Sophia and Robert sat waiting for their Philosophy lecture to begin. The notice board had announced the fact that today’s lecture entitled “Epistemology” would be a double lecture to compensate for the previous cancellation. There were two minutes remaining but no one in the class expected the lecture to begin on time and Jude’s entrance as a consequence passed almost unnoticed. The lecture began exactly on time:
“Epistemology, or Theory of Knowledge is one of the traditional divisions of Philosophy along with Metaphysics, Ethics, Political Philosophy, and Logic. It has been the area of Philosophy most susceptible to influence from Science. It may be too soon to tell, but this century may go down in history as being the Third Major Revolution in the History of Philosophy: the first two revolutions having been initiated by Aristotle and Kant respectively. It is always notoriously difficult to point to exactly when a revolution began, and by the way, as revolutions go this one compared with the other two is a minor affair, but I would suggest that, when Bertrand Russell tried to reduce Mathematics to Logic and then subsequently Logicians went on to use Logic to dismantle much of what had been previously established in Metaphysics and Ethics, this was the firing of the first shot by rebel troops across the bows of traditional philosophy. Prior to this of course Science had been surreptitiously undermining the above key areas of thinking and this state of affairs culminated in the establishment of the school of the Logical Positivists. Science allied itself with Logic and Epistemology in the positivist school, and proceeded to colonise every area of knowledge: dismantling religion, politics, and aesthetics on the way. The resultant philosophical landscape was as open and barren as a desert, with cultural sand-atoms lying juxtaposed ad infinitum in all directions and being shifted only by the winds of scientific and logical methodologies. Almost everything erected by the architects of Aristotle and Kant and their followers had been levelled and all that could be heard in the desert was the wind of the talk of the existence and quantities of X. An American logician by the name of Willard van Orman Quine, inspired by logic and the scientific project claimed: “To be is to be the value of a variable”. In such terminology one can detect the presence of the wraith of a Philosopher who distrusts European metaphysics. Philosophy then responded with the work of Wittgenstein who, in his earlier work spoke for the opposition, but was stopped in his tracks by the collective tonnage of argument from the traditional philosophers. The later Wittgenstein subsequently began restoring the landscape of traditional Philosophy from his base at Trinity College Cambridge where I met him. His restoration of archaic concepts and arguments from the ancient Greeks and the Enlightenment period, occurred in his posthumous works. This restoration work was performed of course with the tools from Wittgenstein’s toolbox.
In last week’s lecture we talked of certainty and the difficulty of specifying the criteria that provide the truth conditions of the physical world. Descartes in response to scientific and mathematical methodologies felt the philosophical landscape being eroded and began to dig the grave of metaphysics by locating certainty epistemologically in an “I”, which thinks. “Cogito ergo sum”, he famously argued: “I think therefore I am. Perhaps he too, like at least one of the pre-Socratics who were responding to the natural philosophers of their time, thought that everything of importance was located in the mind. But like Plato, a fellow traveler, Descartes was a mathematician who surpassed his predecessor by resting his case on methodology. He rested his case on what some commentators have referred to as a skeptical methodology that may be a contradiction, if a methodology’s primary purpose is to coordinate facts and principles systematically. In connection with this point we should also note that a certain kind of mathematician seems to believe only in those ideas he has constructed himself. He “knows” 7+5=12 because he knows the rule for the construction of seven, he also knows the rule for the use of “the plus operation” which requires moving sequentially in the system of numbers, five times. The answer “twelve” then presents itself for inspection like the time on the face of a clock. In this constructed world there is no room for mistakes. Everything works with the precision of the military. We should not forget that Descartes was also a military man who would sometimes search for wars to fight in. The man who could die the next moment, ladies and gentlemen, has no use for ethics or metaphysics. Everything is a variable with a possibly varying value. Logically, a variable is a quantity. What else is a desert, ladies and gentlemen, than a quantity of sand? The desert traditionally is the place to look for God. For Descartes, only God could assure us that our calculations and thought-experiments were not the doings of an evil-demon intent upon imprisoning us in a bubble of false certainty. On Descartes’ right shoulder sat a priest in clerical robes calling out in a desert for God. On his left shoulder sat a philosopher in Grecian robes calling for justice and wisdom, trying to navigate away from the desert of atoms and numbers to a human world. But Descartes never made it out of the desert and settled firstly, for a lone thinker thinking about his landscape, and secondly, for the importance of his own thinking. Descartes’ “Cogito” argument, ladies and gentlemen, was the result of this cocktail of Religion, Mathematics, Science, Psychology and Philosophy. “I think therefore I am” is an epistemological argument, an argument in the theory of knowledge. The argument is solipsistic, a lone predator in a philosophical wilderness and because of this it is unable to acknowledge any of the ethical truths of Socrates, Plato or Aristotle.”
