Ancient Philosophy. Aristotle Logic II. Propositional Attitudes. Intellectual Virtues. Virtues & Non-virtues among Propositional Attitudes

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1 2 Propositional Attitudes There are various possible states of mind that one can have relative to any particular proposition States of Mind Ancient Philosophy Without Conscious Awareness of the Proposition = Ignorance With Conscious Awareness Without Judgment about Truth = Doubt With Judgment about Truth = Judgment Aristotle Logic II Without the Recognizing the Possibility of Error Possibility of Error = Knowledge Not on the basis of On the basis of argument some argument = Conjecture = Opinion (Suspicion) 3 4 Intellectual Virtues One of these states (knowledge) is an intellectual virtue; others are not A virtue is a quality that perfects an individual Human beings can be perfected in two ways Kind of virtue perfect our leading to goodness with respect to our moral character choices & actions intellectual intellect knowledge Virtues & Non-virtues among Propositional Attitudes Νot just any judgment perfects the human intellect A judgment might be made on little evidence (ὑπολέψις, suspicio, suspicion or conjecture) That is not the best that the human mind can do A judgment on the basis of good evidence is better (δόχα, opinio, opinion) But a good argument does not provide certainty The human mind is perfected when it makes a certain judgment, one in which there is no possibility of error (ἐπιστήμη, scientia, knowledge) Jonathan Swift on Opinion As these Noble Houyhnhnms are endowed by Nature with a general Disposition to all Virtues, and have no Conceptions or Ideas of what is Evil in a rational Creature, so their grand Maxim is, to cultivate Reason, and to be wholly governed by it. I remember it was with extreme Difficulty that I could bring my Master to understand the Meaning of the Word Opinion, or how a Point could be disputable; because Reason taught us to affirm or deny only where we are certain, and beyond our Knowledge we cannot do either. Gulliver s Travels, A Voyage to the Country of the Houyhnhnms, ch. 8 Mortimer Adler makes a contrast between the Houyhnhnms & modern man here; we have trouble accepting the concept of knowledge! Sawrey Gilpin, Gulliver Addressing the Houyhnhnms (1771) 5 A place can be made for faith here: St. Thomas defines faith as Faith a habit of the mind which causes the intellect to assent to things not seen (S.T., 2a2ae, 4.1) Aristotle defends the place of a kind of natural faith: we ought to attend to the undemonstrated sayings and opinions of experienced and older people or of people of practical wisdom not less than to demonstrations; for because experience has given them an eye they see aright. (Eth.Nic. VI.11) St. Thomas mentions elsewhere (S.T., 2a2ae, 4.1) faith commonly so called, which has no reference to the beatitude we hope for as does St. Augustine (see next slide) 6

2 7 8 St. Augustine on Faith The Five Intellectual Virtues Aristotle identifies five intellectual virtues (Ethics, bk. 6.3 ff.), all of which would be included in the box labeled knowledge above: For if we attain the knowledge of present objects by the testimony of our own senses, whether internal or external, then, regarding objects remote from our own senses, we need others to bring their testimony, since we cannot know them by our own, and we credit the persons to whom the objects have been or are sensibly present. Accordingly, as in the case of visible objects which we have not seen, we trust those who have, (and likewise with all sensible objects,) so in the case of things which are perceived by the mind and spirit, i.e., which are remote from our own interior sense, it behoves us to trust those who have seen them set in that incorporeal light, or abidingly contemplate them. City of God XI.3 Concerned with that which can be otherwise Concerning things made = Art Concerning things done = Prudence Intellectual Virtues Of ordinary objects Concerned with that which cannot be otherwise Of the highest objects = Wisdom Known discursively = Scientific Knowledge Known intuitively = Intuitive Reason Greek Latin Terminology Common English Translations τέχνη ars art φρονήσις ἐπιστήμη νοῦς prudentia scientia intellectus prudence, practical wisdom science, knowledge, scientific knowledge, understanding intuition, intuitive knowledge, comprehension σοφία sapientia wisdom 9 Comments Of all these, ἐπιστήμη seems to be focal for Aristotle About τέχνη he has little to say. It is the possession of productive knowledge. The person who has it can make things. Some arts