Life and Works

Aristotle was a student of Plato who lived from 384 to 322 BC. He was arguably the most scientific of ancient thinkers, but not because he followed scientific methods. Aristotle developed a system of analysis based upon his metaphysics, employing some aspects of what would eventually give rise to scientific method. Having traveled to Pella in 343 B.C., he began tutoring Philip of Macedon's son, Alexander, who later came to be Alexander the great. He founded his own school at Athens in 334/335 B.C., called the Lyceum, where he enlisted the aid of students in making observations of practically everything that exists. His students were known as peripatetics, and he had with Herpyllus (a slave or his wife) a son named Nicomachus, to whom his Nicomachean Ethics is allegedly addressed. He felt compelled to depart Athens because of anti-Macedonian sentiment, which arose shortly after Alexander's death in 323 B.C., leaving Athens for Chalcis where he died of natural causes. His and his students' investigations supplied the raw material for many of his “scientific” works. Some that survive are Physics, Metaphysics, On the Heavens, On Generation and Corruption, On the Parts of Animals, Categories, Topics, On the Soul, Posterior Analytics, Prior Analytics, Nicomachean Ethics and Meteorologia. The topics of his surviving works range from biology to metaphysics, but many or even all of these are works that likely were not meant for publication. Indeed, the works that were meant to be read seem to have been lost, including some dialogues on Homer and poetry in general, which were said to be even more beautiful than the works of Plato. The breadth and depth of his thought continues to impress scholars [i] and some consider Aristotle to be the greatest polymath of the ancient world. Aristotle's metaphysics leads him to observe and thus to analyze empirically physical objects themselves instead of merely reasoning about them. As a result he created an empirical and logical system of thought that covered not only all of the humanities but all of what moderns call the hard sciences. In fact, Aristotle's contribution to western thinking is so immense that we must limit ourselves to only a few facets of his thinking and a few texts. [ii] Aristotle did not discover causality or causes. Rather, as we have seen, many thinkers before him sought causes of things in nature. These were the first physicists from the western world who had remarkable insights into material reality and who many times expressed themselves in literary form. Aristotle believed in a form of interaction with these predecessors that was similar to the dialogue form Plato used in his dialogues. He critiques his predecessors' work by discussing and critiquing their arguments and thus builds upon earlier insights, but in prose style.

First Principles

It is difficult to discern what comprises a first principle for Aristotle. His first principles can be thought to be a construct of things: elements, causes, motion and a material eidos. [iii] He was the first to create independent sciences and disciplines for various subjects and that is only one reason why articulating his first principle(s) is difficult. Aristotle was heavily influenced by Plato and so Plato's eidos is an intimate part of his thinking. Yet, Aristotle shifts the Platonic eidos from the immaterial reality of Plato to the material realm. [iv] He claims that the matter making up the manifestation of some creature or thing and the form, or eidos, are inextricably bound. Still, he retains the Platonic eidos as part of a metaphysical construct of things that move internally and externally and so become. This metaphysical eidos Aristotle then bound up with matter and motion. In other words, Aristotle thought that something has a nature if it moves into its own principle by becoming what it is:

Of existing things, some exist by nature, others through other causes: by nature animals and their parts exist, and plants, and the simple bodies, like earth, fire, air and water (for these things and things of this sort we say exist by nature), and all of these things seem to differ from the things not put together by nature. For each of these in itself possesses a source of movement and rest, in place or by growth and decrease, or by change; but a bed or a cloak, and other sort of thing that exists, by the manner in which it has happened upon each designation and to the extent that it exists from art, has no in-grown impulse of alteration at all. But by the manner in which they happen to exist of stone or earth or a mixture of these, they possess an impulse, and to that extent, since nature is a source of something and a cause of being moved and of being at rest in that to which it belongs principally, in virtue of itself and not accidentally, <they possess an impulse>. (Aristotle, Physics II, 192b8)

What he meant was that things that grow in and of themselves have a natural movement that can be likened to a particular principle, while things that must be crafted do not have this natural movement and thus no natures. A tiger has a nature, possessing an innate impulse to strive and survive as a tiger, as does a human. Beds and tables possess no nature because they have been crafted by someone; they lack the impulse to come about on their own. Yet, beds and tables exist by nature because they are crafted of things and made by men. Still, what comprises the table may have a nature or be a nature, depending on out of what the table is composed. In this manner Aristotle's perspective differs from Plato who thought that practically anything has an eidos, or what might be thought of as something like a nature, or some kind of organization. It is important to note that Aristotle deliberately avoids making a material element one of his first principles; he consciously avoids making a Platonic eidos a first principle as well, seemingly because he believed that any material principle or metaphysical construct would itself need another piece of matter or principle which would in turn need another first principle. There is then for Aristotle an infinite regress called the third man argument. Aristotle also acknowledged the four elements of Empedocles (earth, air, fire and water), but their status as first principles was for Aristotle dubious and they were not the principle he sought (again one significant reason is because of the third man argument). Some scholars claim that Aristotle argued himself into what is called prime matter, an underlying indefinite pure potentiality that inhered in the largest as well as the smallest and most fundamental of things.

