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  At the foundation of our knowledge, then, and at the foundation of Kant’s philosophy, we have the logical form S is P, which is the form of an elementary judgement. S is the subject thought about, which usually refers to some individual, and P is the predicate, which usually indicates some quality or property that is ascribed to the subject.

  We will say more about S is P when we consider how Kant develops his theory of knowledge out of this logical structure in the Critique of Pure Reason. He will introduce his own terminology, and refer to S as ‘intuitions’ and to P as ‘concepts’. The core ideas will remain the same, though, as we are describing them here.

  Spotlight: Gottlob Frege and mathematical logic

  Kant’s philosophy is grounded in traditional Aristotelian logic, where, as noted, the basic structure is S is P. Here, S represents some subject and P represents some predicate, as in The table is green. Aristotle also uses the words, “all,” “some,” and “none” to generate statements such as All S’s are P, Some S’s are P, No S’s are P, as well as All S’s are not P, and so on. In Kant’s view, this way of understanding logic remained constant for a couple of thousand years, until the 19th century.

  Gottlob Frege (1848–1925) reconceptualized the logical structure of sentences with a more mathematical style, revising for example, All S’s are P (e.g., All tables are green) to read, For all x’s, if x is an S, then x is P (e.g., For all x’s, if x is a table, then x is green). The sentence, Some S’s are P would correspondingly read, For some x, x is an S, and x is P (e.g., For some x, x is a table and x is green). In mathematics-like symbols, All S’s are P would look like .

  Unlike Aristotelian logic, this more mathematical way to symbolize logical relations can more powerfully and clearly express the inner logic of sentences such as Everyone is taller than someone. In this case, we would read it as, For every x, if x is a person, then for some y, y is a person and x is taller than y. In mathematical logic terms, it would look like: .

  In terms of its impact in intellectual history, Frege’s development of mathematical logic is on a par with Edison’s successful construction of a light bulb or the Wright brothers’ successful construction of an airplane. Alan Turing (1912–1954), a specialist in mathematical logic, successfully used his logical knowledge in the British effort to crack the secret German codes during World War II, making a major breakthrough that helped the Allied forces win the war.

  2 Abstraction as a way of thinking

  Imagine sitting on a park bench, watching a group of birds on the grass. Some of them are brown, some are black, some are speckled, some are large, some are small, some are aggressive, some are peaceful, some are chirping, some are quietly resting and some are eating. When we use the concept ‘bird’ to refer to them all, we overlook these differences and think of the birds together as a group, considering them to be all the same as ‘birds’. To capture the thought of ‘bird’, we might even offer a definition: a bird is a warm-blooded animal that has feathers, lays eggs, and has wings and a beak. In the effort to comprehend all birds in a single swoop, these qualities would be part of the ‘essence’ of what a bird is, as we think of ‘bird-ness’.

  Concepts are thus a mixed bag: they have us think superficially by preventing many of the world’s tiny details to come to our explicit notice, but they allow us to group individuals together effectively. Concepts are like boxes (or bags) into which we put groups of similar individuals, usually as a matter of practical convenience. The boxes themselves often fit into each other, like a set of Russian matryoshkas or ‘nesting’ dolls, where the largest doll, which is hollow, has enough space within it to contain the next smallest doll, also hollow, which in turn has enough space to contain a smaller doll, all the way down to the tiniest doll, which is at the centre of the cluster. So it is often with sets of concepts: material things include living things, living things include animals, animals include mammals, and mammals include humans.

  If we return to our group of birds on the grass, we can say that some styles of philosophizing – and Kant’s is one of them – are more interested, for instance, in the concept of a ‘bird’, than in the specific features of any particular bird on the grass, even though some particular bird might be beautiful and interesting as an individual. If one were to develop a philosophy of ‘birds’, so to speak, this kind of philosophy would be formulated very generally, so that it could speak truthfully about each and every bird, no matter where or when a bird might live, no matter how it might look, and no matter what kind of bird it might be.

  If we were to compose a philosophy of religion along similar lines, the same would be true. We would not be concerned with the differences between Christianity, Hinduism or Buddhism, or any other religion. The aim would be to find features that religions have equally in common. We would be searching for the ‘universal’ quality of religion in general – something timeless, true, and always reliable about religion.