cooperate with nature (teaching, medicine, agriculture); Some do not (engineering, architecture, painting). He has much more to say about φρονήσις, concerned with practical knowledge. It is also a moral virtue and is the focus of Ethics VI. The other three are centered on speculative (or theoretical) knowledge. Of these, σοφία is distinct from the other two with respect to its object Of the remaining two, he begins with ἐπιστήμη and then introduces νοῦς once he shows that ἐπιστήμη presupposes νοῦς ( All teaching and learning that involves the use of reason comes from pre-existent knowledge. Post.An. I.1) Ἐπιστήμη & its Source So, what is ἐπιστήμη and how do we get it? Aristotle begins both the Posterior Analytics & the Topics by distinguishing two kinds of argument. These begin with different kinds of premises and produce different products. demonstration (ἀποδείχις, from which we get the word apodictic). dialectic argument Demonstration & the Posterior Analytics The Posterior Analytics takes up two topics Book I discusses demonstration. Its thesis, according to J. Barnes: the sciences are properly expounded in formal axiomatized systems. Aristotle is not the first proponent of such systems, but gives the first full philosophical account of them. Book II discusses definition. It is, on any account, one of the most brilliant, original, and influential, works in the history of philosophy; it determined the course of the philosophy of science and to some extent of science itself for two millennia; it published, developed, and explored the notion of axiomatic science Jonathan Barnes (Introduction to the 2d edition of Aristotle: Posterior Analytics, p. xii)

3 13 14 Genuine & Accidental Knowledge There are two features that distinguish genuine knowledge from a kind of accidental knowledge ἐπιστήμη is cognition (1) that the cause of the fact is indeed the cause, & (2) that things could not have been otherwise For example one does not really know that the sky is blue until one knows why the sky is blue high-energy light rays from the sun [reds & yellows] come straight through the atmosphere, but low-energy rays [blues] get scattered and end up reaching the observer from all directions & one does not fully know why a given person died if all one knows is that they got a disease from which many (but not all) people die The Source of Ἐπιστήμη Such knowledge can come from demonstration Demonstration is a kind of syllogism (that s the genus) A syllogism Aristotle defines as a discourse in which, certain things being stated, something other than what is stated follows of necessity from their being so (Pr.An. I.1 & Topics I.1) The theory of the syllogism is the topic of the Prior Analytics. The foundation of syllogistic is subsumption of a case under a rule in accordance with the dictum de omni & nullo: Derivation & Proof A demonstration is a syllogism productive of scientific knowledge. What does a syllogism have to do to produce scientific knowledge? In answering this question, Aristotle makes an important distinction, ignored by most modern logicians, between derivation from true premises and proof. The standard account of goodness in arguments is that a good argument has two features, which make the argument sound valid form true premises. Examples of sound arguments would thus include Barack Obama is president, therefore Barack Obama is president! But that s not a good argument. It begs the question it asks one to grant precisely what was supposed to be proven. Criteria of a Demonstration Demonstration is a syllogism whose premises are true that makes the argument sound, but is not enough to make it a demonstration first & immediate with respect to the conclusion prior to it better known than it (or, more knowable (intelligible) than it) & cause of it (or, explanatory of it) Two Kinds of Priority Two of these criteria prior to & better known than are ambiguous, depending on what order one has in mind. Priority can be in any order (cf. Categories 12). In the order of knowing, what we see is better known to us (& thus also prior relative to us) than the cause of what we see. For example, the blueness of the sky is better known to us than the laws of the diffraction of light. In the order of being, the universal causes are prior to &, according to Aristotle, in some sense ( naturally or absolutely ) better known than the effect (which we see). For example, the laws of diffraction are prior to the blueness of the sky, which is just an application of them to a particular situation. Two Kinds of Demonstration On the basis of that ambiguity, two kinds of syllogism must be distinguished. Based on the order of knowing demonstration of the fact (ὅτι, quia) from what is better known in itself (the cause) to what is better known to us Based on the order of being demonstration of reasoned fact (διότι, propter quid) or explanatory demonstration from what is better known to us to the cause (which is better known in itself) Examples Aristotle s classic example facts about planets Another example the sphericity of the earth