It seems that Aristotle set out to explain how creatures and things arise in the world and what exactly is the relationship between the form, or organization, of something and its matter. Explaining matter and form as becoming in terms of potency and act seems to have been central to Aristotle's effort at understanding what it is that is the motion of a thing. Things that have an internal movement must be more than merely arrangements of the fundamental matter that comprises them. Otherwise, anyone could arrange matter in the correct way and create anything, god or creature. Aristotle sought what it is in matter that is yet more than mere material – that which produces itself, things and creatures yet remains en-mattered. In other words, he sought the things responsible for what comes to be, but these motions are not the mechanical activities modern science understands as causes. Aristotle set about to deepen human comprehension of the universe through investigation into productive activities that he called aitia, the Greek term meaning “causes.” Causes and things had different kinds of motion to them:

...there is motion only in respect of what kind, how much, and where, for in each of these there is contrary. Now let motion in respect of what kind be alteration, for it has been joined with this common name. But I say the what kind is not the thing in the substance of any thing (since then even the difference is a quality), but it is a passive attribute by which a thing is said to be affected or unaffected. Motion in respect of how much lacks a common name, but in each instance it is growth and decrease, the one tending to a thing's complete magnitude is growth, the other tending from it decrease. Motion in respect of place both in common and in particular is nameless, but let it be called generally change of place, although those things alone are said to be carried along when not on their own coming to a stand is possible for those things changing place. (Aristotle, Physics V, 3 226a).

This motion was intimately involved in what something is and how it manifests:

There is that which exists in completion, but also that which exists in completion and potentially: a thing being this thing, being this much, being this kind, or similarly for the other ways of categorizing being. Relation to something is said to be what exceeds or falls short, or what exists according to acts and being acted upon, and generally what moves (another thing) and what is moved: for the mover is a mover of something moved, and the moved is moved by something moving it, and no motion exists besides [this] in things. For what changes always changes either in substance, or in quantity, or in quality, or in place, and there is no commonality to take from these...and with respect to which is neither...a this, nor a this much, nor a what kind, nor any other kind of being: so that neither motion nor change will be anything apart from the things mentioned, since there exists nothing besides the things mentioned. (Aristotle Physics III, 1).

The word for motion that Aristotle uses is kinesis. He links kinesis to energeia, a term used to express the being-at-work [v] that is the continued actualization and also potential:

With a distinction having come about according to each kind of being between the complete and the potential, the completion of a thing existing by potential – by the manner in which this sort of thing exists – is motion: of the alterable, qua alterable, it is alteration; of the grow-able and its opposite, what can decrease (no name is common to the two), it is increase and decrease, of the generable and destructible it is coming to be and passing away, and of the mobile as far as place it is change of place. (Aristotle Physics, III, 1).

Kinesis of something for Aristotle is a kind of activity belonging to a thing that makes what the thing is a what. In other words, something coming to be moves into what it is, as itself being acted upon and acting in various ways:

And that this is motion, is clear from the following. For whenever the buildable – by which we say this sort of thing exists as itself – exists completely, it is being built, and this thing is building. Similarly learning, healing, rolling, leaping, ripening, aging. And because some of the same things exist potentially and completely, not at the same time or not according to the same thing, but like something fully hot and potentially cold. Many things will act and be acted upon by each other; for in every case they will be act-able and able to be-acted-upon. The result is that the moving is naturally moved, since each such thing moves the thing being moved and itself. (Aristotle, Physics III, 1).