Mark Cavendish, raised his hand and asked:
“But surely there is a great deal of truth in the solipsistic system of Descartes. Take the 30 people sitting here with their thoughts. For all we know everyone is interpreting what you are saying in their individual ways and everyone will take their own truths from this class”
“Well”, “Jude answered, “If that were true, teachers would be redundant: at best our words would be stimuli to be responded to. A collective of solipsists does not a class or a society or a course in philosophy make. We are all sitting here for a collective reason or purpose. The words I utter have a collective reason or purpose because of their content and context. I am, however, inclined to agree with you that there is an individual, psychological component that probably relates to the way in which we understand the content. But there is a very important ethical element in this collective image and that refers to the products of reason that relate to how we ought to live and perhaps also, to how we ought to think. Aristotle made significant philosophical contributions to both of these aspects of our collective image of the teaching situation via his writings on Logic and Ethics.”
A Mathematics major raised his hand tentatively and asked:
“I do not quite understand your objection to the Mathematical claim that reality contains quantities best measured by our number system.
“It’s a long story, but one of my objections would consist in questioning whether we can, in fact, reduce the qualities we are experiencing in reality to quantities. I am sure some of you have come across the following example in the literature for this course: It is claimed by scientific reductionists that “Red is 690 Angström units”. The “is” in that formulation functions logically more like the “is” of identity than the “is” of predication simply because the units must logically be quantities and the quantities involved here seem to be quantities of angstrom units rather than the quality of red. Put more simply, I do not believe that scientific or mathematical characterisation or quantification of qualities are in any sense, essence specifying. The only sensible way to analyse the statement “Red is 690 Angström units”, in my opinion, is to regard it as a “hypothetical”, for example, “If color is measurable in a particular measuring system then red may be 690 Angström units..”. However in retreating to the realm of the quantitatively possible or the hypothetical, we lose the relation to the categorical truth that Aristotle maintained it was the task of science to demonstrate. According to Aristotle, Science should tell us categorically what kind of thing is in the universe. Imaginative hypotheticals belong to the realm of the possibly true and the possibly false.”
The student continued:
“Let’s confine ourselves to Mathematics and the Pythagorean claim that reality is mathematical. Surely there is nothing hypothetical about that claim”
“Good point. The Pythagoreans claim that the qualitative experiences we have of the harmony of harp strings is describable by the relation between numbers and there is also as you say a categorical claim to the effect that reality is mathematical. I pluck the strings of the harp and the sound waves emitted are then measured by a scientist in the vicinity of the vibrations. He also notes, or knows, that the sound waves are an effect of the vibration of the strings. These are the first links in a chain of phenomena which are required if we are to be permitted to speak categorically about the qualitative harmony of the qualitative notes heard by a listener in the vicinity of the vibrations. Of course the listener may have been listening to a novice learning to play the harp and the sound/notes may not have a harmonic quality at all: but even in this case there is no motivation to reduce the experience to its quantitative measurable characteristics. Why? The scientist is actually measuring waves of vibration and in doing so could conceivably ignore the sound as heard by any listener. If this makes sense then the two are not identical. Sound is received and processed by our perceptual system that can of course operate quantitatively. We complain, for example, that the sound is too loud or too low. Notwithstanding this observation, the primary purpose or telos of our perceptual system, is to detect change in general but also to discriminate, to detect differences between entities. We hear, for example, that one note is different to another, that these notes are harmonic and those are not. In arguing about the differences between the quantitative and the qualitative we refer to what Aristotle called categories of being. For him, Being had many meanings of which the meaning “substantial being”, was at one point in his work the most important. The quantitative and the qualitative are two aspects of being or reality. The quantitative aspect of reality is certainly the concern of the physical or natural scientist. The mathematician, for example, may concern himself with the structure of space and time that may well be infinite if Pythagoras is right about our number and geometrical systems being a reflection of reality and its infinite structure. Another aspect of reality is qualitative: this aspect is concerned with the way in which our perceptual system organises physical phenomena into a system of differences, using perceptual difference as the criterion: red is different to blue which is different to yellow, which is different to green and each is different to every other. This is just one chapter of a long story. So, to cut this long story short I will just say that in answer to your question I would admit that space and time is probably best described quantitatively using the tools of the mathematician. I might be prepared to concede that matter is also potentially infinite in a number of respects and is best described and explained using the instruments of the scientist. But this admission does not rule out that space and time can and perhaps should be investigated qualitatively—in terms of our experience of them. Here the long stories of the great novelists might contribute to this kind of investigation. The lived space and time of the body and its body image might, to take another example, be usefully investigated by phenomenological psychologists such as Merleau-Ponty. Finally, the lived space and time of a consciousness oriented towards the memory of its past and towards the future of its projects might be usefully investigated by existential psychologists such as Sartre and Heidegger.
