When we were investigating essence, we saw that our intellect holds universals, not individuals, meaning that, from the “standpoint of intelligibility” (ItP), being is essence. A second standpoint, however is that of being as things actually are. This is substance:

Substance is a thing or nature whose property is to exist by itself, or in virtue of itself (per se) and not in another thing. (ItP)

The “thing or nature” in this definition is the “subject of action itself (that which primarily exists) and to its nature considered precisely as a nature or essence” (ItP). The “subject of action” is also referred to as a suppositum, or person, “which is nothing but the substantial nature completed by a particular modality (subsistence or personality) which terminates it, as a point terminates a line, (without adding anything to it in its order of nature) and renders it absolutely incommunicable … But when we distinguish and contrast the nature (not terminated) and the subject of action, the term substance remains attached to the nature (not terminated) and is then contrasted with the subject of action taken as such.” (ItP) I would invite you to think about this hard definition before we proceed.

What it meant by existing “by itself” or “in itself” (per se) is that the being can exist on its own (ItP). For instance, a particular individual — Aristotle — can exist on his own and has no need to exist in another thing. On the other hand, a feeling, such as sorrow, cannot exist on its own — it has to exist in a human being, such as Aristotle.

Things that cannot exist on their own are called accidents:

An accident is a nature or essence whose property is to exist in something else. (ItP)

Notes on Substance

The substance of an object, so long as that object exists, is as such immutable. (ItP)

Since substance refers to the thing in itself, or the fundamental nature of the thing, its substance cannot change unless the thing changes, in which case it stops existing.

In the language of philosophy substance is intelligible in itself (per se) and sensible only accidentally (per accidens). (ItP)

This is because substance is “invisible, imperceptible by the senses. For the senses do not apprehend being as such” (ItP). Our senses perceive only the accidents of things, however, this does not mean that the accidents are unrelated to the substance. We can determine the substance of things in this manner. (ItP)

Parmenides of Elea had famously denied change using the two fundamental axioms of philosophy: Identity (being is what it is) and Non-Contradiction (being is not what it is not). Change involves taking being, which is identical to itself, and converting it into something which is not longer identical to itself, thus violating the two axioms.

Aristotle was faced with this problem: change seems to occur, but does not seem possible due to these two axioms. He solved this by distinguishing between act and potentiality in material things, which he defines as composites of act and potentiality. Act refers to being, and potentiality refers to the power of being something.

A ball is in potency to be here or there; a piece of metal, once modeled into a spoon, is in act as a spoon. Maritain explains act below:

We are not concerned, at least not primarily and chiefly, with an act in the ordinary sense of the word, with doing or action. Action or operation is indeed an act, being in act, but it is what is termed the secondary act (actus operationis). Action presupposes being. And the primary act is the act of being (actus existentiae), moreover of being a particular thing (actus essentiae). … Clay, once modelled, is a statue in act, water at 32° Fahrenheit is ice in act, and the moment anything effectively is one thing or another and especially the moment anything exists. (ItP)

Potentiality, as Maritain states, is actually between being and non-being; since potentiality is something indeterminate, it is actually not intelligible, nor can it exist on its own without act. It is prima materia, or first matter, which is potentiality itself.

With these concepts clear, we can now explain change.

The product of change arises neither out of being in act nor out of nothing, but from potential being. In other words, the action of the efficient cause draws, educes, from the potentiality of the subject the determination, the form, which was wanting in the starting-point of the change and characterises its goal, as when the action of fire educes from the potentiality of water (the water is cold, but can be hot) the determination (a specific intensity of heat) which characterises it as the result of the change. The change is the transition from potentiality to act, or, more accurately, according to a definition to which we must return later, it is the act of a thing in potentiality taken precisely in respect of its potentiality: actus exsistentis in potentia prout in potentia. (ItP)

Notes on Act and Potency

Nothing is educed from potentiality to act except by some being in act. It is plainly impossible that that which is in potentiality, that which is capable of having a determination or a perfection but does not have it, should give to itself what it lacks, so far as it does not possess it, that is to say, so far as it is in potentiality. (ItP)

This is the same thing as saying that potentiality, which does not possess being per se, cannot cause itself to come into being. This is the equivalent of saying that a rock cannot move itself even though it has the potential of being moved. It must be moved by some being in act (e.g your hand).

Act is prior to potentiality. A consequence of the preceding axiom. (ItP)

This is the equivalent of saying that, for something to be changed, or even have the potential to be changed, it needs to exist. Being is prior to change (ItP).

Potentiality is essentially relative to act and is for the sake of the act (potentia dicitur ad actum). It is indeed only in relation to the act that the potentiality can be conceived (only in relation to being white that we can conceive the power of being white) (ItP)

This is self-explanatory.

The essence of a thing is what that thing is necessarily and primarily as the first principle of its intelligibility. (ItP)

Previously, we saw that the object of the intellect was being, meaning that essence refers to being of something insofar as it is intelligible. The essence of man is “the rational animal”. Note that strictly speaking, only universals are intelligible — this fact becomes more apparent when we study Arisotelian-Thomistic psychology. Suffice it to say, that, when you think of a particular man, say Socrates, what is first intelligible is that he possesses the essence of man, and later that he possesses the accidents of being Greek, being a philosopher, etc. The primary thing which Socrates is is man. While characteristics like being Greek and being a philosopher are inseparable from the individuality of Socrates, they are not primary characteristics, and they can be removed without affecting his being as man.

As Maritain says:

We must therefore conclude that these characteristics have their ground in what the object is necessarily and primarily, but as an individual, or, in what we may term the individual nature of the thing. (By individual nature we mean incommunicable to any other object, or if you prefer, wholly circumscribed.) (ItP)

Maritain says that essences are neither individual nor universal. They are individual, since they really exist in every individual we perceive them in. They are universal, since they exist universally in the mind. The way that they are so is a more complex topic for a later time.

This is a brief summary of essence, also known as quiddity, or nature.

Philosophy, as was stated before, is distinguished from all other sciences by its focus on the highest causes. It is therefore the queen of all natural sciences. As a result of its speculative nature, it is easier to attain certain conclusions in philosophy than in other sciences, where the attainment of knowledge is restricted by the quality and quantity of data, as well as the randomness and complexity of the natural world. But first, how do we know whether our philosophical conclusions are true, or whether we can attain philosophical knowledge at all? That is the subject of the field of Metaphysics which is called Epistemology — or Criticism.

Truth

What is a true or truthful word? A word which expresses, as it really is, the speaker’s thought; a word in conformity in that thought. What, then, is a true thought? A though which represents, as it really is, the thing to which it refers; a though in conformity with that thing. We therefore conclude that truth in the mind consists in its conformity with the thing. (ItP)

There are some, the sceptics, who, seeing the multitude of philosophical errors committed by men, doubt that truth can be attained at all. They either doubt our reasoning capacity or the power of our senses to observe reality. Both propositions are self-contradictory, for if our reason is defunct, we cannot reason whether our reason is defunct or not; and, if our senses were unreliable, there would be no basis to assert that proposition, since all data for reasoning comes from the senses.