A thing also moves from itself and into itself as it continues its being-at-work. It is necessary to understand that the energeia or the being-at-work of something is for Aristotle the moving organization that is its being, that being which for Plato is called an eidos. Aristotle contends that such activity is in the world as something material: being-at-work. It is not in another, allegedly deeper and immaterial part of reality, as for Plato. That activity has its own motion into itself, but it also may exist as potential for another thing. As a result, things have in and as themselves a kind of potential, for Aristotle. They possess motions that not only make them what they are, but make them possibly other things, and they are not necessarily always the same motion:

But the fullness of what exists potentially, whenever existing completely and working, not as itself but just as movable, is motion. I mean by “just as” the following. Bronze is a statue potentially, but similarly it is not the fulfillment of bronze by which it is bronze that is motion. For it is not the same thing to exist as bronze and to exist as some potentiality, since if they were the same thing simply and by definition, the completion of bronze as bronze would have been motion. But they are not the same, as has been stated. This is clear in contraries. For to be potentially healthy and to be potentially ill are different, since being healthy and being ill would be the same thing. The underlying thing both being sick and being healthy, whether humour or blood, is one and the same. Since they are not the same thing, just as color is not the same as being visible, the fulfillment of the potential, as potential, is motion. (Aristotle, Physics III, 1).

Causation and Cosmology

Aristotle understood causality as the thing (that material eidos) acting in and for itself, and thus his metaphysics, along with the third man argument seen above, compelled him to refrain from establishing a simple, material first principle. [vi] In other words, Aristotle establishes four causes in order that observations of particular causality may lead to a deeper understanding of a manifestation of anything. When one articulates the causes, the depth of the what of any thing emerges:

For since our labor is for the sake of knowing, and we think we do not thus far know each thing until we have taken hold of the why of each thing (and this is the taking up of the first cause), it is clear that we must do this about both coming to be and passing away and about all natural change, so that, once we know sources, we may try to lead back to them each of the things that are sought. (Aristotle, Physics II, 3).

Aristotle's analysis is not restricted to matter or to empirically verifiable aspects of things, and in this sense his method does not resemble scientific method. That is, a cause may be the skill or knowledge someone has or the arrangement of something and its purpose, which differs greatly from the sort of cause associated with modern science. His perspective on causes one may call metaphysics. One Aristotelian cause is the material that comprises a something. It is something without which the movement, or nature, cannot manifest.

One manner of cause is said to be, then, that out of which something comes into being, while being an underlying presence in it, as bronze of a statue or silver of a bowl, and other kinds of these things. (Aristotle, Physics II, 3).

The bronze of a statue is a kind of material from which a statue may be made. There are other substances from which a statue can be made, of course, but they must have certain qualities: resilience, aesthetic beauty in themselves and perhaps the ability to melt, or at least the ability to be formed into some shape or organization. One way to understand matter here is that it is a kind of being-at-work itself that possesses another characteristic of potential as well. The continued whatness of bronze does not change but the motion of the potential for being statue acts through its being-at-work. Matter may be interpreted here as another being-at-work, or a mysterious part of the universe that cannot be articulated; there is also prime matter, which has been interpreted to be an indeterminate mass of pure potentiality. [vii] Another of Aristotle's causes has been called the formal cause. It is the organization of what something is or the what.

In another manner [cause] is the form (eidos) or pattern, and this is the reasoning of the “to be what it is”, and the kinds of this thing (as of the two-to-one ratio octave, and broadly number), and the parts that are in the reasoning. (Aristotle, Physics II, 3).

One will recall that the octave is the two-to-one numeric ratio applied by Pythagoreans to the lengths on a musical scale. Certain distances on one chord produce similar sounds. Without the specific distance of the chords and without the particular material in specific arrangement comprising a string that produces a musical sound there would be no similarity of vibration that produces a sound. Each thing that is necessary to produce the sounds in the length relationship of two-to-one or one-half is itself an arrangement needed to form the octave. These differing but harmonized arrangements are the producers of the octave and thus formal causes, or formal producing activities. Thus, there is a relationship and order to the formal cause and it has an arrangement to it, but [viii] Aristotle is not making the formal cause numeric in nature, as we have seen, other than to state that there is an organization, which may in turn be analyzed mathematically or logically. [ix] A thing's nature has a kind of activity that produces a fullness, one that the assessment of its eidos by mathematicians lacks. The fullness is articulated for Aristotle in its motion. One can see aspects of the modern conception of geometry and calculation as abstractions that must be proven here. Aristotle thinks of geometry as not numbers spatially extended, but as the outline of things that must be filled. What fills it is motion of a specific kind. So, a natural thing in movement is the fullness of something actually moving as itself. [x] A third cause is what may be called the motive or the efficient cause:

...it is that from which the initial source of change or of rest is, as the legislator is a cause, or the father of a child, or broadly the making of what is being made, or the changing of a thing being changed. (Aristotle, Physics II, 3).