In short I agree with Aristotle that there are many different kinds of explanation as to why reality is as it is. Some explanations will have a quantitative character and some will have a qualitative character. As a matter of fact, one might believe, as many philosophers have done, that the qualitative explanations may be more philosophically interesting.
Robert put up his hand and asked:
“Have you given us a complete argument for the existence of qualities and how is this relevant to the relation between epistemology and metaphysics?”
“Upon being confronted by something which is aqua-marine blue a philosopher might ask “What is aqua-marine blue?” and receive the obvious answer that it is a shade of a colour. The philosopher may then ask: “What is colour?” and receive the answer “A quality”. The answers up to this point may be within the scope and limits of our knowledge. The further question: “What is a quality?” and its answer: “A quality is a quality of something real” may take us into the realm of metaphysics, the realm which Heidegger designates as the study of being qua being. So, in answer to your question the answer “A quality” may be an epistemological terminus of the questioning. In other words that something is a quality is an epistemological justification for it being a colour. An epistemologist may not be able to justify that colours exist but he can justify that red or aqua marine are colours. The interesting question here is whether it makes sense to ask whether qualities exist. I will leave this open.
The Mathematics major raised his hand again:
“Ok I understand it is difficult to state categorically what the relation of Mathematics to reality is, but it seems to me that Mathematics is a system of knowledge that has its own methods of justification for the truth of its claims, if we exclude for the moment the ultimate justifications for mathematical truth. Surely there is not much doubt that 7+5=12 is true”
“Yes I take your point but let me in the name of leaving that question open, challenge you with a question on an epistemological level: Would you want to claim, for example, that “7+5=12 is true” has a more secure justification than the statement, “Michelangelo’s sculpture “Times of the Day” is a beautiful work of art”
“Well disputes about 7+5=12 don’t break out amongst mathematicians as they seem to do among art critics or the general population”
“Good point. You are appealing to the principle of inter-subjective agreement amongst mathematicians who are in agreement over the methods they use to solve even more difficult problems than that raised by the issue of what the sum of 7 plus 5 amounts to. Thus far we are in agreement. With respect to the judgment about whether an art object is beautiful or not, I think we are in the realm of whether a technical activity has uniquely created a universal feeling that one can speak with a universal inter-subjective voice about. This realm requires an understanding of the Greek terms techné and arête as well as how the ideas of the good or the excellent organises perception and action. Art as distinct from craft is curious in that it is a deliberated-upon series of action which does not call for action on the part of the spectator: the call is for a suspension of any commitment to action, an activation of perception and thought which in turn should “quicken”(to use Kant’s term) in the appreciator a general attitude about our lives. This attitude is referred to in Wittgenstein’s earlier work by the term sub specie aeternitatis, a term that means looking at the world in wonder and seeing it under the aspect of the timeless. Kant in his work the “Critique of Judgment” described this attitude in terms of a boundless happy outlook on life. Now perhaps a mathematician may wish to claim that 7+5=12 is a timeless truth, a truth for all time. What the mathematician means by this is that nothing can happen in the world to change a 7 into a 6 or into an 8: similarly nothing could happen in the application of the operation +5 so that instead of landing on 12 when applied to 7 it lands on 11 or 13 instead. The happenings in the world are irrelevant to numbers once they have been inserted into a framework of calculation. A temperature may change from 15 degrees centigrade to 20 degrees centigrade but the number 15 cannot change into the number 20, unless it is inserted into an equation: e.g. 15+5=20. But even in this case it does seem somewhat odd to insist that the number 15 has changed into the number 20. Numbers are differentials, discrete entities, and it would seem therefore to be more natural to insist that the number 15 retains its identity even after undergoing the operation of the addition of 5. To illustrate this, imagine I am given the task of counting the cows in two towns. I discover 15 cows in Plymouth and 5 cows in Exeter. In the report I write that there are a total of 20 cows in the two towns but surely somewhere in the report I refer to the 15 cows in Plymouth and the 5 cows in Exeter. Here it seems that the number of objects engages with the concept of identity but I nevertheless think it is an open question whether the identity of the number, the 15 cows from Plymouth, is part of the space time continuum, or whether it is part of the thought quantifying the space time continuum. Many philosophers in relation to this question would side with the critical idealists against the Pythagorean realists, the latter rather than the former “