Despite this, it is not good to overestimate the capabilities of the intellect. This would be the error that Aristotle and St Thomas Aquinas would oppose, and which Maritain opposes, called rationalism. This error, typical of enlightenment thinkers, as well as today’s New Atheists, supposes that truth is easy to acquire, and therefore man’s mind ought to be freed to discover truth. Maritain says that they tend in three distinct directions: subjectivism, which where every man considers himself his own criterion of truth, “not the object to be known, a position which is the dissolution of knowledge.” (ItP); individualism, which is similar to subjectivism, and “calls upon each philosopher to work out a philosophy entirely on his own, and create an original and novel view of the universe (Weltanschauung).” (ItP); and finally naturalism, “which claims to attain to a perfect wisdom by the unassisted powers of nature, and rejects all divine teaching.” (ItP)

It is interesting to focus on all the types of rationalism, for today they are often taken together as the striking marks of a scientific atheist (or, in some strains of thought, “scientific pantheist”) worldview. First, naturalism is taken as a starting point. According to these “scientists”, God does not exist, or at least His existence is unknowable, and they adhere to a view of the physical universe that ranges from a determinist clock (the New Atheists, most leftists) to a newer view Heraclitus’s universe full of raging spirits (e.g the “Bronze Age Pervert”, aka Dr. Costin Alameriu from Yale University — this view is more right-winged that the other). The left and the right wing elements of this Atheism also differ in that the left tends to prefer subjectivism, which is to say that all individuals’ truths are equally valid, and, as a corollary, society needs to be organized to allow people to act out their truths; the right, exemplified in the person of Alameriu, borrows from the manly and aristocratic Ancient Greek society in saying that many people are not suited for the finding of truth, and that only a select few can pursue it. This individualism, where those suited create their own Weltschauung, pursuing the ultimate truth, pursuing “Will” in the Nietzchean sense. For Alameriu, the Will almost seems to be the ultimate reality, which, as the Physicists held, animates everything. Man, and Nature, are just manifestations of this Will, which Alameriu believes is manifest in the sublime complexity of the natural world, the beauty of its creatures, and the mystery which it presents.

Both these philosophies, however, have a similar eschatology, deeply tied to a political vision of the world. The former, the left-winged one, regards Nature as the ultimate obstacle to be conquered by technology. This is a natural consequence of subjectivism, since, no matter the insanities that some may grow in their heads, Nature denies them with a hard no. While the moral law of God is written in man’s heart, it can be ignored, seemingly safely (at least for a little while), due to God’s immeasurable Mercy. However, the laws of Nature are hard limits. Good luck trying to get around the fact that like charges attract, or that water forms hydrogen bonds with other water molecules, or, more crucially, that biological differences exist between human individuals and groups. However, technology can conquer nature, and, if the 20th and 21st centuries have shown anything at all, is that technology can seemingly conquer biology, our own human nature. The hope, then, is that all differences, that all natural hierarchy (they denied the supernatural one) be conquered, so that everyone can live happily ever after in a future best expressed as “fully automated luxury space communism”.

The rationalism of Alameriu adores Nature as a manifestation of the “Will” which, according to him, is present in everything. For him the “Will’s” action in nature must be helped along by a program of breeding in order to improve the quality of the human race — eugenics. The “Will’s” only law is vitality and Nature — in effect its only law is itself, since it is identified with Nature. However, as Alameriu himself admits, both Nature and human civilizations go through peaks and troughs; Ancient Greece and the Renaissance being peaks, and contemporary “civilization”, which he declares to be dedicated to the multiplication of inferior biological types (not untrue), being a deep trough. If Nature, and, by extension, the “Will” allows for such deep troughs, why is it assumed that the “Will” desires the greatest biological type? If the “Will” is the “Will to Power” why is it assumed, as Alameriu does, that history, despite rises and falls, tends to produce greater and greater biological types in order to actuate this “Will” rather than produce these great biological types to make them suffer, as a way of holding power over itself.

One possibility is that the “Will” is erratic and violent, like, to paraphrase him, the personality of the Greek man who always desired to rule, completely and pettily, over the polity. Then there is no guarantee that the “Will’s” will will not become some sort of immolation, as described above. Another option is that the “Will” is not one, but that there are two or more “Will’s” fighting for power over matter in a violent way. This is absurd, because it is unclear how matter would be transferred from the control of one “Will” to another, it is unclear what exactly the goals of the “Wills” would be, and, given how matter, as observed by Heraclitus, changes from one form to another, moves easily, and is in a state of overall flux, it is impossible to see how the “Wills”, which are identified with matter, could attack each other in such a state of interconnection.

The Object of the Intellect

A second question in Epistemology is with regards to the object of the intellect — when the intellect perceives truth, or an idea, what exactly is it perceiving?

To answer this question it is sufficient to ask oneself whether there does not exist an object which is always present to the mind when the intellect functions? Such an object does exist. Whatever I know by my intellect, there is always some being or mode of being present to my mind. There is, however, nothing else except being which is always present in this way. If, for example, I think of a quality, a magnitude, or a substance, in all these cases alike I think of some being or mode of being; but there is nothing except being which is common to these three objects of thought, and therefore present in all three alike. We therefore conclude that being is the formal object of intellect, that is to say, the object which it apprehends primarily and in itself (per se primo) and in function of which it apprehends everything else. (ItP)

This is a tremendous result — the being is the object which the intellect perceives. The argument is that everything that is present to the mind is something which possesses being — it either exists, or is one of being’s potential states (which is to say it could exist). If we suppose that we think of an idea that possesses no being, we are really thinking about nothing at all. Hence, being is the object of intellect.

Maritain discusses objections to this theory: how do we think about ideas like blindness, or of a hole? These ideas are defined by an absence of being. However, they are interpreted as absences of being within another structure of being. Blindness lacks the being of the capacity to see; holes lack being compared to the surrounding space.

Next, we will look at a brief overview of Aristotelian metaphysics.

The greatest of the pre-Socratics, Parmenides of Elea invented the field of metaphysics and started the field of philosophy proper. He elevated philosophy from the mere physical to the speculative, and correctly perceived the true nature of being.

In his poem On Nature, Parmenides notes that there is being (that which is) and nonbeing (that which is not) in the world. Only being is worthwhile to investigate, since “Thou canst not know what is not — that is impossible — nor utter it”.

Parmenides lays down the Law of Non-Contradiction and uses it to refute Heraclitus’ arguments that a thing can exist and not exist. Furthermore, he uses it to prove that being cannot come from nonbeing, since that would imply things that are not becoming things that are. In addition, it is unimaginable what “source could it [nonbeing] have drawn an increase”, and “what need could have made it arise later rather than sooner”.

Being is “complete, immovable, and without end. Nor was it ever, nor will it be; for now it is, all at once, a continuous one.” Being is complete, which is to say it contains “in itself every perfection” (ItP). This is correct, since everything outside of being does not exist, and imperfections lack being, thus being is the perfections. Being is immovable, which is to say it lacks motion, change. This is true, since being cannot become nonbeing (this would violate the Law of Non-Contradiction), and being cannot become more being — it already is being. Being and non-being are contradictories. Being and nonbeing are similar to the statements “being on the moon or not being on the moon” (CdF). You are either on the moon or you are not, and there is no intermediate point where you are both on and off the moon. Being is without end, which is to say it is eternal — it never has changed, not has it come out of nonbeing, nor will it come into nonbeing.

“Nor is it divisible, since it is all alike, and there is no more of it in one place than in another, to hinder it from holding together, nor less of it, but everything is full of what is. Wherefore it is wholly continuous; for what is, is in contact with what is.” Parmenides has stated that being is identical to itself (Law of Identity), and therefore there is no being that is more being than other being — everything is being. There is only nonbeing available to keep it apart, but since nonbeing does not exist, it does not matter. Therefore being cannot be divided.

Consequences of Being

And as he contemplated pure being, he perceived that this being is completely one, absolute, immutable, eternal, without becoming, incorruptible, indivisible, whole and entire in its unity, in everything equal to itself, infinite and contain in itself every perfection. But while he thus discovered the attributes of him who is, he refused to admit that any other being could exist, and rejected as a scandal to the reason the being mingled with non-entity, because produced from nothingness, of every creature. (ItP)

Using his conclusions on the nature of being, Parmenides argued that (a) change cannot occur and (b) that the world was an illusion. Since something is identical with itself, if it ceases to be itself by change, it creates something new ex nihilo, which is against both the laws of Identity and Non-Contradiction. Parmenides’ student, Zeno of Elea, expanded on this idea with his famous paradoxes, such as that of the arrow. Zeno posited that for an instantaneous amount of time, the arrow was not actually moving, but staying still1. However, since the whole period of time is composed of these instantaneous moments, motion is impossible.

As Maritain states above, Parmenides denied that sensible reality existed, because it did not possess the attributes of being. Things in reality are neither one (they often have multiplicity); are not immutable (they seem to change); and are definitely not perfect. Thus Parmenides denied the existence of everything other than pure being.

It would not be until Aristotle that these quagmires raised by Parmenides would be resolved; that the subject that endures change would be found; and that reality would be explained as the mingling of being and non-being.

The Greek philosophers were the first to pursue philosophy, per se, for its own sake. Before, philosophy was confused with religion, as in the Hindu doctrines or in Buddhism, but now philosophy was freely pursued as a science, separate from religion.

The Physicists

The first Greek philosophers were called the Physicists, because their philosophies aimed to understand the behaviour of the world. Thus, these philosophers were focused on matter, which is to say, the sensible object of philosophy. Change was the phenomenon that most fascinated them:

Since the most universal and most important phenomenon of nature is change, especially the change by which one body becomes another (e.g. bread becomes flesh, wood fire), they concluded that the original matter of which all things are fashioned must be identical in all, the common subject of all corporeal changes. But since they were still unable to conceive any impalpable or invisible principle, they thought they had discovered this matter in some one of the elements perceived by the senses. (ItP)

Maritain states that these philosophers recognized the reality of change, as well as the reality that all matter was in some way alike, since all things can be transformed into all other things. Therefore, there must be some commonality between all types of matter. These philosophers perceived this commonality not as a metaphysical principle, but as sameness in matter.

Thus Thales of Miletus famously said that everything was made of water. Other philosophers followed, with Anaximenes saying that everything was made of air, Heraclitus fire, and Anaximander the “boundless, (by which he understood the indeterminate …), a fusion of all the contraries”. (ItP)

One problem arises with this theory: If, as Thales understood it, everything is derived from “the primordial waters” (ItP), why would the primordial waters change at all? Ditto for all the other philosophies. This is because, as Maritain states, whatever these elements were, they were always understood to be a vital, fecund force, thus causing change. This is the hylozoist philosophy because “it ascribed life … to matter”. (ItP)

This “materialistic monism which teaches the existence of a one [sic] single substance of a material nature” inevitably leads to pantheism, which is to say the identification of God with the universe, where in Aristotelian-Thomistic philosophy, God and the universe are distinct. It also leads to “evolutionism, which attempts to explain everything by an historic process of unfolding, development, or evolution of something pre-existent.” (ItP) Does this sound familiar?

The basics of Darwinian evolution were already being taught in the 6th Century before Christ, initially by Anaximander, but later by Empedocles, who Maritain says is an improvment in speculation compared to the others.

Empedocles:

explained the origin of living beings by the separate production of the individual organs and members, e.g. the head, eyes, arms, which were subsequently joined by chance in every possible combination, of which only those have survived which were fitted to live (cf. the Darwinian principle of the survival of the fittest) . (ItP)

As we shall see, the evolutionary account is more complex than that.

Heraclitus

Heraclitus was the greatest of the physicists because he alone articulated the problem of change through the errors he made in his heroic, but self-contradictory, philosophy. Heraclitus said that change was the only reality, because “change has no abiding and permanent subject identical with itself”. (ItP) Heraclitus famously said that you cannot step into the same river twice, because the subject was always changing. That “the very moment we touch an object, it has already ceased to be what it was before.” (ItP) This is called the doctrine of flux.

Heraclitus also held the doctrine of the unity of opposites. This is because, in his doctrine of change, he denied that a thing can be identical with itself, because that thing is always changing (the thing is both identical and not identical to itself). He therefore denied the Law of Identity. This means that opposites are the same since an attribute can both exist and not exist in a species at the exact same time.

Democritus

Democritus formalized the evolutionist doctrines of the previous physicists into his atomic theory. As Maritain says, in order to find something unchanging in Heraclitus’ flux, he used his imagination and imagined that being itself was divided into atoms, which interacted with each other in order to produce all phenomena. These atoms would be arranged in different ways in order to produce different materials. They would differ “only in shape, order and position.” (ItP) This philosophy is called atomism, but Maritain uses the term “mechanical” (ItP), since it is more precise.

In this fashion the Parthenon could be “explained” as the result of throwing stones one on another during an indefinite term of years (ItP)

Anaxagoras

Anaxagoras is interesting, because he determined, contra all the other physicists, that the material cause, which is to say the material composition of an object, is insufficient to explain it. (ItP)

We must also discover the agent that produces them (the efficient … cause) and the end for which the agent acts (the final cause). Is it, as Plato was to ask later, a sufficient explanation of the fact that Socrates is sitting in prison to say that he has bone, joints, and muscles arranged iin a particular fashion? (ItP)

In addition, for recognizing “a separate Intelligence … to which the ordering of the universe is due, he alone, as Aristotle remarks ‘kept sober’ when all the other philosophers of his period, drunk with the wine of sensible appearances, ‘spoke at random’1” (ItP)

History of Philosophy

Logic

History of Philosophy: An Introduction

The Divisions of Logic

Logic: Apprehension and Terms

Logic: Judgment and Propositions

Logic: The Predicables

Reasoning, the Laws of Logic

The Structure of a Syllogism

Jacques Maritain says that initially religion and philosophy were confused — the former intends to give man truths that are higher than himself, which he cannot attain by reason alone, but the latter is based truly on reason. However, in the Indian, Persian, and Chinese schools, philosophy often came bundled with a religion. It was only the Greeks who recognized that philosophy was a separate science from religion.

Some of the problems that these philosophers grappled with are:

The Problem of Being: What is the nature of being? Why do things exist?

The Problem of Change: Why and how do things change from one form to another?

The Problem of Evil: Why does evil exist?

All these are perennial problems, which all philosophies, in all times have to answer. These are primarily metaphysical problems, which is to say that they deal with the deepest questions of being and reality.

But why are these problems? Let us analyze each question.

1. Being: Our senses tell us that things exist. But why do things exist rather than not exist? This is in, different senses, both a religious and philosophical question, which is why Hinduism and the Persian Manicheanism have different creation myths in order to explain this problem. In addition, the precise nature of being is not really known. What does it mean for something to exist? What is the nature of “being” itself, without any characteristics attached to it? This is the most profound question in all of philosophy.

2. Change: Our sense tell us that things change from one form to another. Water boils, condenses, and freezes. Rivers flow. But what are things exactly made of, and what are the laws governing the change of phenomena? This may seem to be completely covered by the natural sciences, but the natural sciences only give us the laws governing physical phenomena, not the nature of the phenomenon itself. In Greece, this would give us the physicist Heraclitus, who claimed that nothing was permanent and that one could not step in the same river twice, and the heroic Parmenides of Elea, who grasped the nature of being and bravely denied change itself.

3. Evil: Finally, there is the problem of evil. This is self-explanatory. Why is there evil in the world? Why do people do bad things, and why do unfortunate events befall both good and bad people alike? This is primarily a religious question, but it influenced the development of philosophy through Manicheanism and Plato’s theory of sin. In addition, philosophy is a useful tool to more precisely understand the truths of religion, particularly in such tricky problems like this.

For this series, the plan is to give an overview of philosophy, from Hinduism to the Major Socratics, Plato and Aristotle.

A Syllogism is valid when its conclusion follows from its premises. The syllogism: “All men are mortal, Socrates is a man, therefore Socrates is mortal” is valid because the conclusion follows from its premises. However, the following syllogism is valid but has an untrue conclusion:

1. All cats are math geniuses

2. Jimmy is a cat

3. Therefore, Jimmy is a math genius

The conclusion follows from the premises, making it valid, but it is untrue since one of its premises is false.

On the other hand, a syllogism can come to the correct conclusion, but can be completely invalid!

1. All cats are carnivores

2. Jimmy is a cat

3. Therefore, Jimmy is tw has five claws on each paw

It may be that Jimmy has five claws on each of his paws, but the conclusion ultimately does not follow from the premises — it is a non sequitur.

If all the premises of a syllogism are true, and the syllogism is correctly reasoned, we say that the syllogism is sound.

But how do we reason through a syllogism correctly?

Deductive and Inductive Reasoning

Deductive Reasoning is when we start with a general principle that we know to be true and use that to find some premise that follows from it. In the famous Socrates example, our principle is that “all men are mortal”, and then we apply it to the case of Socrates. By its very nature of moving from a principle to something that follows from this principle, the conclusions of deductive syllogisms are likely to have a smaller extension than the principle (SL). Deductive reasoning is certain, and not based on probabilities.

Inductive Reasoning is when one takes several data points and uses that to determine a general principle. A famous example that both Jolivet and Kreeft use is as follows:

1. All heat is tw expands Copper, Bronze, and Steel

2. All Copper, Bronze, and Steel are metals

3. Therefore, all heat is tw expands metals

The nature of induction is to go from the particular extension to the universal. Note that induction is probabilistic, since, unless the entire universe is known, a metal may be found that shrinks when exposed to heat. A funny example is, in Latin, an expression arose to the effect that a black swan did not exist. It was perfectly reasonable to assume so, as all the swans found in Europe had not been black. However, more than 1500 years later, Dutch explorers found a black swan in Western Australia. (Wikipedia, Black Swan Event) This is all to say that inductive reasoning is probabilistic and will be dealt separately. For now, we will focus on deduction.

Parts of the Syllogism

A proposition contains three propositions and three distinct terms: the major term (T), the minor term (t), and the middle term (M). (CdF)

The major term is the term with the greatest extension, the minor term is the term with the smallest extension, and the middle term is between both in extension (CdF). In a syllogism, the middle term connects the major and minor terms, allowing what is true about the middle term in relation to the major term to apply to the minor term, which is contained within it. This should sound familiar to the dictum de omni. The dictum de nullo also applies to the syllogism, since if the minor term is contained within the middle term, and something is negated about the middle term, we can say that that same thing is negated about the minor term

We can label the terms in the following syllogism:

M T

1. All men are mortal

t M

2. Socrates is a man

t T

3. Socrates is mortal

We can see here that the middle term should never be in the conclusion of the proposition (CdF). This is because the proposition at the end is supposed to be relating the minor term to major term.

Rules of the Syllogism

In order to determine the validity of a syllogism, Aristotle developed six rules.

1. “A syllogism must have three and only three terms.” (SL)

It is obvious why a syllogism should have three terms. One of the ways that this rule is violated is through the use of ambiguous terms.

For instance:

All dogs are twi able to bark

Some constellations are dogs

Therefore, some constellations can bark (CdF)

Superficially, it may seem that there are three terms present in the syllogism, but there are four, since the term “dogs” is used ambiguously. In the first proposition, “dogs” means the animal, but in the second, “dogs” means a representation of the animal.

2. “A syllogism must have three and only three propositions.” (SL)

This rule flows from the essential structure of the syllogism. Any argument that violates this rule is not a syllogism at all. (SL)

There are other, valid forms of argumentation that have more or less propositions, but we have not studied them yet.

3. “The middle term must be distributed at least one. The violation of this rule is called The Fallacy of the Middle Term.” (SL)

If you recall, if the middle term is not “distributed” (if it is not used in its whole extension — we need the knowledge of its whole extension for the syllogism to work), a relationship is not established between the two.

Kreeft gives a good example:

[T] [M]

All Communists insist on the abolition of private property

[t] [M]

This candidate insists on the abolition of private property

[t] [T]

Therefore this candidate must be a Communist. (SL)

The syllogism is invalid since it is possible that the candidate could not be a communist but be of some other political persuasion (anarchist, esoteric monk, etc) and believe in the abolition of private property. (SL)

Since the middle term is never distributed over the major and minor terms, they become like islands and therefore have no connection to each other, so that the dictum de omni cannot be applied.

4. “No term that is undistributed in the premise may be distributed in the conclusion. The violation of this rule is called The Fallacy of Illicit Minor or The Fallacy of Illicit Major, depending on whether it is the minor term or the major term that contains the fallacy.”

This makes sense, because if we do not have the knowledge of the whole extension of a term, it does not make sense to make judgments about the whole extension of the term.

Kreeft gives an example:

Compassion is a virtue.

Justice is not compassion.

Therefore justice is not a virtue. (SL)

This is plainly wrong, because justice may not be identical to compassion but still may be a virtue. More strictly, in the first proposition, “virtue” is taken in only part of its extension— compassion is one of the virtues. The conclusion, however, is a universal negative proposition, meaning that both terms are taken in universal extension. But “virtue” was only taken in part of its extension previously, so the syllogism falls apart.

5. “No syllogism can have two negative premises. The fallacy here is called simply the fallacy of Two Negative Premises.” (SL)

When both the major and minor terms are related negatively to the middle term, we do not know how they are related to each other. Remember, it is not necessarily true that “the enemy of my enemy is my friend” (SL)

In this case, the enemy of your enemy could also be your enemy. Kreeft gives two excellent examples, each with the same logical form, one reaching a false conclusion and the other reaching a true one:

Odd numbers are not even numbers. Birds are not fish.

Three is not an even number. Humans are not fish.

Therefore three is not an odd number. Therefore humans are not birds. (SL)

6. “If one premise is negative, the conclusion must be negative; and if the conclusion is negative, one premise must be negative.” (SL)

Corollary 1: “No syllogism may have two particular premises. … Any syllogism that violates this rule will also violate Rule 3 or 4.” (SL)

This rule makes sense if you think about what the structure of a syllogism with two particular premises could look like:

Some S is A

Some A is P

Therefore, some S is P

This is invalid because “some” means that S may not be included in P’s extension. Kreeft gives an example:

Some jewels are green.

And some green things are alive.

Therefore some jewels are alive. (SL)

This also applies to syllogisms that contain only negative particular propositions.

Corollary 2: “If a syllogism has a particular premise, it must have a particular conclusion. … The ‘weakness’ of particularity in the premise must be reflected in the conclusion. The conclusion always follows the weaker premise: particular or negative.” (SL)

Kreeft gives an interesting example:

All dogs are animals.

Some dogs are poodles.

Therefore all poodles are animals. (SL)

While the conclusion may accidentally be true, the logical form is invalid, since the category “poodles”, if we know nothing about what a poodle is, may include things that are not dogs.

Mood and Figure of a Syllogism

The mood of a syllogism is “the quality and quantity of its three propositions” (SL) For instance, AEE represents a syllogism with a universal affirmative major premise, a universal negative minor premise, and a universal negative conclusion. When written in this manner, the major premise is always first, then the minor premise, then the conclusion, though in an actual syllogism the order of the premises does not matter.

The figure of a syllogism is the placement of the middle term. There are four possibilities: the middle term can be

(1) the subject of the major premise and the predicate of the minor premise (= the “first figure”)

(2) the predicate of both premises (= the “second figure”)

(3) the subject of both premises (= the “third figure”)

(4) the predicate of the major premise and the subject of the minor premise (= the “fourth figure”)

Medieval logicians identified nineteen valid moods of a syllogism (CdF) and organized them based on figure. They invented the “Barbara Celarent” mnemonic in order to memorize all of them. Each of the vowels represents a proposition in a mood, and each line is a figure:

[Fig. 1] Barbara, Celarant Darii, Ferio (AAA, EAE, AII, EIO)

[ Fig. 2] Camestres, Cesare, Baroko, Festino (AEE, EAE, AOO, EIO)

[Fig. 3] Darapti, Disamis, Datisi, Felapton, Bokardo, Ferison (AAI, IAI AII, EAO, OAO, EIO)

[Fig. 4] Bramantip, Camenes, Dimaris, Fesapo, Fresison (AAI, AEE, IAI, EAO, EIO) (SL)

Now you have all of the basic tools to start analyzing arguments! In order to grow your logic skills, it is useful (and interesting) to logically analyze the arguments in philosophical works. Some recommendations are Plato’s Gorgias and Boethius’ Consolation of Philosophy.

Reasoning is “the operation by which the spirit, from two or more known relations, concludes another relation which is derived logically from them.” (CdF) Reasoning is one aspect of rationality, which fundamentally distinguishes man from other animals.

Kreeft explains that the definition of rational includes:

wisdom, intuition, understanding of the nature or essence of a thing (the “first act of the mind”), self-knowledge, moral conscience (awareness of good and evil), and the appreciation of beauty, as well as reasoning and rational calculation (the “third act of the mind”) (SL)

Reasoning also includes judgment (“the second act of the mind”).

The verbal expression of reasoning is an argument, of which one of the forms is the syllogism. (CdF) The following is a famous example:

1. All men are mortal

2. Socrates is a man

3. Therefore, Socrates is mortal

The syllogism works because of the laws of logic, worked on by many Pre-Socratics, such as Parmenides of Elea, but ultimately perfected by Aristotle.

The Laws of Logic

Kreeft distinguishes between the laws of logic and physical laws, saying that, while it may be conceivable for the behaviour of the force of gravity to be slightly or very much different, it is not possible to conceive of the laws of logic being different, they are the result of the immutable nature of God. He says that while physical laws may conceivably be violated by God (e.g Jesus walked on water), logical laws may not be violated — God cannot make the statement all squares have 5 sides true:

—If, of course, God exists. It is not clear what reality these laws are dependent on if there is no God; but in any case they are eternal, unchangeable, necessary truths. If God exists, these laws are descriptions of the nature of God. (SL)

As we later shall see, Aristotle and St. Thomas prove the existence of God. In any case, the laws of logic are necessary truths, true in every world, while the physical laws are contingent truths, which can conceivably be overrided. (SL)

The first law of logic is the Law of Identity, which is formulated by Kreeft to be “a thing is what it is” (SL). While it may seem obvious, this law was first discovered by Parmenides of Elea, and he used it to deny change (in philosophical terms, change is referred to as “motion”). If you recall, the argument went as follows:

If a thing is what it is, then motion is not possible since if it changes, it becomes what it is not. But this violates the Law of Identity since if a thing is what it is, it cannot become what it is not. Thus motion is not possible.

Parmenides was handily refuted by Aristotle, but the refutation will be covered later.

The corollary of the Law of Identity is the Law of Non-Contradiction: “a thing is not what it isn’t; x is not non-x”. (SL)

There is the Law of the Excluded Middle: “a thing is either x or not x. A predicate must be either affirmed or denied of a subject; there is no third possibility. A proposition is either true or false, there is no third possibility.” (SL)

Additionally, there are three more laws which are more explicitly applied in a syllogism.

There is the dictum de omni (law about all): “Whatever is universally true of a subject must be true of everything contained in that subject”. (SL) This means that when I say that all men are mortal, since Socrates is contained within the subject man, he must be mortal too. (SL)

There is the dictum de nullo (law about none): “Whatever is universally false of a subject must be false of everything contained in that subject”. (SL) If I say that all men are not pure spirits, and that Socrates is a man, it follows that Socrates is not a pure spirit.

There is the third principle that “two things identical with one and the same third things are identical with each other”. (SL) Kreeft explains:

For the “third thing” is the “middle term,” the common term with which the other two terms are compared. In the classic example above, “Socrates” and “mortal” are both compared with a common third term, or “middle term,” “men.” …

The negative corollary of principle (3) is that if there are two things, one which is identical with a third thing and the other of which is not, the those two things are not identical with each other. (SL)

All these laws seem self-evident because they are. It is modern logic and philosophy which denies them and places itself into completely escapable conundrums. In the next article, we are going to look at the syllogism proper, as well as the different forms which it can take.

There are five ways the predicate of a proposition can be related to its subject: “A predicate may be a genus, specific difference, species, property or accident of its subject. These are called the five ‘predicables’”. (SL) Some of these predicables we already know, but it is useful to review what they are, and the commonalities between them: “The five predicables are a classification of predicates based on the standard of how close the predicate comes to stating the essence of the subject”. (SL)

They are:

1. Species: The species “states the whole essence of the subject” (SL). It is the the essential definition spoken of in “Logic: Apprehension and Terms”. In the proposition “Man is a rational animal”, “rational animal” is the species. A species is composed of a genus and specific difference.

2. Specific Difference: This is what makes the species different from all others in its genus. “Rational” is the specific difference of man from all other animals.

3. Genus: The genus “states the generic or common aspect of the essence of the subject.” (SL) For man, the genus would be “animal”. Jolivet defines it as the idea “immediately superior in terms of extension”. (CdF)

4. Property: A property is an aspect that is not the definition of the subject, but follows from its essence. A property of man that follows from his rationality is that he can use language.

5. Accident: An accident is an aspect of a subject that does not follow from its essence, and, if changed, would not affect the essence of the subject. An example of this is having or not having a ring finger. If I removed your ring finger you would still be human1.

Jolivet continues: “Judgment necessarily encloses, then, three elements: a subject, which is the object of which something is affirmed or denied; an attribute or predicate [predicate is the most common term], which is what is affirmed or denied of the object [e.g immortality is denied of man]; [and] an affirmation or a negation.” (CdF)

Definition of a Proposition

Like the term is the verbal expression of an idea, the proposition is “the verbal expression of a judgment. It is composed, like judgment, of two terms, subject and predicate, and one verb called a copula… because it unites or separates the two terms.” (CdF) Jolivet goes on to explain that the copula is always the verb “to be”, taken only in the relative sense, which is to say does not presume that the subject exists. The only time when a judgment affirms or denies the existence of an object is in the types of propositions like “bread is that which exists”. Note that the predicate contains “that which” (abbreviated to “tw”). This is because the structure of the proposition used in philosophy — S (subject) is/are/is not/are not P (predicate) — does not tolerate a proposition like “bread exists”. This in turn is due to the structure of syllogisms and the relations between propositions, since it is easier to define laws when all the propositions are in a standardized form.

Kreeft defines when to use tw and “that which is” (twi) in one’s propositions. The goal is to convert the predicate to a noun. If the predicate is a verb, we use tw. If it is a adjective, we use twi. (SL)

In addition, it is worthwhile to discuss the differences between modern and Aristotelian views on propositions. According to Kreeft:

Modern logic texts look at it [propositions] in terms of extension, and of class inclusion. This is why they call simple propositions “categorical” propositions: because they relate two “categories” to each other. … in modern logic, any things in the world can simply be classified at will into mental boxes, and then those boxes are compared as to population (extension, not comprehension). Thus in modern logic “all men are mortal” means “the set of beings that we classify as men is included in the larger set of beings that we classify as mortals.” … in Aristotelian logic a proposition does more than that. It deals also with the real natures of things, our knowledge of these natures, and the expression of that knowledge and those natures in the meanings (comprehension) of terms. Thus “all men are mortal” means that all beings that have the essence of humanity have the property of mortality as part of that essence, or as a consequence of that essence. (SL)

Again, we see how Aristotelian logic aims to discover the real natures of things, whereas modern logic aims to manipulate things by placing them into arbitrary categories.

Types of Judgments and Propositions

Jolivet classifies propositions from four points of view: from the point of view of the form and matter; from the point of view of the quantity and the quality; from the point of view of the combinations of quality and quantity; and from the point of view of the relationships between the extension of universal propositions. (CdF)

Form and Matter

a) From the point of view of form. We can distinguish affirmative and negative judgments.

b) From the point of view of matter. We can distinguish analytic and synthetic propositions.

Analytical propositions are judgments in which the attribute [predicate] is identical to the subject (like in the case of the definition: “man is a rational animal”), essential to the subject (“man is rational”), a property1 of the subject (“circles are round”).

Synthetic propositions are judgments whose attribute [predicate] does not express anything essential or which is a property of the subject: “This man is old”, “The weather is clear”.2 (CdF)

Quantity and Quality

Quantity refers to whether the proposition is universal — covers all cases of the subject — or particular — covers only some cases of the subject. The quality of the proposition refers to whether the copula denies or affirms the predicate.

Combinations of Quantity and Quality

There are therefore four types of propositions:

(A) Universal Affirmative: All S is P

(I) Particular Affirmative: Some S is P

(E) Universal Negative: No S is P

(O) Particular Negative: Some S is not P

The letters beside the propositions denote them. According to Kreeft, they are derived from the vowels in the latin words affirmo (to affirm) and nego (to deny). (SL)

Relationships Between the Universal Propositions

a) In the affirmative (A), the subject is taken in its entire extension, but the predicate is taken only on one part of its extension: “Man is mortal” means that man is one of the mortals, which is to say one part of the mortal beings.

b) In the negative (E), the subject and the attribute [predicate] are both taken in their whole extensions: “No man is a pure spirit” means that man is not any of the pure spirits. (CdF)

Relations Between Propositions

Jolivet defines opposition as “the relation between two propositions, which, having the same subject and the same predicate, have one quality or quantity that is different, or, at the same time, a quality and a quantity that are different.” (CdF) The concept of opposition is how you get the famous square of opposition shown above, where the relationship between each type of proposition is clearly delineated.

Contradictory Propositions

Contradictory propositions differ “in both quantity and quality”. (CdF) There are two pair of contradictory propositions: A and O, and E and I. Each pair cannot both be “true and false. If one is true the other is necessarily false”(CdF), and vice versa.

Contrary Propositions

Contrary propositions differ in only quality and refer to the two universal propositions: A and E. Two contraries “cannot be true at the same time … but both can be false at the same time.” (CdF)

Subcontrary Propositions

Subcontrary propositions differ only in quality and refer to the two particular propositions: I and O. Two subcontraries cannot be false at the same time, but both can be true at the same time.

Subaltern Propositions

Subaltern propositions differ only in quantity and refer to two pairs of propositions: A and I, and E and O. If the universal proposition in the pair is true, that means that the particular proposition is also true. But if the particular proposition is false, that means that the universal proposition is also false.

Conversion of Propositions

Conversion of propositions means changing one type of proposition to another. “Let us take the following proposition: ‘No circle is a square.’ It is possible to express the same truth by transposing the terms and making the subject a predicate and the predicate a subject: ‘No square is a circle’.” (CdF) Conversion is important since it allows us to express propositions in ways where their meaning may be more apparent or useful.

Conversions of Propositions

Jolivet lays out a general rule of conversion of propositions:

The proposition that is the result of the conversion should not affirm (or deny) more that the initial proposition. It follows that the quantity of the proposition either does not change (simple conversion) or, on the contrary, its quantity does change (accidental conversion). (CdF)

What he states here is that, since you cannot get more information out of a single statement than what is stated, the ways to convert propositions are either to maintain or reduce their quantity.

Converting A Propositions

A universal affirmative proposition is converted into a particular affirmative proposition:

Like in the proposition: “All men are mortal”, man is universal, and mortal is particular. [see “The Relationships between Universal Propositions” above] We have, therefore, that “Some mortals are men”. (CdF)

Jolivet states that conversions of A propositions are not reciprocal (except in the below case). (CdF) You cannot go from “Some mortals are men” to “All men are mortal”, since you do not have enough information to determine whether there are any men that are immortal.

There is another type of conversion, that of definitions, which is the only time that A propositions can be converted simply and reciprocally, which is to say that they can be converted without changing the universal quantity of the propositions. Jolivet gives an example: “‘Man is the rational animal’, ‘the rational animal is man’”. (CdF)

Converting E Propositions

A universal negative can be converted simply and reciprocally, without changing its quantity. Jolivet states: “‘No man is a pure spirit’, ‘no pure spirit is a man’.” (CdF) Note that since the extension of both the subject and predicate are universal, it is possible to convert this proposition reciprocally.

Converting I Propositions

A particular affirmative is converted simply and reciprocally. (CdF) “Some men are carpenters” is converted to “Some carpenters are men”.

Converting O Propositions

Jolivet explains the complex conversion of the O proposition:

[The O proposition] cannot be converted ordinarily. In the proposition “Some men are not doctors”, it is make the subject man an attribute [a predicate], because it would then have a universal extension … “Some doctors are not men”. (CdF)

What he is saying here is that, in a particular negative proposition, the predicate has a universal extension and the subject has a particular extension. Thus, you cannot switch the predicate and subject around since the subject does not have a sufficiently large extension to be a predicate.

Contraposition is the only way to convert O propositions properly. Kreeft explains:

Beginning with “Some S is not P,” we obvert to “Some S is non-P,” then convert to “Some non-P is S,” then obvert to “Some non-P is not non-S”. (SL)

Obversion is Kreeft’s term for negating the copula and the predicate, which is based on “the principle that two negatives make a positive and cancel each other out.” (SL)3

To convert the above proposition: “Some men are not doctors” we can follow the steps laid out by Kreeft:

1. Obvert: “Some men are not doctors” becomes “Some men are non-doctors”.

2. Convert: “Some men are non-doctors” becomes “Some non-doctors are men”.

3. Obvert: “Some non-doctors are men” becomes “Some non-doctors are not non-men”

If you think about the last proposition, it becomes clear that it is saying the same thing as the initial proposition.

Apprehension is the act of understanding an idea. For a child, this may be learning what a cat or a unicorn is, and for an adult it may be learning what a double integral is. This act of the mind leads to an idea, a concept of the thing that one apprehends. One of the main differences of Aristotelian philosophy is that it argues that these concepts actually correspond to the forms of things, how things actually are. An idea may represented by a term, which is merely a verbal representation of an idea. It is conceivable that the word cat could have come to mean the concept of a dog and vice versa.

Jolivet adds that “terms can … include multiple words (for example, the good God, certain men, a brilliant action), that do not however form a single logical idea”. (CdF) What he is trying to say is that when we say that a man is good and a food is good, good is meant in two different ways; in the first, it means that a man is virtuous, but in the second it means that the food is delicious. “Good” is still one term but is used ambiguously, as we will later explain.

An idea can viewed from the point of view of comprehension and extension. Comprehension refers to what an idea actually means. For instance, a triangle is comprehended by the definition “a closed, 2-dimensional shape with 3 straight sides”. A triangle drawn in a moving car may have curved, irregular sides, but, viewed from the point of comprehension, that does not mean that it is not a triangle, it just means that there are defects in the construction (the “matter”) of the triangle and it just does not live up too well to the definition. Extension refers to all the instances that an idea corresponds to. In the case of the triangle, this could refer to all the instances of triangles in the world. Kreeft says that this is the way that most people today conceive of ideas, which can lead to some absurd conclusions.

For instance, the fact that there are badly drawn triangles does not mean that we need a new definition in order to encompass those badly drawn triangles; there is a material defect which makes those triangles not correspond as well to the form of triangle. Similarly, simply because some people are born with ambiguous genitalia mean that they form a new sex category or that the “old” categories of male and female are incorrect — it just means that there is a material defect (chromosomal abnormality, exposure to chemicals, etc) that stops them from actuating the form (male or female) that they were supposed to be.

Jolivet points out that “comprehension of an idea is in an inverse relationship with its extension”. (CdF) What this means is that a simple concept, such as “animal”, has a massive extension, but a small comprehension (e.g the concept is not very complex). But a more complex concept, such as “rational animal”, has narrowed the extension to humans, but broadened its comprehension.

Additionally, Jolivet introduces the traditional Aristotelian notions of genus and species. Genus he describes as the “superior idea in regards to extension”, and species as the “inferior [in extension] in regards to the former”. (CdF) Simply put, this means that the genus of an idea will always have a greater extension than the species. For instance, the genus of man is “animal” and his species is “man”. Animal will always have greater extension than man, and for that reason it is the genus. Jolivet further explains: “In principle, an idea that contains itself other general ideas (animal in relation to man, birds, fish, etc) is called genus, and species all ideas that only contain anything except individuals”. (CdF)

Classification of Ideas and Terms

Jolivet divides ideas into three categories in order to explain the difference between them. Kreeft adds several more. I picked the most useful of Kreeft’s classes and placed them at the end, since, strictly speaking, they are not classifications of ideas or terms, but instead a result of the (often bad) uses of terms.

1. “From the point of view of the perfection of the idea”

Jolivet distinguishes between adequate/inadequate, clear/unclear, and exact/vague aspects of an idea:

An idea is adequate when it represents in spirit all the elements of the object. It is inadequate in the opposite case.

An idea is clear when you can recognize the object from all others; and unclear in the opposite case.

Kreeft explains this very well: “The term ‘quasar’ is clear to those who know modern astronomy but not to those who do not”. (SL)

Back to Jolivet:

An idea is distinct or confused [Jolivet’s term for exact and vague, respectively] when it allows us to know or not to know the elements of which it is composed. A clear idea can be confused: A gardiner has a clear, but not distinct, idea … of the flowers which he cultivates. On the other hand, a distinct idea is necessarily clear.

Jolivet juxtaposes the gardiner to the botanist, who knows all the parts of the flower and therefore has an exact idea of what the plant is. The gardiner’s idea of the flower is clear — he can distinguish it from others — but he has not the expertise of finding out the exact parts of the plant, such as the functions and morphology of its organs, etc.

2. “From the point of view of the idea’s comprehension and extension”

With regards to comprehension, an idea is either “simple or complex, based on whether it comprehends one or many elements. The idea of being (that which is) is simple; the idea of man (rational animal) is complex.” (CdF)

There are three types of terms from the point of view of extension: singular, particular, and universal. (CdF)

A singular idea refers to one individual. Plato, that book, this pen.

A particular idea is “applied indeterminately to only one part of a species or to a determined class. Some ducks.” (CdF) In the term “some ducks”, it is applied indeterminately, since it is unknown how one is distinguishing the ducks. In the term “green ducks”, it is clear what class of ducks one is referring to.

A universal idea “includes all individuals of a genus or a given species: [all] men, [all] circles”. (CdF) Jolivet points out that the singular case is a special case of the universal idea, since “it is limited to a single individual, it exhausts its extension”. (CdF)

3. “From the point of view of the idea’s relationships with other ideas”

Traditionally, there exists the distinction between contradictories and contrary ideas. Contradictories are when one idea excludes another. (Cdf) For instance, “being and non-being; being on the moon and not being on the moon”. (CdF) Contraries are when an intermediate point can be defined between two ideas: “black or white; avaricious and prodigal; being in Bilbao or being in Pamplona”. (CdF)

The reason why being on the moon and not being on the moon are contradictories whereas being in Bilbao or being in Pamplona are contraries lies in the definition of the idea. One is either on the moon or not on the moon — there is no intermediate state of superposition where one is both on the moon and not on the moon. Location-wise, even if you are between earth and the moon, you are not on the moon, you are in space. In contrast, whereas one is either on the moon or not on the moon, one can be in other places than Bilbao or Pamplona: one can be in Madrid, or Kansas City, which are intermediates to the ideas of being in Bilbao or Pamplona.

Ambiguity

Kreeft defines ambiguity as “‘having more than one meaning’. Strictly speaking no term is ambiguous unless it is used ambiguously.” (SL) For instance, I can say that a man is good and a meal is good, but, whereas the former means virtuous and capable, the latter means tasty and nutritious. “But a good man is not tasty and nourishing, except to a cannibal”. (SL) This is the problem of ambiguity, but there is a very way to fix it: “Defining a term”. (SL)

Univocal, Equivocal, and Analogical Uses of Terms

Terms are either univocal, equivocal, or analogical. A univocal term has one and only one meaning. An equivocal term has two or more quite different and unrelated meanings. An analogical term has two or more meanings that are (a) partly the same and partly different, and (b) related to each other. (SL)

When the term “capybara” is used in the statements: “I pet a capybara” and “I saw a capybara”, it is used univocally, since it only has one meaning. When a pirate marks “X” on a map and when I send “Xs and Os” to my loved ones, “X” is used equivocally. In the former, “X” represents buried treasure, but in the latter it represents a kiss. When I call an eraser a “rubber” and the material used for making tyres “rubber”, I use “rubber” equivocally, for the “rubber” of an eraser is not the same as the “rubber” of a tyre.

Definition of Terms

Definition of Definition

“Logical definition consists of, in effect, exactly circumscribing the comprehension of an object; in other words, saying what a thing is.” (CdF)

When defining something you describe only the comprehension of a thing, and you make no judgment on whether it exists or not. A definition is saying what an idea is, and contains no judgment on whether the idea exists in reality or not. I may come up with the idea of pigs that can fly, which in fact contains no judgment on whether pigs fly or not, but merely contains an idea. The only time a judgment can be made that does not exist solely based on the idea of it is in the case of contradictory ideas. The famous cases here are the round square, or the triangle with four sides. Since, by definition, squares cannot be round and triangles cannot have four sides, we can safely assume that they do not exist. In fact, many philosophical controversies are due to contradictory definitions, or at the very least misunderstanding of them.

Types of Division

Jolivet distinguishes between two types of division: nominal and real. Nominal definitions refer to what a word means. “To say that the word ‘to define’ means ‘to delimit’ is to give a nominal definition.” (CdF)

“The real definition expresses the nature of a thing.” (CdF) This is in fact an extreme claim compared to what most modern philosophy teaches. If you recall, modern philosophy teaches that the real nature of things are unknowable and that words and definitions are just shorthand that the human mind uses to not get overwhelmed by the amount of information. Aristotle rejects this and states that reality is (a) intelligible to the human mind, and (b) that the definitions of things actually encapsulate what things are.

Jolivet says that there are two types of real definitions: essential and descriptive.

The essential definition is the most precise and “real” of these definitions because it describes a thing’s essence; that is, what it actually is. It is performed by finding the “closest genus and the specific difference. We can define man in this way: rational animal; animal is the closest genus, which is to say the idea immediately superior in terms of extension to man; and rational is the specific difference, which is to say the quality which, added to a genus, constitutes a species distinct from all the other species of the same genus.” (CdF)

The descriptive definition “enumerates the most distinguishing external characteristics of a thing in order to distinguish them from all the others. (The ram is a ruminant with an elongated face, stooped nostrils, sluggish eye) This definition is used in the natural sciences.” Jolivet says that this definition is used when an essential definition is lacking, which makes sense in the natural sciences. When one is first investigating something, say an electron, one possesses no notion of what it is. The charge, the size, the mass of an electron may be known, but this is sufficient only to distinguish it from other things. Absent a complete theory of physics, the essence of an electron will remain unknown, and only experimental data describing what an electron is will give us its definition.

How to Divide Ideas

Definition of Division

Jolivet defines division as “distributing a whole into its parts” (CdF). Division is performed for further study of an idea. Kreeft further notes that division is performed across “the extension of a term” (SL).

Types of Wholes

Jolivet defines a whole as “anything that can be divided, whether physically or at least conceptually, into its elements”; there are three classes of wholes: “physical, logical, and moral”. (CdF)

Physical wholes are made of parts which “are really distinct”. Jolivet distinguishes between physical wholes that are "quantitative, where it is composed of homogenous parts: a block of marble; essential, when the whole forms a complete essence: man; potential, where it is composed of different faculties: the human soul since it is composed of intellect and will; accidental, when composed of parts that are united accidentally: a table, a pile of rocks.” (CdF)

There are also metaphysical wholes, whose “parts cannot be distinguished except by reason”. (CdF) A metaphysical whole is a “universal notion who contains in itself other subjective parts. It is this way that the genus contains the species. [an example is] the idea of animal in reference to the rational animal (man) and the irrational animal (brute).” (CdF)

Finally, there are moral wholes, “whose parts, although actually distinct and separated, are united by the moral tie of the same end: a nation, an army, a family, etc.” (CdF) Jolivet states that moral wholes always refer to a collective.

Rules of Division

For a division to be a good division, it must be exclusive, exhaustive, and possess only one basis for division. (SL)

Jolivet defines exclusivity as follows: “it should not enumerate elements except those that are really distinct from each other.” (CdF) Kreeft gives an example: “Dividing political systems into monarchical, constitutional, and democratic violates this rule because a regime could be both monarchical and constitutional, as well as both democratic and constitutional.” (SL)

Exhaustiveness is defined as a: “complete or adequate [division], which is to say that it enumerates all the elements of which it is composed of.”(CdF) Again, Kreeft gives a good example: “Dividing the term ‘meat’ into beef and lamb violates this rule because it omits pork1.”(SL)

The division should have only one basis because “it should proceed from members which are really opposed to each other. The following division: my library is composed of books of philosophy and books with good spines, would go against this rule, since having a good spine is not opposed to philosophy”. (CdF)

Logic is the science of the “ideal laws of thought and the art of applying them correctly”. (CdF) Strictly speaking, logic is not part of philosophy. Whereas philosophy aims to study the first causes of reality, logic merely focuses on describing how to think correctly. Furthermore, logic can be applied to other fields, such as physics and chemistry, in order to elucidate the correct methodology to use to find truth. Logic is a pre-philosophy, used for finding the correct way to demonstrate philosophical truths.

Today, there exist two broad types of Logic: Aristotelian logic and symbolic logic. Aristotelian logic, based on Aristotle’s 4th century Organon, was taught universally in the West until the publication of Bertrand Russell’s and Alfred North Whitehead’s Principia Mathematica in 1913; the new symbolic logic was proposed primarily due to some “unfashionable … presuppositions” (SL) in the “old” logic. The exact presuppositions are a subject for metaphysics, but suffice it to say that, since most modern philosophers rejected Aristotle’s assumptions in favour of Hume’s, symbolic logic, outside the Catholic Church, became the most dominant form of logic.

Why should you study Aristotelian Logic, and Aristotelian philosophy more generally? Peter Kreeft gives a two main reasons, summarized below:

1. Aristotelian Logic is concise and concrete

2. Aristotelian Logic is logical

On the first one, I will quote Kreeft directly:

in a logic text book misleadingly entitled Practical Reasoning in Natural Language, the author takes a full six pages of symbolic logic to analyze a simple syllogism from Plato’s Republic that proves that justice is not rightly defined as “telling the truth and paying back what is owed” because returning a weapon to a madman is not justice but it is telling the truth and paying back what is owed.

The second one refers to the “problem of material implication” in symbolic logic where any proposition implies a true proposition, and any false proposition implies every proposition. The problem is quite technical and requires its own article, but suffice it to say that it should make you highly suspicious of the assumptions of symbolic logic.

What are the parts of Logic?

Jolivet distinguishes between two parts of logic: formal and material.

Formal refers to the “correct form of the intellectual operations … which assures the agreement of the thought with itself” (Cdf). The intellectual operations are connected with Aristotelian psychology and they represent “apprehension, judgement, and reason”.

Material concerns itself with the “special rules that derive from the nature of the object of investigation”. (CdF) One of the ways that it does this is by investigating the “conditions of certainty”, but distinguishes itself from Epistemology in that Epistemology aims to know whether human faculties can attain truth or not (CdF).

For the next article in the logic series, we are going to look at terms and concepts.

These are what the philosophers would call natural sciences, and their goal is, like all sciences, to get to “knowledge that is certain, general, and rigorous… with truths validated for all cases, all times, and all places, and which are united by their causes and principles” (TdF). Through this definition, we see how the philosophers considered philosophy to be a science, and in fact a greater science than the natural sciences, since while the natural sciences are concerned only with “the determinism of natural phenomena … philosophy has its object in discovering the most universal causes, which is to say the first causes of everything.” (TdF) We see that, while the natural sciences merely describe physical phenomena, philosophy, at its core, is interested in the deepest questions of reality, “including immaterial phenomena and that which is not accessible except by reason”. (TdF)

Like any science, philosophy has a method. Since philosophy concerns itself with the whole of reality, one of the sources of philosophical knowledge is sense experience. This is the most basic way that we can come to know reality, and in fact is the foundation for all further reasoning. Thus, Jolivet declares that philosophy is in the first place an “experimental method.” (TdF) Secondly, since “philosophy, due to its end, is essentially metaphysical, which is to say it aims beyond sense experience and towards first cause, it needs to have need of reason.” (TdF) Finally, in the Catholic Church, philosophy distinguishes itself from theology in that it does not make use of revealed truths, but only of “natural reason”. (TdF)

The Parts of Philosophy

Jolivet divides philosophy into two parts: “That which can be considered in itself and that which can be considered in relation to others.” (TdF) The first is what is called speculative philosophy, which is where the center of philosophy really is. Paraphrasing Jolivet, it concerns itself with principally with metaphysics, which is to say the fundamental structure of being (Ontology), the study of God (Theodicy), and the study of the possibility of attaining truth (Epistemology). It also concerns itself with natural philosophy, which is to say the “material world itself [Cosmology] and man [Psychology]” (TdF). In this scheme, logic is prior to philosophy, and, strictly speaking, not part of it. Its aim is to “determine the conditions of internally coherent thought (formal logic) or … to define the methods for every discipline by which their objects may be studied (material logic)” (TdF)

The second part of philosophy (“that which can be considered in relation to others”) is practical philosophy. Jolivet states that this philosophy teaches us how to attain “the absolute good” (TdF). There are two divisions to this philosophy: philosophy of art and moral philosophy. The former concerns itself with producing things, and in particular beautiful things. The latter concerns itself with doing things, which is to say, the choice of actions which are excellent. The former requires no virtue. Indeed, it is possible to be very good at making things but otherwise a very bad person, as the stereotype of the artistic scumbag tells us.

The goal for this course is to give readers enough background knowledge so that they can start to read the Metaphysics of Aristotle and the Summa Theologicae of St. Thomas Aquinas. It is not intended to be particularly rigorous, but it is intended to challenge the assumptions that some readers may have about philosophy.

What is this course based on?

The Logic portion of this course is based on my own English translation of parts of a Spanish translation of Régis Jolivet’s work Curso de Filosofia (trans. Leandro de Cesmas, O.C.), which is an excellent and very clear course. These sections are supplemented with Socratic Logic by Peter Kreeft, which is an excellent textbook in English, though it misses a few things that Jolivet covers. For the History of Philosophy and Metaphysics portions I will be leaning on Jacques Maritain’s An Introduction to Philosophy.

As these works will be cited and quoted often, it is useful to abbreviate them. The abbreviation guide is below (all citations are in MLA style):

(CdF): Jolivet, Régis. Curso de Filosofia. Translated by Leandro de Cesmas, 4th ed., Club de Lectores, 1978.

(SL): Kreeft, Peter. Socratic Logic. 3.1 ed., St Augustine’s Press, 2010.

(ItP): Maritain, Jacques. An Introduction to Philosophy. Translated by E. I. Watkin, Sheed & Ward, 1930.

All other citations are either cited in the MLA style and placed at the end of the relevant article or, if citing an image, the link is just placed in the relevant image.

Another useful work is Aquinas by Edward Feser, but this is not cited in the text.

What is the timeline for this project?

The aim is to be constantly updating and editing the textbook, but rough drafts of each of the traditional parts of Aristotelian philosophy will be published on a somewhat fixed schedule.

By April 2026, we aim to finish the Logic Course and History of Philosophy section, as well as make a small introduction to Aristotelian Metaphysics.

Do I need to Pay?

This text is 100% free and will remain freely available. However, you can support the project by buying a paid subscription, even for one month. All money will be reinvested into improving and maintaining the project.

How do I Start?

Take a look at the Table of Contents.