The motive cause is similar to the modern notion of cause, as that which produces or acts upon another thing in the first place. There is a generative quality to this cause as in all Aristotelian causes, but the motive, or sometimes-called efficient, cause may be more properly called the initial interaction between cause and caused or perhaps the physically active cause. It is the initial motion and interaction between things that makes up this cause in the sense that there are things causing and being caused externally at the beginning of change. The last cause, sometimes called the final cause, explains why something has come to exist, or its purpose. Its end is not necessarily to produce a human purpose for something, but to produce some kind of activity that can be defined as the end or goal of something:

...it (cause) is meant as an end. This is the “for the sake of which”, as health is of walking around. Why is he walking around? We say “so that he becomes healthy,” and in speaking in this manner we think to have given the cause. (Aristotle, Physics II, 3).

This cause, coupled with the formal cause, is more completely representative of the Platonic eidos. One may even think of the formal and final causes as the same but immersed in different acts of what becomes. When something attains its fullness, it attains such fullness as what it already was and what it was and is to become. Such is the final cause. One can think of human DNA as analogous. When matter goes into the design of the creature whose DNA guides it, the end goal is that pattern or organization that is the DNA, or the structure of what the creature will be. We call it genotype. The actual manifestation is the phenotype. The genotype and the phenotype are inextricably fused for Aristotle, not only in creatures and men, but in anything that possesses the impulse of nature. The final cause is that towards which the impulse of motion directs itself in order to become what it is by nature. The Platonic eidos is sometimes interpreted as an ideal, or as something to which to strive. The final cause is similar, but of course it is in the matter whereas the Platonic eidos is immaterial and “outside” of becoming. We must keep in mind that though we have seen roughly what are the causes for Aristotle, his work contradicts itself perhaps, or at least there is an effort to explain and then reexplain that makes his thoughts twist and turn on the page one reads. Perhaps it is the case that Aristotle recognized how fused together are these causes such that no one articulation suffices, but elements of each enter into different being-at-works:

For cause is spoken of in many ways, and of those of the same form, one prior and one later, as in [the cause] of health is the doctor and also the craftsman, and [the cause of] the octave [is] the double and also number, and always all-encompassing things as related to particular ones. (Aristotle, Physics II, 3).

And all of them, both those things said naturally and those said by chance, are some potential things and other things working , as of building a house, either the builder or the builder building. And similarly it will be articulated for what things the causes are causes for the things that have been said, as [cause] of this statue or a statue or generally an image, and of this bronze or of bronze or generally of material, and the same with the things having happened by chance. Further, these things weaving themselves together (and being woven) [with] those will be said, such as not Polycleitus nor a sculptor but the sculptor Polycleitus. (Aristotle, Physics II, 3).

Aristotle examined becoming and thus sought to understand Plato's eidos in terms of how things bring about things. He was compelled to accomplish this task by looking at the things around him and then reasoning. At the same time that he developed an observational method, and probably as a result, Aristotle noted that there exist rules for thinking. The effort at articulating the rules for logic seems to be linked to the effort at finding causes. At the same time, Aristotle's logic rules make clear how his predecessors reasoned and allowed future thinkers to analyze the arguments of the tradition, as seen in the arguments given above for ancient thinkers. These efforts at explaining things in terms of cause make Aristotle an authentically analytic thinker, which is to say that an essential aspect of his thinking is based upon observation and then later reasoning over the various observations of animals, of substances, of politics, and of other objects and creatures one finds in the universe. That he is analytic is not to say that he concentrates on logic and the rules of logic alone. Aristotle's metaphysics compel him to observe and then reason. One seeks to understand what the causes are, and so the eidoi, of a particular thing's motion. Observation and thought were already fundamental aspects of Greek thinking, but Aristotelian causes articulated precisely what to observe and how to reason in order to make sound arguments about the general aspects of each thing as it is being-at-work. It is for these reasons that we can call Aristotle a scientific thinker, but be careful to know that he is no scientist. He never would have thought that one first needs an hypothesis that was well-thought, a theory that was followed by empirical verification. While observation was an essential aspect of his thinking, the control methods and supposedly objective verification process of science were virtually unknown to him. In fact, Aristotle may not even have possessed any awareness of object reality in the scientific sense. The notion that there exists an objective state of things that may be assessed by reason and reached through the senses whereby an empirical verification of a theory may take place was not a part of his observational method at all. In fact, he would have been averse to empirical verification, other than the use of observations. Again, Aristotle observed and assessed through reason, but never did he or his students empirically verify an already-systematized theory. [xi]