4 Aristotle on Planets Demonstration of the fact that the planets are near 1. All non-twinkling lights are near to us. 2. All planets are non-twinkling lights. 3. So, all planets are near to us. Explanatory demonstration of why planets don t twinkle 1. Νο light that is near to us twinkles. 3. All planets are near to us. 2. So, nο planets twinkle. 19 Sphericity of the Earth: Demonstration of the Fact Surface of the Sea Spherical. That the water has a bulge and is approximately round is shown thus: Let a signal be set up on the seacoast and a ship leave port and sail away so far that the eye of a person standing at the foot of the mast can no longer discern the signal. Yet if the ship is stopped, the eye of the same person, if he has climbed to the top of the mast, will see the signal clearly. Yet the eye of a person at the bottom of the mast ought to see the signal better than he who is at the top, as is shown by drawing straight lines from both to the signal. And there is no other explanation of this thing than the bulge of the water. For all other impediments are excluded, such as clouds and rising vapors. John Sacrobosco, Tractatus on the Sphere (c.1230) Any body on which ships lose sight of a tower on the shore this way are spherical. The earth is a body on which lose sight of a tower on the shore this way. So, the earth is spherical Demonstration of the Reasoned Fact Any bodies composed of parts all of which have an equal tendency to move to its center are spherical The earth is a body composed of parts all of which have an equal tendency to move to its center So, the earth is spherical. On the Heavens II.14 Note that in 2006, the IAU defined a planet as a body which: 1.is in orbit around the Sun. 2.is massive enough to be a sphere by its own gravitational force; & 3.has cleared the neighborhood around its orbit. The Insufficiency of Demonstration But not all knowledge can come from demonstration (Post.An. I.3) Aristotle rejects two alternatives That there is no knowledge. The argument for this thesis would be: 1. All syllogisms that have premises that are themselves undemonstrated do not secure their foundations. 2. No syllogisms that do not have secure foundations provide knowledge. 3. So, No syllogisms that have premises that are themselves undemonstrated provide knowledge. 4. Any argument all of whose premises are demonstrated without reliance on undemonstrated premises is an argument which leads to an infinite regress, which is impossible. 5. So, there is no knowledge That there is knowledge, but that all truths are demonstrable. This depends upon demonstration being circular or reciprocal, which Aristotle rejects. He argues that not all knowledge depends on demonstration. This makes another access to principles necessary. Hence, another virtue νοῦς (intuitive understanding) the virtue by which we know the postulates of geometry Euclid s Elements the great success story Demonstration & Mathematics From a few basic distinctively geometrical postulates & common notions, Postulates 1. To draw a straight line from any point to any point. 2. To produce a finite straight line continuously in a straight line. 3. To describe a circle with any center and distance. 4. That all right angles are equal to one another. 5. That, if a straight line falling on two straight lines make the interior on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles. Common Notions 1. Things which are equal to the same thing are also equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be subtracted from equals, the remainders are equal. 4. Things which coincide with one another are equal to one another. 5. The whole is greater than the part. he deduced many amazing geometrical truths Demonstration & Mathematics (cont d.) I.47 [The Pythagorean Theorem:] In rightangled triangles the square on the side opposite the right angle equals the sum of the squares on the sides containing the right angle. Remark to XIII.18 No other figure, besides the said five figures [sc., pyramid, octahedron, cube, icosahedron, & dodecahedron; cf. XIII.13-17], can be constructed by equilateral and equiangular figures equal to one another.