Robert raised his hand again:
“But is it merely the agreement of a community of mathematicians which justifies the truth of 7+5=12? Surely the mere existence of an activity or group of activities cannot make something true? Is it not rather the Scientist who is the true follower of Pythagoras? If a scientist claims that All Swans are white and reality throws up a non-white swan, the claim has to be abandoned. Reality is the standard by which he measures his truth claims.”
“And yet Plato, dedicated follower of Pythagoras that he was, seeks his standard not in the fluctuating ever changing stream of reality but rather in the forms the mind uses to understand reality. But I take your point, because perhaps it is Aristotle who is the true follower of Pythagoras and because Plato could not philosophically explain how the forms came to be in the mind. His pupil Aristotle took the plunge and insisted that the forms are out there in the ever-fluctuating river of reality. He saw the order in these processes of fluctuating change, an order he claimed was produced by the essence of things: essences that make things what they are. This order is tracked by our thought enabling the concepts we use to classify and categorise events in the world to be combined in what Heidegger called a veritative or truth making synthesis. Reality gives rise to classification and categorisation that in turn gives rise to the truth of our statements. Aristotle saw that the problem with Plato’s forms was the fact that they disguised the different metaphysical weights different forms possessed. The two statements “Heraclitus is pale” and “Heraclitus is human” have basically the same metaphysical status for Plato. There is this metaphysical form of paleness and Heraclitus is a part of this form or participates in it. He participates in the form of Humanity in similar fashion. Aristotle saw that these two statements have very different logical implications. Heraclitus spends a day on the beach and is tanned as a result and everyone complements him on his healthy tan. No one regrets the loss of his paleness. On the other hand, were Heraclitus to lose his humanity everyone who knew him would regret this loss. Confronted by the non-human remnant of Heraclitus, there may even be a reluctance to use his name to call him. Whatever we are now confronted with would belong to some other category of reality than human substance. We know that Heraclitus himself thought that he had lost his humanity and had become a divine being. Aristotle’s world is constituted of a manifold of essences and in this account reality is quite clearly the standard bearer of our knowledge of the physical world. My objection to your claim that modern scientists are the true followers of Pythagoras is simply that I wonder whether Pythagoras would subscribe to the reductionism we see in modern science. The categories of substance, quality, action, time and place are ruthlessly reduced to the categories of quantity and relation. Pythagoras made no statements about the humanity of harp players. He was concerned to describe and explain the physical vibrations of the harp strings and the relation of these vibrations to the experienced harmony of sounds produced.
Sophia raised her hand
“Can you give us a concrete example of how the combinations of terms belonging to different categories can generate Truth?”
Take the two expressions “Parmenides” and “is swimming”. Hopefully we all agree that these two expressions refer to different kinds of things in reality—firstly, what Aristotle called human substance and second, the action of a living creature possessing a body with arms and legs. Combine these two terms into one and you get “Parmenides is swimming”: this is a proposition that claims something to be true of or in reality. This can be demonstrated by asking what makes this statement true. Clearly Parmenides walking up a hill will not make the statement true and the observation that Heraclitus is swimming in the river will also not make the statement true: only certain very specific events occurring in combination in reality will suffice to make the statement true. Parmenides, that particular form of human substance possessing arms and legs that he uses to swim across the river is what is needed. In other words reality needs to manifest firstly the criteria for the existence of this particular form of human substance we call Parmenides and secondly the criteria for that activity or action we call swimming.
