Aristotle’s most famous contribution to logic is the syllogism, which he discusses primarily in the Prior Analytics. A syllogism is a three-step argument containing three different terms. A simple example is “All men are mortal; Socrates is a man; therefore, Socrates is mortal. ” This three-step argument contains three assertions consisting of the three terms Socrates,man, and mortal. The first two assertions are called premises and the last assertion is called the conclusion; in a logically valid syllogism, such as the one just presented, the conclusion follows necessarily from the premises.
That is, if you know that both of the premises are true, you know that the conclusion must also be true. Aristotle uses the following terminology to label the different parts of the syllogism: the premise whose subject features in the conclusion is called theminor premise and the premise whose predicate features in the conclusion is called the major premise. In the example, “All men are mortal” is the major premise, and since mortal is also the predicate of the conclusion, it is called the major term.
Socrates” is called the minor term because it is the subject of both the minor premise and the conclusion, and man, which features in both premises but not in the conclusion, is called the middle term. In analyzing the syllogism, Aristotle registers the important distinction between particulars and universals. Socrates is a particular term, meaning that the word Socrates names a particular person. By contrast, man andmortal are universal terms, meaning that they name general categories or qualities that might be true of many particulars. Socrates is one of billions of particular terms that falls under the universal man.
Universals can be either the subject or the predicate of a sentence, whereas particulars can only be subjects. Aristotle identifies four kinds of “categorical sentences” that can be constructed from sentences that have universals for their subjects. When universals are subjects, they must be preceded by every, some, or no. To return to the example of a syllogism, the first of the three terms was not just “men are mortal,” but rather “all men are mortal. ”
The contrary of “all men are mortal” is “some men are not mortal,” because one and only one of these claims is true: they cannot both be true or both be false. Similarly, the contrary of “no men are mortal” is “some men are mortal. ” Aristotle identifies sentences of these four forms—“All X is Y,” “Some X is not Y,” “No X is Y,” and “Some X is Y”—as the four categorical sentences and claims that all assertions can be analyzed into categorical sentences. That means that all assertions we make can be reinterpreted as categorical sentences and so can be fit into syllogisms. If all our assertions can be read as premises or conclusions to various syllogisms, it follows that the syllogism is the framework of all reasoning.
Any valid argument must take the form of a syllogism, so Aristotle’s work in analyzing syllogisms provides a basis for analyzing all arguments. Aristotle analyzes all forty-eight possible kinds of syllogisms that can be constructed from categorical sentences and shows that fourteen of them are valid. In On Interpretation,Aristotle extends his analysis of the syllogism to examine modal logic, that is, sentences containing the words possibly ornecessarily. He is not as successful in his analysis, but the analysis does bring to light at least one important problem.
It would seem that all past events necessarily either happened or did not happen, meaning that there are no events in the past that possibly happened and possibly did not happen. By contrast, we tend to think of many future events as possible and not necessary. But if someone had made a prediction yesterday about what would happen tomorrow, that prediction, because it is in the past, must already be necessarily true or necessarily false, meaning that what will happen tomorrow is already fixed by necessity and not just possibility.
Aristotle’s answer to this problem is unclear, but he seems to reject the fatalist idea that the future is already fixed, suggesting instead that statements about the future cannot be either true or false. Organon: The Structure of Knowledge Summary The Categories, traditionally interpreted as an introduction to Aristotle’s logical work, divides all of being into ten categories. These ten categories are as follows: Substance, which in this context means what something is essentially (e. g. , human, rock) * Quantity (e. g. , ten feet, five liters) * Quality (e.g. , blue, obvious).
* Relation (e. g. , double, to the right of) * Location (e. g. , New York, home plate) * Time (e. g. , yesterday, four o’clock) * Position (e. g. , sitting, standing) * Possession (e. g. , wearing shoes, has a blue coat) * Doing (e. g. , running, smiling) * Undergoing (e. g. , being run into, being smiled at) Of the ten, Aristotle considers substance to be primary, because we can conceive of a substance without, for example, any given qualities but we cannot conceive of a quality except as it pertains to a particular substance.