  Some theorists who have developed this line of thought have suggested that the moral qualities of every religion serve as the common ground. Since each religion instructs people to be good, it makes little difference what religion a person happens to believe in, if we focus exclusively on this moral essence.

  With respect to human beings, Kant’s philosophy adopts the same kind of attitude. He is not especially interested in the differences between people. He is concerned with what we have in common, and what is always equally present in each of us.

  This idea that there is an ‘essence’ to human beings is not new. It stems from the long heritage of ancient Greek philosophy which characterizes the human being as a rational animal. For Kant, ‘rational’ specifically means ‘logical’, and so by his lights, if there is a human being, then the person will have logic as an essential feature. This is an important point to remember for understanding Kant.

  As noted, Kant believes that S is P is the most basic logical form, so for Kant, if there is a human being, then the person’s knowledge and experience will follow the contours of this elementary logical form. Kant argues that the world appears to us as it does (e.g., we experience a world with blue skies, loud sounds, hard tables and such), precisely because we think in terms of this elementary form of judgement. The structure comes from us.

  Later on, our discussion of Kant’s theory of knowledge will show how Kant appeals to an inventory of basic logical forms – he obtains a list of twelve from the logic books of his day – to identify the fundamental kinds of judgements which we use to think about the world. For the most part, they are variants of the S is P logical format. Kant’s philosophy is based on the general idea that since we are essentially logical beings, we cannot help but create a logically structured world for ourselves.

  Key idea: Identifying the essence of a group

  To achieve universal results in philosophy, it helps to attend exclusively to the qualities that a group of things equally share – the essence of the group – and to disregard their accidental differences in detail. If we consider humanity as a single group, disregarding the individual differences between people, as Kant does, one is in the position to write a philosophy true for all people for all time.

  So far, we have been discussing the idea of abstraction, and how Kant’s interests are defined not in reference to any specific people and their distinctive features, but reside in the concept of human beings in general. He abstracts away from differences between people and attends to features that everyone has in common, a central one of which is the capacity to think logically.

  Kant’s philosophy puts abstractive thought to use in another way, and to understand this, we can consider not a set of birds, but some single bird. Let us now think abstractly about that bird.

  Using general terms to describe the situation, suppose that there is a thing in front of us which happens to be a bird, which has a particular colour and particular shape. Suppose it is a large bluebird. Kant believes that we can conceive of this thing in various ways by focusing exclusively on this
or that one of its aspects. We can consider it as just a ‘thing’, for instance, and disregard its kind, its shape and its colour. Or we could attend only to the thing’s shape, and disregard its colour, along with what kind of thing it happens to be. Or we could attend only to the object’s kind – as we did originally when regarding the original group of birds as simply ‘birds’ – and disregard the object’s particular shape and colour.

  Being able imaginatively to separate out such features of things, holding them up individually for reflection and considering them in isolation from everything else, is a crucial feature of Kant’s style of philosophizing. He grounds some of his most influential arguments on the ability to separate imaginatively, for example, a thing’s shape from its colour, or a thing’s shape from any thought of what kind of thing it happens to be. Kant expands this way of thinking to the point where he asserts that at bottom, our experience divides into three fundamental aspects: (1) shapes and numbers, (2) colours, tastes, sounds and other sensory qualities, and (3) concepts, which we use to understand the kinds of things we are experiencing.

  When we discuss Kant’s theory of space and time, his moral theory and this theory of beauty, this ability to separate one sector of experience from another will prove to be essential to understanding his arguments. The process compares well to chemical analysis, where we begin with some complicated compound or mixture, and then separate it into its component substances or elements. As a matter of philosophical theorizing, Kant similarly divides our experience into a geometrical/mathematical sector, a sensory sector and a conceptual sector, which fuse together to create our experience of the world.

  3 Searching for underlying presuppositions

  The idea of a ‘presupposition’ is easy to grasp. A presupposition is what one needs to assume, if something – and this ‘something’ could be anything at all that one wishes to consider – is to be true or is to exist. Consider the words in this sentence. For someone to read the words and understand them, we must presuppose that the person understands the English language. For someone to add a few numbers together, one must presuppose that the person knows how to count. For someone to drive a car well, one must presuppose that the person understands the difference between driving slowly and driving rapidly, and between driving on the left side of the road and driving on the right. Presuppositions determine the background context. They are the soil from which our more detailed knowledge extends.