Robert raised his hand:
“How would you characterise human substance? Does it take the place of Platonic forms in Aristotle’s system?”
“In a sense, yes. All other categories depend upon substance for their existence. You cannot, for example have swimming without some human or animal-like substance doing the swimming. The substance that Parmenides possesses is not shareable amongst a number of things but this substance is a bearer of properties that are shareable. Parmenides may, for example weigh more than 65 kilograms and this may be true of many other human substances. If we see him walking up the hill after his swim we may ask the question “What is it?” and there are two possible answers: “Parmenides” or “a human being”. The latter answer refers to what Aristotle would refer to as the formal cause of “Parmenides”.
The Mathematics major raised his hand:
“What kind of substance is number, then?”
“Mathematicians speak of the cardinal and ordinal aspects of the number system and some have defined its cardinal aspect in quantitative terms and some have defined the ordinal aspect of the number system in relational terms. The philosopher when confronted with these two aspects, of course begins to wonder whether one aspect is the primary aspect and the other secondary. One route we can use to investigate this matter would be to ask the questions “Quantities of what?” “Relations between what?” The answer some mathematicians have been inclined to give in both cases is “Units”. The quantities are quantities of ones and relations are relations with respect to a sequence of ones. Quantities seem then to be generated by an operation or rule n plus one. This rule can be seen to be ruling the idiosyncratic fluctuations of the stream of events in reality by measuring it in terms of the same plus the same. Thus, imposing a unitary measure on the before’s and after’s in relation to time. We should notice here the relation of the terms “unit” and “unitary”. It was an ancient dream of Parmenides and perhaps of some philosophers coming after him to gather all difference and plurality in the world into the “One”, the “unitary”. Condense everything into one point. Now we can imagine the entrance of Pythagoras and his reflections into the debate on the relations between a starting point and a resting point: an operation, which generates an actual straight line from two potential mathematical points. And from lines we can generate triangles and even circles and every imaginable and conceivable shape except perhaps square circles. So what we have is a continuous space made up of points lacking extension and a time made up of mathematical units each following upon one another, capable of measuring vast extents of past and future time, maybe even up to infinity. This space can of course be divided up into discrete parcels with both concepts and numbers and the continuous motion of certain physical processes is clear evidence that time is continuous. Some mathematicians believe of course, that the structures of space and time have been “discovered”. Perhaps it has been easier to explore their discreteness rather than their continuous nature. And if everything that happens, must happen in space and time, then it is small step to take, to claim that what has been discovered is the structure of the world, is a structure which has been constructed by points and numbers out of given continua. The claim is that everything in space and time is measurable and the question then becomes, are things determinable in their existence only because they are measurable, or are the forms of things more than the quantities and relations that can be predicable of them. To return to one of the examples discussed earlier we can now ask: does the sound of the harp require not just the form that organises vibrations in the air when strings are plucked, but also the form of a perceptual apparatus that can experience sounds: sounds which are not just experienced as too loud or too low but also harmonious: as organised in time in accordance with qualitative rules which state, for example, that the three sounds I am now hearing build a harmonious theme together and are therefore more than just noises occurring in the world.”
A music major raised his hand and asked:
“But where is the substance? Are you saying it is the human musician that chooses to create three sounds. Is substance the human intention to produce a harmonious constellation?”
“Excellent answer to your own question. The human musical agent familiar with the art he has been trained in, that is, the musician, has been trained to realise or actualise the musical forms he has learned, perhaps as a consequence of a lifetime of striving to produce melodious or harmonious themes pleasant to the ear and congruent with that attitude of mind Kant described as a boundless outlook onto a happy future. On the basis of this training the artist intends to produce pleasure with his creations. Aristotle, in similar vein, might have claimed that the pleasure which supervenes upon the hearing of the musicians melodious or harmonious creations is partly caused by the appreciator learning how sound can be organised in time and is partly constitutive of eudaimonia or the flourishing life.