5 The Appeal of Euclid: Thomas Hobbes 25 The Appeal of Euclid: Bertrand Russell 26 He was 40 years old before he looked in on Geometry; which happened accidentally. Being in a Gentleman s Library, Euclid s Elements lay open, and twas the 47 El. libri I [the Pythagorian Theorem]. He read the Proposition. By G, sayd he (he would now and then swear an emphaticall Oath by way of emphasis) this is impossible! So he reads the Demonstration of it, which referred him back to such a Proposition; which proposition he read. That referred him back to another, which he also read. Et sic deinceps that at last he was demonstratively convinced of that trueth. This made him in love with Geometry. At the age of eleven, I began Euclid, with my brother as tutor. This was one of the great events of my life, as dazzling as first love. John Aubrey on Thomas Hobbes in his Brief Lives The Appeal of Euclid: Albert Einstein 27 The Appeal of Euclid: Edna St. Vincent Millay 28 At the age of 12 I experienced a second wonder of a totally different nature: in a little book dealing with Euclidean plane geometry, which came into my hands at the beginning of a school year. Here were assertions, as for example the intersection of the three altitudes of a triangle in one point, which though by no means evident could nevertheless be proved with such certainty that any doubt appeared to be out of the question. This lucidity and certainty made an indescribable impression upon me. For example I remember that an uncle told me the Pythagorean theorem before the holy geometry booklet had come into my hands. After much effort I succeeded in proving this theorem on the basis of the similarity of triangles for anyone who experiences [these feelings] for the first time, it is marvelous enough that man is capable at all to reach such a degree of certainty and purity in pure thinking as the Greeks showed us for the first time to be possible in geometry. Euclid alone has looked on Beauty bare. Let all who prate of Beauty hold their peace, And lay them prone upon the earth and cease To ponder on themselves, the while they stare At nothing, intricately drawn nowhere In shapes of shifting lineage; let geese Gabble and hiss, but heroes seek release From dusty bondage into luminous air. O blinding hour, O holy, terrible day, When first the shaft into his vision shone Of light anatomized! Euclid alone Has looked on Beauty bare. Fortunate they Who, though once only and then but far away, Have heard her massive sandal set on stone Demonstration & Theology Can there be a demonstrative knowledge of nature? St. Thomas asks (Summa Theologiae, 1a, 1.2) whether sacred doctrine is a science He means, does it provide knowledge by demonstration? He answers that it is like a science in some ways It does demonstrate conclusions from premises. But it is unlike it in others Its premises are known by faith, not by νοῦς. Aristotle s biological works are not organized this way, which has been the cause of much comment. Aristotle wrote (Part.An. I.6): These preceding statements, then, have been put forward thus in a general way, as a kind of foretaste of the number of subjects and of the properties that we have to consider in order that we may first get a clear notion of distinctive character and common properties. By and by we shall discuss these matters with greater minuteness. After this we shall pass on to the discussion of causes [explanations]. For to do this when the investigation of the details is complete is the proper and natural method, and that whereby the subjects and the premisses of our demonstration will afterwards be rendered plain. Barnes suggests that the History of Animals does the collection of facts. the Parts of Animals & the Generation of Animals offer explanations Aristotle does not get to demonstrations.