Aristotle articulated his cosmology in various works, but the most complete actual cosmology was his De Caelo, or “On the Sky”, which was accepted as true for more than 18 centuries. There he articulated a world composed of the four elements: earth, air, fire and water. These naturally move up or down in a sublunary realm with fire being the most light and earth heaviest. Objects are composed of the different elements and they are imperfect because their elements are displaced, the natural places for the elements being where they tend to go. Fire ascends and earth drops, for example. Bodies move thus naturally and we have already seen how a natural motion is a part of all things. Stars and planets are more exalted bodies that move in circles and earth lies in the center of the universe with the celestial bodies circling it. The initial motion of bodies was begun by a prime mover that is itself desired [xii] by all the other bodies. The prime mover manifests itself in no way because otherwise it would be imperfect; celestial bodies are moved by the prime mover and the movement radiates downward into other spheres that surround earth; the matter that comprises the celestial sphere is the eternal aether. These spheres number 55, explaining and predicting the motions of the stars, as the celestial bodies were affixed to each of the spheres. The principles that govern the celestial sphere are not for Aristotle the same as the ones that govern the sublunary sphere. The celestial sphere and its occupants are eternal while the sublunary sphere, with its elements, are mortal. This universe has always existed because it is perfect, and it will always exist. Obviously, Aristotle made use of observations in creating this model. Aside from the fact that most of his assertions are wildly inaccurate, it is notable that his 55-sphere system did somewhat accurately predict celestial motions. Aristotle himself recognized the speculative nature of his musings and expressed hope that another, more informed, theory may emerge.

Argumentation

Keeping Aristotle's perspective in mind, we are able to re-articulate his rules of logic that we discussed in the first part of this blog. A re-articulation will make clear how his metaphysics, his logical rules and his analytic method work together. Aristotle noticed certain things about how human beings reasoned. He formulated the first rules for argumentation, guidelines for the formation of good reasoning. Good reasoning involves not only observations that are true, or what moderns may call facts. Observations must be understood such that they have a connection to one another, and the more certain the relationship between specific observations, the more firm foundation will be the thought about a specific topic. [xiii] Aristotle began with propositions, which are statements taken to be true. If there exists no connection between the propositions, then no conclusion can follow. But if there is a connection between the propositions, then new information and insight may follow:

If then one wants to prove syllogistically A of B, either as an attribute of it or as not an attribute of it, one must assert something of something else. If now A should be asserted of B, the proposition originally in question will have been assumed. But if A should be asserted of C, but C should not be asserted of anything, nor anything of it, nor anything else of A, no syllogism will be possible. For nothing necessarily follows from the assertion of some one thing concerning some other single thing. Thus we must take another premiss as well. If then A be asserted of something else, or something else of A, or something different of C, nothing prevents a syllogism being formed, but it will not be in relation to B through the premisses taken. Nor when C belongs to something else, and that to something else and so on, no connexion however being made with B, will a syllogism be possible concerning A in its relation to B. For in general we stated that no syllogism can establish the attribution of one thing to another, unless some middle term is taken, which is somehow related to each by way of predication. For the syllogism in general is made out of premisses, and a syllogism referring to this out of premisses with the same reference, and a syllogism relating this to that proceeds through premisses which relate this to that. But it is impossible to take a premiss in reference to B, if we neither affirm nor deny anything of it; or again to take a premiss relating A to B, if we take nothing common, but affirm or deny peculiar attributes of each. So we must take something midway between the two, which will connect the predications, if we are to have a syllogism relating this to that. If then we must take something common in relation to both, and this is possible in three ways (either by predicating A of C, and C of B, or C of both, or both of C), and these are the figures of which we have spoken, it is clear that every syllogism must be made in one or other of these figures. The argument is the same if several middle terms should be necessary to establish the relation to B; for the figure will be the same whether there is one middle term or many. (Aristotle, Prior Analytics I.23).[xiv]

If an argument has a good connection, it can be said to be valid. Yet, validity only means that there are statements possessing some set of things in common with one another and because of that commonality, one can make a new statement about them. This new statement is called an inference. It is information derived form the propositions one is using that was not present until the argument came about.

• All quadrupeds are wild animals.
• All tigers are quadrupeds.
• Thus, all tigers are wild animals.