One important conclusion from this division into categories is that we can make no general statements about being as a whole because there are ten very different ways in which something can have being. There is no common ground between the kind of being that a rock has and the kind of being that the color blue has. Aristotle’s emphasis on the syllogism leads him to conceive of knowledge as hierarchically structured, a claim that he fleshes out in the Posterior Analytics. To have knowledge of a fact, it is not enough simply to be able to repeat the fact.
We must also be able to give the reasons why that fact is true, a process that Aristotle calls demonstration. Demonstration is essentially a matter of showing that the fact in question is the conclusion to a valid syllogism. If some truths are premises that can be used to prove other truths, those first truths are logically prior to the truths that follow from them. Ultimately, there must be one or several “first principles,” from which all other truths follow and which do not themselves follow from anything.
However, if these first principles do not follow from anything, they cannot count as knowledge because there are no reasons or premises we can give to prove that they are true. Aristotle suggests that these first principles are a kind of intuition of the universals we recognize in experience. Aristotle believes that the objects of knowledge are also structured hierarchically and conceives of definition as largely a process of division. For example, suppose we want to define human.
First, we note that humans are animals, which is the genus to which they belong. We can then take note of various differentia, which distinguish humans from other animals. For example, humans walk on two legs, unlike tigers, and they lack feathers, unlike birds. Given any term, if we can identify its genus and then identify the differentia that distinguish it from other things within its genus, we have given a definition of that term, which amounts to giving an account of its nature, or essence.
Ultimately, Aristotle identifies five kinds of relationships a predicate can have with its subject: a genus relationship (“humans are animals”); a differentia relationship (“humans have two legs”); a unique property relationship (“humans are the only animals that can cry”); a definition, which is a unique property that explains the nature or essence of the subject; and an accident relationship, such as “some humans have blue eyes,” where the relationship does not hold necessarily. While true knowledge is all descended from knowledge of first principles, actual argument and debate is much less pristine.
When two people argue, they need not go back to first principles to ground every claim but must simply find premises they both agree on. The trick to debate is to find premises your opponent will agree to and then show that conclusions contrary to your opponent’s position follow necessarily from these premises. The Topicsdevotes a great deal of attention to classifying the kinds of conclusions that can be drawn from different kinds of premises, whereas the Sophistical Refutations explores various logical tricks used to deceive people into accepting a faulty line of reasoning. Physics: Books 1-4.
The Physics opens with an investigation into the principles of nature. At root, there must be a certain number of basic principles at work in nature, according to which all natural processes can be explained. All change or process involves something coming to be from out of its opposite. Something comes to be what it is by acquiring its distinctive form—for example, a baby becomes an adult, a seed becomes a mature plant, and so on. Since this the baby or the seed were working toward this form all along, the form itself (the idea or pattern of the mature specimen) must have existed before the baby or seed actually matured.
Thus, the form must be one of the principles of nature. Another principle of nature must be the privation or absence of this form, the opposite out of which the form came into being. Besides form and privation, there must be a third principle, matter, which remains constant throughout the process of change. If nothing remains unchanged when something undergoes a change, then there would be no “thing” that we could say underwent the change. So there are three basic principles of nature: matter, form, and privation.
For example, a person’s education involves the form of being educated, the privation of being ignorant, and the underlying matter of the person who makes the change from ignorance to education. This view of the principles of nature resolves many of the problems of earlier philosophers and suggests that matter is conserved: though its form may change, the underlying matter involved in changes remains constant. Change takes place according to four different kinds of cause. These causes are closer to what we might call “explanations”: they explain in different ways why the change came to pass.
The four causes are (1) material cause, which explains what something is made of; (2) formal cause, which explains the form or pattern to which a thing corresponds; (3) efficient cause, which is what we ordinarily mean by “cause,” the original source of the change; and (4) final cause, which is the intended purpose of the change. For example, in the making of a house, the material cause is the materials the house is made of, the formal cause is the architect’s plan, the efficient cause is the process of building it, and the final cause is to provide shelter and comfort.