6 31 32 Hypothetico-deductive Reasoning & the New Science Galileo, Demonstration & the Hypothetico-Deductive Method In attempting to explain a set of facts, one proposes an hypothesis (theory) that explains the facts (i.e., a simple coherent account from which the facts can be predicted) what was really needed [in the nineteenth century] was a logical system that would allow physicists to truly understand why the atom behaved as it did, so that they could successfully predict not only the atom s observed behavior but new phenomena that had not yet been observed. Physicists call such a logical system a theory. This word is much misunderstood by non-scientists. When a physicist talks about a theory, he does not mean a hunch, guess, or unproven hypothesis. He means a logical system of ideas that ties together a large number of observations of the real world into a coherent and understandable pattern. Galileo makes early use of this method. One of the causes of his problems was that the Church still subscribed to the Aristotelian standard as a criterion for when a non-literal (i.e., metaphorical) interpretation of Scripture was to be preferred to a more literal interpretation found in the Church Fathers. Galileo first offered only a hypotheticodeductive argument for Copernicanism. He later attempted to meet the higher standard, but his arguments were not demonstrations Sheldon Glashow, Interactions, p. 51 St. Robert Bellarmine & Scientific Reasoning 33 Another Challenge to the Demonstrative Ideal 34 Second, I say that, as you know, the Council [of Trent] prohibits expounding the Scriptures contrary to the common agreement of the holy Fathers. And if Your Reverence would read not only the Fathers but also the commentaries of modern writers on Genesis, Psalms, Ecclesiastes and Josue, you would find that all agree in explaining literally (ad litteram) that the sun is in the heavens and moves swiftly around the earth, and that the earth is far from the heavens and stands immobile in the center of the universe. Third, I say that if there were a true demonstration that the sun was in the center of the universe and the earth in the third sphere, and that the sun did not travel around the earth but the earth circled the sun, then it would be necessary to proceed with great caution in explaining the passages of Scripture which seemed contrary, and we would rather have to say that we did not understand them than to say that something was false which has been demonstrated. But I do not believe that there is any such demonstration; none has been shown to me. It is not the same thing to show that the appearances are saved by assuming that the sun really is in the center and the earth in the heavens. I believe that the first demonstration might exist, but I have grave doubts about the second, and in a case of doubt, one may not depart from the Scriptures as explained by the holy Fathers. The significance of micro-structure suggests another problem for the complete adequacy of Aristotle s method The principles of atomic theory are not known by direct experience of atoms. 1. Compounds are an assemblage of discrete units called molecules. 2. There is a smallest unit of any element that may enter into chemical combinations (atoms). a. Atoms of the same element are all alike. b. Atoms of different elements have different masses and differ in their chemical and physical behavior. 3. Every molecule is a combination of a definite number of particular kinds of atoms. a. Molecules of the same compound have the same composition. b. The mass of a molecule is the sum of the masses of the atoms that it contains. 4. In chemical reactions, atoms are combined, separated, or reshuffled, but never created or destroyed. John Dalton ( ) Another Challenge to the Demonstrative Ideal 35 Dialectic & the Topics 36 But scientific explanation in terms of microstructure approximates the demonstrative ideal. In atomic theory, the facts of chemical combination, &c. are deduced from the principles of atomic theory. These principles are consistent with other things we know about the world as fundamental as we can think of prior in the order of being in some sense simpler true first & immediate prior to the facts more intelligible than the facts Dialectic argument takes generally accepted propositions as premises Dialectic argument produces either of two things Ideally, it lays the foundation for νοῦς. Falling short of that it produces opinion. It takes a proposition beyond the quality of conjecture (assent based on slight causes), but does not turn it into knowledge (as it leaves open the possibility of error). Much of what one sees by νοῦς would be the defintions of things (statements of their natures). So, much of the Topics is devoted to securing definitions. It is in that context that Aristotle distinguishes definitions from other things that can be predicated. cause of the facts cause of the facts

7 37 38 The Five Predicables The Predicables Definition Specific Difference Property Genus Accident Definition According to Aristotle, a definition is a statement of the essence of a thing. Its form is always genus + specific difference. In a definition, the term being defined and the definition convert. E.g., man is (by definition) a rational [specific difference] animal [genus]. Specific Difference This is a part of the definition. Genus Something in the category of substance & predicated of several things of different kind. For example, animal is in the category of substance & is predicated of man, sheep, & ox, 39 Property The Predicables (cont d.) Something that does not show a thing s essence but belongs to that thing alone (& therefore is convertible with it) Some properties are absolute, being grounded in the thing s essence For example, being a used of language is a property of man Accident Aristotle offers two definitions of accident (1) anything which is not definition, property, or genus (2) anything that can belong or not belong to the thing These definitions are not equivalent. Aristotle prefers the second because it is not negative it tells what an accident is, rather than what it is not.