“But”, the music major continued, “Not everyone appreciates good music”.
“Agreed. I don think we can suggest that 7+5=12 is good mathematics. It is just mathematics. But I am sure a mathematics teacher might put a comment on a student assignment: “ a good answer”, “ a good proof” etc. In doing this he is probably expressing an attitude towards the skill the pupil is demonstrating. What we need to bear in mind here, however, is that the comment by the teacher is designed to initiate the pupil into the form of life of mathematics. I think I have been unclear here and you have as a consequence shifted amongst the meanings of good. The harmonious three notes from the harp is good music in a different sense from the sense of “good” you are referring to. But since my lack of clarity has caused this, let me stipulate that we are talking about a good piece of music in your sense. Could we then reasonably say that there could be disagreement in attitude toward the music? So, let us take an example of Mozart’s music. Surely one could imagine different attitudes to the music, one listener, finding it boring, another finding the music wonderful. I don’t think that any appreciator would be able to argue coherently that Mozart’s music is not good in the sense you mean. I do not deny that it is possible for someone to personally not like the piece in question. But such a response in the above circumstances must be a personal response and by definition fails to meet the criteria of the general disinterested attitude great composers expect from their audience. This disinterested attitude entails that one abstract from one’s personal likes and dislikes and apply established norms and standards to the art works one encounters. One may also be speaking comparatively and believe other music is more interesting. But even this would probably be a personal comparison and not meet the criteria of the general disinterested attitude that constitutes good taste. There may be radical disagreement over the work of a composer who does not set out with the intentions to create in their audience this general disinterested attitude but instead is perhaps aiming to arouse a nationalistic sentiment. In this case, one could imagine a critic criticising the music for not possessing a genuine artistic intention. We are now in the realm of aesthetic judgments, which are judgments about artistic action or activity. Music is interesting in that it can be performed. This fact introduces an interesting aspect of Art, namely, that a great violinist of the day can imitate Mozart. Shakespeare’s plays are also imitations of great tragedies from which we can learn much about reality. Perhaps someone might want to say that we can learn more from history than we can from Shakespeare’s plays and I would question this by pointing out that the narratives of art explore the continuum of everyday life more than narrative history does. History we should bear in mind dissects the continuum into discrete events and focuses on events of magnitude which politicians for example must pay attention to. However, the everyday continuum is the medium in which most people live their lives and it is partly the responsibility of Art to present events which everyman can learn something from. It should also be pointed out that we could learn theoretically by coming to understand something and we can learn practically by appreciating for example that good actions have good consequences and tragic actions have tragic consequences. This is the practical and ethical logic which inhabits much of our literary and performing arts.”
An Arts student asked:
“But is all art attempting to imitate reality in order to learn something from it. Is there not art which has a purely cathartic intention—purifying the emotions of the tribe, so to speak”
Interesting question. Which takes us into the realms of Psychology and the emotions. There is a psychological theory, which is not defended by academics but maintains that the mere experiencing of an emotion is beneficial for mental health. Let’s take a crude example. Say someone insults me. It is better, it is argued, for me to demonstrate my anger in response to the insult than to bottle it up, either going home and then beating up my wife or not expressing the anger at all and dropping dead of a heart attack at 50. This is called popular comparative psychology and it certainly does not meet the criteria of more academic philosophical psychology which believes that emotions can and should be tempered by reason, i.e. it is better to view the insult with the right attitude: either disdain or indifference if it is unmotivated, and either embarrassment or of purely cognitive interest if it is motivated. But in response to this it might be claimed that if one is going to teach a temperamental child to control their emotions, art may be able to play a role here. Seeing King Lear trying to call forth love from his three daughters by the bribe of a kingdom and the tragic consequences of such an act might be a useful learning episode in a man’s ethical development. Everything depends here on what is meant by “cathartic”. The mere repetition or feeling of an emotion produces no desirable effect unless it occurs in some kind of reflective or intellectual context enabling the experiencer to create a psychological distance to the feeling. Indeed habitually expressing anger at insults, for example, may merely serve to habituate the behavior which, in accordance with practical and ethical logic and over long periods of time lead to misfortune”
Robert raised his hand:
“You referred to ethical development and you have argued previously that ethics is objective and its objectivity is connected to concepts embedded in what you called the ought-system of concepts. But surely our aesthetic judgments must be subjective, a matter of feeling or emotion!”
“Yes, thank you Robert for your point. I have been using a large brush to represent emotion when much finer strokes are needed. Firstly let me say that emotions, though subjective are cognitive, that is they are purposive if I am acting, and they manifest an attitude both when I am acting and perceiving something emotionally. The putative insult, if it is not childish, may have mature intent, to call into question my character or my agency in the world. Now above I claimed that I could respond with indifference or embarrassment. I may be indifferent because I do not feel that I need to demonstrate my integrity or agency but suppose I become angry and demonstratively strike the table in my anger as a challenge to the person behind the insult. I might even shout out “Who do you think you are?” Now one can imagine an argument ensuing in which the insulter motivates his insult, and indifference or embarrassment supervene on my part. If, that is, the argument calls attention to something I had not realised about one of my actions which was the focus of the insult, e.g. “Did you not realise that when you said what you did about Mathematics it offended her because she was a Mathematician”. What we have here is a subjective exchange about people’s feelings but I would maintain that it is nevertheless cognitive. The cognitive lesson I learned was the following: theoretical objections to the assumptions of Mathematics could be regarded as offensive in the opinion of individual Mathematicians. That is, I learned a lesson in practical logic, namely, that one ought not to say what I had said. Your question has shifted us nicely onto the grounds of “Action” and “Judgment”. “Action”, as we have seen was one of the categories of Aristotle and “The Critique of Judgment” was the title of one of the works of Kant. Now neither Kant nor Aristotle specifically set about classifying kinds of actions but both philosophers operatively referred to kinds of actions in their various theories. Aristotle’s virtue theory, for example, discussed the Greek term arête that is variously translated as virtue or excellence, in an attempt to characterise “the good” as definitive of what action is striving to achieve. He also talked about eudaimonia or the flourishing life. This term “action” in relation to the flourishing life introduces a possible philosophical problem into the discussion, namely that “action” is a psychological term, which cannot be objectively characterised. This mistake is also sometimes connected to a mistaken psychological view of logic that believes that logic is descriptive of how we do reason and not prescriptive of how we ought to reason. We find certain popular philosophers reasoning that “If logic prescribes laws of thought and there is evidence that there are people who do not reason logically, then the laws do not hold universally” After all, it is argued if stones in a normal gravitational field failed to obey the law of gravity we would abandon the law. What has been argued in previous lectures is that someone committing a murder does not suffice to overturn the law relating to murder. Here as in logic, the law determines how we ought to judge the action. Now the point of this in the context of the Arts is that of course not everyone appreciates good music but they ought to, and even though this is a subjective matter we judge them correctly to be insensitive, meaning that they ought to have a feeling they do not have. Furthermore we believe that sensitivity of this kind probably leads to flourishing lives. Kant’s analysis of aesthetic judgment relies on a theory of mind he defends in earlier works. This theory maintains that sensory experiences of the world can be ordered by the rule-governed concepts of our faculty of understanding and it is this dualistic interaction that underwrites our knowledge claims. In aesthetic contexts, however the sensory manifold is ordered by a general emotion or attitude which emerges from the activity of understanding, and functions subjectively or self- reflectively as exemplary and universal. In answer to the earlier question relating to the inter-subjective nature of mathematical agreement, I agree it is easier to arrive at agreement in relation to a conceptual rule governed activity such as mathematics than it is in relation to an intuitively organised activity such as art but nevertheless the exemplary universality of our thought in the aesthetic case surely demands agreement even if in fact that agreement is more difficult than agreement over objective rules. Furthermore there are notorious disagreements amongst mathematicians when they discuss their theories. Mathematicians are not, for example in agreement over whether non Euclidean geometry is dependent upon certain truths of Euclidean geometry. This disagreement looks purely theoretical but brought down to earth will affect the relation of the theory to space. One can wonder in the light of non- Euclidean assumptions whether the statement “the shortest distance between two points is a straight line” is necessarily true. I see by the clock on the wall that we have overrun by 20 minutes so we will stop at this point. Some of what I have alluded to today will be relevant to next week’s lecture on “Science and the Theory of Knowledge”