Natural objects, such as plants and animals, differ from artificial objects in that they have an internal source of change. All the causes of change in artificial objects are found outside the objects themselves, but natural objects can cause change from within. Aristotle rejects the idea that chance constitutes a fifth cause, similar in nature to the other four. We normally talk about chance in reference to coincidences, where two separate events, which had their own causes, coincide in a way that is not explained by either set of causes.
For instance, two people might both have their own reasons for being in a certain place at a certain time, but neither of these sets of reasons explains the coincidence of both people being there at the same time. Final causes apply to nature as much as to art, so everything in nature serves a useful purpose. Aristotle argues against the views both of Democritus, who thinks that necessity in nature has no useful purpose, and of Empedocles, who holds an evolutionary view according to which only those combinations of living parts that are useful have managed to survive and reproduce themselves.
If Democritus were right, there would be as many useless aspects of nature as there are useful, while Empedocles’ theory does not explain how random combinations of parts could come together in the first place. Books III and IV examine some fundamental concepts of nature, starting with change, and then treating infinity, place, void, and time. Aristotle defines change as “the actuality of that which exists potentially, in so far as it is potentially this actuality. ” That is, change rests in the potential of one thing to become another.
In all cases, change comes to pass through contact between an agent and a patient, where the agent imparts its form to the patient and the change itself takes place in the patient. Either affirming or denying the existence of infinity leads to certain contradictions and paradoxes, and Aristotle finds an ingenious solution by distinguishing between potential and actual infinities. He argues that there is no such thing as an actual infinity: infinity is not a substance in its own right, and there are neither infinitely large objects nor an infinite number of objects.
However, there are potential infinities in the sense that, for example, an immortal could theoretically sit down and count up to an infinitely large number but that this is impossible in practice. Time, for example, is a potential infinity because it potentially extends forever, but no one who is counting time will ever count an infinite number of minutes or days. Aristotle asserts that place has a being independent of the objects that occupy it and denies the existence of empty space, or void.
Place must be independent of objects because otherwise it would make no sense to say that different objects can be in the same place at different times. Aristotle defines place as the limits of what contains an object and determines that the place of the earth is “at the center” and the place of the heavens as “at the periphery. ” Aristotle’s arguments against the void make a number of fundamental errors. For example, he assumes that heavier objects fall faster than lighter ones.
From this assumption, he argues that the speed of a falling object is directly proportional to an object’s weight and inversely proportional to the density of the medium it travels through. Since the void is a medium of zero density, that would mean that an object would fall infinitely fast through a void, which is an absurdity, so Aristotle concludes that there cannot be such a thing as a void. Aristotle closely identifies time with change. We register that time has passed only by registering that something has changed.
In other words, time is a measure of change just as space is a measure of distance. Just as Aristotle denies the possibility of empty space, or void, Aristotle denies the possibility of empty time, as in time that passes without anything happening. Physics: Books 5-8 Summary There are three kinds of change: generation, where something comes into being; destruction, where something is destroyed; and variation, where some attribute of a thing is changed while the thing itself remains constant.
Of the ten categories Aristotle describes in the Categories (see previous summary of the Organon), change can take place only in respect of quality, quantity, or location. Change itself is not a substance and so it cannot itself have any properties. Among other things, this means that changes themselves cannot change. Aristotle discusses the ways in which two changes may be the same or different and argues also that no two changes are opposites, but rather that rest is the opposite of change. Time, space, and movement are all continuous, and there are no fundamental units beyond which they cannot be divided.
Aristotle reasons that movement must be continuous because the alternative—that objects make infinitesimally small jumps from one place to another without occupying the intermediate space—is absurd and counterintuitive. If an object moves from point A to point B, there must be a time at which it is moving from point A to point B. If it is simply at point A at one instant and point B at the next, it cannot properly be said to have moved from the one to the other. If movement is continuous, then time and space must also be continuous, because continuous movement would not be possible if time and space consisted of discrete, indivisible atoms.
Among the connected discussions of change, rest, and continuity, Aristotle considers Zeno’s four famous paradoxes. The first is the dichotomy paradox: to get to any point, we must first travel halfway, and to get to that halfway point, we must travel half of that halfway, and to get to half of that halfway, we must first travel a half of the half of that halfway, and so on infinitely, so that, for any given distance, there is always a smaller distance to be covered first, and so we can never start moving at all.
Aristotle answers that time can be divided just as infinitely as space, so that it would take infinitely little time to cover the infinitely little space needed to get started. The second paradox is called the Achilles paradox: supposing Achilles is racing a tortoise and gives the tortoise a head start. Then by the time Achilles reaches the point the tortoise started from, the tortoise will have advanced a certain distance, and by the point Achilles advances that certain distance, the tortoise will have advanced a bit farther, and so on, so that it seems Achilles will never be able to catch up with, let alone pass, the tortoise.
Aristotle responds that the paradox assumes the existence of an actual infinity of points between Achilles and the tortoise. If there were an actual infinity—that is, if Achilles had to take account of all the infinite points he passed in catching up with the tortoise—it would indeed take an infinite amount of time for Achilles to pass the tortoise. However, there is only a potential infinity of points between Achilles and the tortoise, meaning that Achilles can cover the infinitely many points between him and the tortoise in a finite amount of time so long as he does not take account of each point along the way.
The third and fourth paradoxes, called the arrow paradox and the stadium paradox, respectively, are more obscure, but they seem to aim at proving that time and space cannot be divided into atoms. This is a position that Aristotle already agrees with, so he takes less trouble over these paradoxes. Aristotle argues that change is eternal because there cannot be a first cause of change without assuming that that cause was itself uncaused. Living things can cause change without something external acting on them, but the source of this change is internal thoughts and desires, and these thoughts and desires are provoked by external stimuli.
Arguing that time is infinite, Aristotle reasons that there cannot be a last cause, since time cannot exist without change. Next, Aristotle argues that everything that changes is changed by something external to itself. Even changes within a single animal consist of one part of the animal changing another part. Aristotle’s reflections on cause and change lead him ultimately to posit the existence of a divine unmoved mover. If we were to follow a series of causes to its source, we would find a first cause that is either an unchanged changer or a self-changing changer.
Animals are the best examples of self-changers, but they constantly come into being and pass away. If there is an eternal succession of causes, there needs to be a first cause that is also eternal, so it cannot be a self-changing animal. Since change is eternal, there must be a single cause of change that is itself eternal and continuous. The primary kind of change is movement and the primary kind of movement is circular, so this first cause must cause circular movement. This circular movement is the movement of the heavens, and it is caused by some first cause of infinite power that is above the material world.
The circular movement of the heavens is then in turn the cause of all other change in the sublunary world. Metaphysics: Books Alpha-Epsilon Knowledge consists of particular truths that we learn through experience and the general truths of art and science. Wisdom consists in understanding the most general truths of all, which are the fundamental principles and causes that govern everything. Philosophy provides the deepest understanding of the world and of divinity by pursuing the sense of wonder we feel toward reality.
There are four kinds of cause, or rather kinds of explanation, for how things are: (1) the material cause, which explains what a thing is made of; (2) the formal cause, which explains the form a thing assumes; (3) the efficient cause, which explains the process by which it came into being; and (4) the final cause, which explains the end or purpose it serves. The explanations of earlier philosophers have conformed to these four causes but not as coherently and systematically as Aristotle’s formulation.
Aristotle acknowledges that Plato’s Theory of Forms gives a strong account of the formal cause, but it fails to prove that Forms exist and to explain how objects in the physical world participate in Forms. Book Alpha the Lesser addresses some questions of method. Though we all have a natural aptitude for thinking philosophically, it is very difficult to philosophize well. The particular method of study depends on the subject being studied and the inclinations of the students.
The important thing is to have a firm grasp of method before proceeding, whatever the method. The best method is that of mathematics, but this method is not suitable for subjects where the objects of study are prone to change, as in science. Most reasoning involves causal chains, where we investigate a phenomenon by studying its causes, and then the cause of those causes, and so on. This method would be unworkable if there were infinitely long causal chains, but all causal chains are finite, meaning that there must be an uncaused first cause to every chain.
Book Beta consists of a series of fifteen metaphysical puzzles on the nature of first principles, substance, and other fundamental concepts. In each case, Aristotle presents a thesis and a contradicting antithesis, both of which could be taken as answers to the puzzle. Aristotle himself provides no answers to the puzzles but rather takes them as examples of extreme positions between which he will try to mediate throughout the rest of the Metaphysics. Book Gamma asserts that philosophy, especially metaphysics, is the study of being qua being.
That is, while other sciences investigate limited aspects of being, metaphysics investigates being itself. The study of being qua being amounts to the search into first principles and causes. Being itself is primarily identified with the idea of substance, but also with unity, plurality, and a variety of other concepts. Philosophy is also concerned with logic and the principles of demonstration, which are supremely general, and hence concerned with being itself. The most fundamental principle is the principle of noncontradiction: nothing can both be something and not be that same something.
Aristotle defends this principle by arguing that it is impossible to contradict it coherently. Connected to the principle of non-contradiction is the principle of the excluded middle, which states that there is no middle position between two contradictory positions. That is, a thing is either x or not-x, and there is no third possibility. Book Gamma concludes with an attack on several general claims of earlier philosophers: that everything is true, that everything is false, that everything is at rest, and that everything is in motion.
Book Delta consists of the definitions of about forty terms, some of which feature prominently in the rest of the Metaphysics, such as principle, cause, nature, being, and substance. The definitions specify precisely how Aristotle uses these terms and often distinguish between different uses or categories of the terms. Book Epsilon opens by distinguishing philosophy from the sciences not just on the basis of its generality but also because philosophy, unlike the sciences, takes itself as a subject of inquiry. The sciences can be divided into practical, productive, and theoretical.
The theoretical sciences can be divided further into physics, mathematics, and theology, or first philosophy, which studies first principles and causes. We can look at being in four different ways: accidental being, being as truth, the category of being, and being in actuality and potentiality. Aristotle considers the first two in book Epsilon and examines the category of being, or substance, in books Zeta and Eta, and being in actuality and potentiality in book Theta. Accidental being covers the kinds of properties that are not essential to a thing described.
For example, if a man is musical, his musicality is accidental since being musical does not define him as a man and he would still be a man even if he were not musical. Accidental being must have a kind of accidental causation, which we might associate with chance. That is, there is no necessary reason why a musical man is musical, but rather it just so happens by chance that he is musical. Being as truth covers judgments that a given proposition is true. These sorts of judgments involve mental acts, so being as truth is an affection of the mind and not a kind of being in the world.
Because accidental being is random and being as truth is only mental, they fall outside the realm of philosophy, which deals with more fundamental kinds of being. Metaphysics: Books Zeta-Eta Summary Referring back to his logical work in the Categories, Aristotle opens book Zeta by asserting that substance is the primary category of being. Instead of considering what being is, we can consider what substance is. Aristotle first rejects the idea that substance is the ultimate substrate of a thing, that which remains when all its accidental properties are stripped away.
For example, a dog is more fundamental than the color brown or the property of hairiness that are associated with it. However, if we strip away all the properties that a dog possesses, we wind up with a substrate with no properties of its own. Since this substrate has no properties, we can say nothing about it, so this substrate cannot be substance. Instead, Aristotle suggests that we consider substance as essence and concludes that substances are species. The essence of a thing is that which makes it that thing.
For example, being rational is an essential property of being human, because a human without rationality ceases to be human, but being musical is not an essential property of being human, because a human without musical skill is still human. Individual people, or dogs, or tables, contain a mixture of essential and inessential properties. Species, on the other hand—for instance, people in general, dogs in general, or tables in general—contain only essential properties. A substance can be given a definition that does not presuppose the existence of anything else.
A snub, for example, is not a substance, because we would define a snub as “a concave nose,” so our definition of snub presupposes the existence of noses. A proper definition of a thing will list only its essential properties, and Aristotle asserts that only substances have essential properties or definitions. A snub nose, by contrast, has only accidental properties—properties like redness or largeness that may hold of some snubs but not of all—and per se properties—properties like concavity, which necessarily holds of all snubs but which is not essential.
Physical objects are composites of form and matter, and Aristotle identifies substance with form. The matter of an object is the stuff that makes it up, whereas the form is the shape that stuff takes. For example, the matter in a bronze sphere is the bronze itself, and the form is the spherical shape. Aristotle argues that form is primary because form is what gives each thing its distinctive nature. Aristotle has argued that the definitions of substances cannot presuppose the existence of anything else, which raises the question of how there can be a definition that does not presuppose the existence of anything else.
Presumably, a definition divides a whole into its constituent parts—for example, a human is defined as a rational animal—which suggests that a substance must in some way presuppose the existence of its constituent parts. Aristotle distinguishes between those cases where the parts of an object or definition are prior to the whole and those cases where the whole is prior to the parts. For example, we cannot understand the parts of a circle without first understanding the concept of circle as a whole; on the other hand, we cannot understand the whole of a syllable before we understand the letters that constitute its parts.
Aristotle argues that, in the case of substance, the whole is prior to the parts. He has earlier associated substance with form and suggests that we cannot make sense of matter before we can conceive of its form. To say a substance can be divided by its definition is like saying a physical object can be divided into form and matter: this conceptual distinction is possible, but form and matter constitute an indivisible whole, and neither can exist without the other. Similarly, the parts of a definition of a substance are conceptually distinct, but they can only exist when they are joined in a substance.
Having identified substance with essence, Aristotle attacks the view that substances are universals. This attack becomes effectively an attack on Plato’s Theory of Forms, and Aristotle argues forcefully that universal Forms cannot exist prior to the individual instances of them or be properly defined and so cannot play any role in science, let alone a fundamental role. He also argues against the suggestion that substances can be genus categories, like “animal” or “plant.
” Humans and horses, unlike animals, have the property of “thisness”: the words human and horse pick out a particular kind of thing, whereas nothing particular is picked out by animal. Genuses are thus not specific enough to qualify as substances. Book Eta contains a number of loosely connected points elaborating Aristotle’s views on substance. Aristotle associates an object’s matter with its potentiality and its form with its actuality. That is, matter is potentially a certain kind of substance and becomes that substance in actuality when it takes on the form of that substance.
By associating substance with form and actuality, Aristotle infers a further connection between substance and differentia: differentia are those qualities that distinguish one species in a genus from another. Book Eta also contains reflections on the nature of names, matter, number, and definition. Metaphysics: Books Theta-Nu Summary Book Theta discusses potentiality and actuality, considering these concepts first in regard to process or change. When one thing, F, changes into another, G, we can say that F is G in potentiality, while G is G in actuality.
F changes into G only if some other agent, H, acts on it. We say that H has active potentiality and F has passive potentiality. Potentiality can be either rational or irrational, depending on whether the change is effected by a rational agent or happens naturally. Aristotle distinguishes rational potentiality from irrational potentiality, saying that rational potentiality can produce opposites. For example, the rational potentiality of medicine can produce either health or sickness, whereas the irrational potentiality of heating can produce only heat and not cold.
All potentialities must eventually be realized: if a potentiality never becomes an actuality, then we do not call it a potentiality but an impossibility. A potentiality is also determinate, meaning that it is the potential for a particular actuality and cannot realize some other actuality. While irrational potentialities are automatically triggered when active and passive potentialities come together, this is not the case with rational potentialities, as a rational agent can choose to withhold the realization of the potentiality even though it can be realized.
Aristotle identifies actuality with form, and hence substance, while identifying matter with potentiality. An uncarved piece of wood, for example, is a potential statue, and it becomes an actual statue when it is carved and thus acquires the form of a statue. Action is an actuality, but there are such things as incomplete actions, which are also the potentiality for further actions.