This argument has good form, and so it is valid because if we accept that all quadrupeds are wild animals and that all tigers are quadrupeds, we can come to a reasonable conclusion that all tigers are wild animals because they share a set or category: quadrupeds. This commonality allows us to draw a new inference from information we already possessed. Yet, it may not be the case that all quadrupeds are wild animals, and thus the argument would not be true even though it makes proper connections. The information in the premises must say something true about the world. Here is the observation that one makes in order to form good, sound arguments. Recall some of the statements of earlier thinkers. These assertions may be true or not true, but many assertions of the early Greek physicists are mere observations that are taken as universals. That they are not universal, or perhaps even not true, is what seriously complicates an argument. One wants, of course, to make good inferences, so arguments must possess a commonality that allows good form, but the premises (observations) must also be true. If the argument has true premises and good form, then it is said to be sound. So, while validity in argumentation is necessary, soundness of argument is the true goal.

Aristotle talks of argumentation in terms of sets of things. Remember that he thought the eidos was in the material comprising something. An eidos in fact is a kind of general category of existing things that possesses a kinesis and an energeia. We have seen that these terms assist in explaining being-at-work or what-it-is-to-be [xv] for a thing, or its nature. So, when he observed things in nature, Aristotle was seeking the eidos of some particular thing, its four causes. He was looking not just for what mechanical cause made something happen, but he sought also the “why” and the arrangement of it. Thus, he looked for formal and final causes. [xvi] When he made observations about things, he was able to say of them that they always or never had certain characteristics or that some of them had and some had none of certain characteristics. He was looking for the part of something that made it was it is as well as that part of it that made it potential for becoming something else, or a part of something else. When there was a connection between two things, he was able to say something about the eidos of what he examined:

• All quadrupeds are land-based creatures.
• All Tigers are quadrupeds.
• All Tigers are land-based creatures.

All of the set of quadrupeds belongs to the set of land-based creatures. So, nothing that is a quadruped is not a land-based creature. Because we know something about all quadrupeds (Let's assume this statement is true), we can say something about any other thing that belongs to this group. These a mathematician may call sets of things. When sets overlap, we can make statements about that overlapping, like the statement “All Tigers are land-based creatures.” What Aristotle sought in part was the connection that demonstrated how beings-at-work were motions in common, and these motions in common were causes in the sense that all causes had a kind of motion to them, which in turn was in part the formal and final cause and so the material eidos as well. Aristotle needed some kind of premise with which to make his arguments and he thus needed to observe first; he reasoned later with the observations made. The significance of Aristotle's contribution is that his metaphysics compelled him to create a method of observation and reasoning. He observed and sought what is the motion of a given thing and then reasoned in order to understand it more. The observation was for Aristotle a direct link to the nature of a given thing. Given the titanic influence Plato had on the ancient world, such an observational method concentrating on things that become rather than the being of things was a radical step towards what we now call science.

There were four kinds of statements that said something about the eidos, or the sets of different things. These are called categorical propositions. Notice the word “categorical.” One seeks categories of different things in the world and statements about them that are true. When these statements are made, they form sets of things that may be related to one another. The relation to one another reveals something new, another inference, about the subjects in the statements. One kind of statement made a claim about all of the members of a specific set of things. These are A statements:

All X are Y.

Every X is in the category of Y. The statement “All tigers are land-based animals” is just one such statement. All of the set of tigers are creatures in the set of land-based animals. Another statement made a claim about the exclusivity of the two sets. These are E statements:

No X are Y.

This statement means that of the set of Ys there are no Xs in the set of Y. This statement also means that none of the set of Y are in X because if there is no connection between Xs and Ys, then there must be no connection between Ys and Xs. These sets, or categories, are exclusive. “No tigers are sea-dwelling creatures” is one such statement. A third kind of statement means that some of one set of things is in another. These are I statements:

Some X are Y.

This statement means that there is at least one X, and it is in the same set of things as Y. There may be more than one X in the set of Y, but we are justified in saying that there is at least one. “Some tigers are animals friendly to humans” is one such statement. The fourth kind of statement is a negation of the third kind. These are O statements:

Some X are not Y.

These assertions mean that there is at least one X, and that X is not in the set of Y. “Some tigers are not animals friendly to humans” is one such statement. One can see how observation of the natural world is imperative to making claims about certain things. When a statement is made, it means that there has been no reflection upon this natural occurrence other than to observe how one natural thing relates to another. The fixed relationships between the statements can be summed up by the traditional square of opposition, which shows the truth values of the four statements with respect to one another: