his slaves to provide for his material needs, enjoyed the freedom to think and speculate on the causes and first principles of things. This man of leisure was the scholar who spent his time in the contemplation of the deepest philosophical issues, much like you Socrates. 
Y: And this was considered to be a natural state of affairs?
X: Indeed. Some men were considered to be born to freedom while others had a natural disposition to slavery. And because this was considered to be their natural state, their truth, then it was seen as an injustice for the free master not to rule and the enslaved not to serve.
Y: And in the design of the perfect city it was these free masters, once they were sufficiently trained in philosophy, who were to be rulers of the city.
X: They were. Since they were the most perfect of men, and the city was to be the most perfect of cities, each did justice to the other. It was a natural and perfect state of affairs. 
S: Was a free man defined as independent?
X: Yes.
S: And being independent meant he was his own principle, he was an end in himself, having his own truth and nature within him?
X: Yes.
S: Then it would seem that freedom too is shaped by the logic of identity and non-contradiction. Freedom has its identity as an end in-itself to an end.
X: You have forgotten something here. The ancients believed that even above the first principles of truth, nature and freedom, there was a still higher form of perfection which each of them expressed, a supreme principle called the good?
S: What do you understand by this good?
X: The good was the necessity that made truth true, nature natural, and freedom free. It was supreme happiness. 
S: Why happiness?
X: Because the good is the perfection of necessity lived perfectly.
S: The perfect character?
X: Yes. When truth can be thought and lived in harmony with itself, this is the character of the supremely good, virtuous and happy human being. 

Let us see how Aristotle puts all this in his own words.

On truth, he says, 

When the objects of an inquiry, in any department, have principles, causes, or elements, it is through acquaintance with these that knowledge and understanding is attained. For we do not think that we know a thing until we are acquainted with its primary causes or first principles, and have carried our analysis as far as its elements. Plainly, therefore, in the science of nature too our first task will be to try to determine what relates to its principles … Thus we must advance from universals to particulars; … Knowledge is the object of our inquiry, and men do not think they know a thing till they have grasped the ‘why’ of it (which is to grasp its primary cause). So clearly we too must do this as regards both coming to be and passing away and every kind of natural change, in order that, knowing their principles, we may try to refer to these principles each of our problems. (Physics, 1.1 & 2.3).[8]

On nature he says,

there must be something that imparts motion not with something else but with itself, or else there will be an infinite series. If, then, anything is a mover while being itself moved, the series must stop somewhere and not be infinite. Thus, if the stick moves something in virtue of being moved by the hand, the hand moves the stick; and if something else moves with the hand the hand also is moved by something different from itself. So when motion by means of an instrument is at each stage caused by something different from the instrument, this must always be preceded by something else which imparts motion with itself. Therefore, if this is moving and there is nothing else that moves it, it must move itself. So this reasoning also shows that, when a thing is moved, if it is not moved immediately by something that moves itself, the series brings us at some time or other to a mover of this kind. (Physics, 8. 5).[9]

And on freedom he says, 

any human being that by nature belongs not to himself but to another is by nature a slave· and a human being belongs to another whenever, in spite of being a man, he is a piece of property, i.e. a tool having a separate existence and meant for action … That one should command and another obey is necessary and expedient. Indeed some things are so divided right from birth, some to rule, some to be ruled … This is also true as between man and the other animals; for tame animals are by nature better than wild, and it better for them all to be ruled by men because it secures their safety.  Again, as between male and female the former is by nature superior and ruler, the latter inferior and subject. (Politics, I.v.)[10]

Notice how we have moved from some dry old logic to the first principles of truth, nature, and freedom. It is small step now to take the logic of mastery, through its first principles, to current issues regarding, for example, human’s relations to animals, and man’s relation to woman. In our next lecture we go straight to class, gender and race as modern expressions of prejudice and inequality. In all of the lectures to follow, in some way, we will be testing the hypothesis that the roots of prejudice and inequality lie in the conceptions of truth, nature and freedom, and in the logic that grounds them and carries them. 


References

[1] The following is a summary of work by Louis F. Groarke, and can be found at https://iep.utm.edu/aris-log/

[2] Metaphysics, IV.3.1005b23-24, Ross.

[3] Ibid., IV.3.1005b19-20.

[4] Ibid., IV.6.1011b13-14.

[5] De Interpretatione, 9.18a28-29, Ackrill

[6] Note too that here Aristotle elaborates a logic that is designed to describe what exists in the world.  We may well wonder then, how many different ways can we describe something?  In his Categories (4.1b25-2a4), Aristotle enumerates ten different ways of describing something.  These categories (Greek=kategoria, deriving from the verb to indicate, signify) include (1) substance, (2) quantity, (3) quality, (4) relation, (5) where, (6) when, (7) being-in-a-position, (8) possessing, (9) doing or (10) undergoing something or being affected by something.  In the Topics (I.9, 103b20-25), he includes the same list, replacing “substance” (ousia) with “essence” (ti esti).  We can, along with Aristotle, give an example of each kind of description: (1) to designate something as a “horse” or a “man” is to identify it as a substance or to attribute an essence to it; (2) to say that the wall is four feet long is to describe it in terms of quantity; (3) to say that the roof  is “white” is to ascribe a quality to it; (4) to say that your weight is “double” mine is to describe a relation between the two; (5) to say something happened in the market-place is to explain where; (6) to say it happened last year is to explain when; (7) to say an old man is sitting is to describe his position; (8) to say the girl has shoes on is to describe what she possesses; (9) to say the head chef is cutting a carrot with a knife is to describe what he is doing; and finally, (10) to say wood is being burned in the fireplace is to describe what it means for the wood to undergo burning or to be affected by fire. From: https://iep.utm.edu/aris-log/

[7] See https://www.bloomsbury.com/uk/socrates-on-trial-9781350053717/

and  https://socratesontrial.org/

[8] Aristotle, (1984) The Complete Works of Aristotle, vol. 1, edited by Jonathan Barnes, Princeton, Princeton University Press. 

[9] Aristotle, 1984.

[10] Aristotle, (1981) The Politics, translated by T.A Sinclair, London, Penguin.

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