  The activity of discerning and disclosing presuppositions is different from that of drawing logical implications. Take as an example 4 = 2 + 2. If we know that 2 = 1 + 1, we can infer that 4 = 1 + 1 + 1 + 1. We can draw potentially an infinite number of inferences from 4 = 2 + 2, once it is recognized, for instance, that 1 = ¼ + ¾ and that 1 = ¼ + ¼ + ¼ + ¼. Such inferences could go on forever.

  The process of looking for presuppositions, however, is different. With respect to disclosing presuppositions, we can ask in the case of 4 = 2 + 2: What is required for there to be a statement such as 4 = 2 + 2 at all? How is 4 = 2 + 2 possible? One answer is that, to begin with, we must presuppose a mathematical system. Another is that we must assume that the meanings of the numerical symbols remain constant from one day to the next. Another would be – possibly – that there is a prior social practice called ‘adding’ in which people engage.

  This last presupposition may seem reasonable. Suppose, however, that one believes that 4 = 2 + 2 has been true from eternity, as might a follower of Plato. If so, then the equation would be true independently of whether there happen to be human beings who speak to each other about mathematics. For 4 = 2 + 2 to be true, social practices might not be required.

  The above example shows that the search for presuppositions can sometimes lead to uncertain or puzzling results. It also suggests – and this complicates the situation considerably – that what counts as a presupposition can depend on the philosophical commitments one has operating in the background.

  Kant has a special way to describe the activity of looking for presuppositions. If we have an object in front of us such as a bird, a human, a wheel, or a mathematical statement, Kant will ask, ‘How is it possible?’ for there to be a bird, or a person, or wheel, etc. The question, ‘How is it possible?’ is asking for the presuppositions involved in the thing’s presence. In the case of the bird, an answer would be: for a bird to be in front of us, we must presuppose a spatial location for the bird to be in. We must also presuppose a time in which we can experience the bird. These are broad and basic presuppositions, exactly of the kind that Kant’s philosophy aims to disclose.

  A simple way to express this quest for presuppositions is in the following form of argument:

  Question: ‘How is P possible?’

  1 We know that P.

  2 If Q were false, then P would be false.

  3 So Q must be true.

  Using our bird example above, we could say:

  1 We know that there is a bird in front of us.

  2 If there were no space for the bird to be in, then there could be no bird in front of us.

  3 So there must be space for the bird to be in (i.e., we must ‘presuppose’ the presence of space to begin with, for there to be an experience of a bird).

  This style of argumentation can sometimes go wrong. Consider the following:

  1 We know that the glass is filled with water.

  2 If it were false that someone had filled the glass with water, then there would be no water in the glass.

  3 So, someone filled the glass with water.

  The problem is in the second step. There are other ways in which the glass might have become filled with water. Perhaps the water came from a leak in the ceiling.

  In the other example above, where it is argued that we need to presuppose space in order to perceive a bird, one might question the argument – again, in the second step – by asserting that a ‘bird’ is really nothing more than a collection of ideas in my mind. Since there is no ‘space’ in my mind, there is no need to presuppose space for the ‘bird’ to be in. The upshot is that one should always adopt a cautious attitude towards arguments that claim to reveal and establish presuppositions, because they can sometimes go wrong, despite looking very reasonable. Kant often uses such arguments.

  To conclude and summarize, we can observe that Kant’s way of thinking and arguing has a number of key features:

  1 Kant assumes that Aristotelian logic is fundamental to human thought and being, and that among the various logical forms, S is P is the most basic.

  2 Kant assumes that human beings are essentially logical beings who think necessarily in terms of logical forms.

  3 Kant separates the generic features of physical objects into three basic kinds, namely, ‘concepts’, ‘shapes/numbers’ and ‘sensations’.

  4 Kant tries to disclose underlying presuppositions for our experience by using questions such as ‘how is it possible that…?’

  Study questions

  1 According to Plato, which item would best reflect the nature of truth: (1) a passing cloud, (2) an apple, (3) a human body, (4) a rock? Why? Does Plato believe that there is anything truer than these items?

  2 Do you believe that the geometrical definition of a circle had been true (or similarly, equations such as 2 + 2 = 4) long before human beings came onto the earthly scene? Why or why not?

  3 Using letters (e.g., as in All T’s have P, as above), how would one write out the logical form of the following argument: ‘All cats have four legs, all dogs have four legs, and therefore all cats are dogs’. Is this a valid form of argument?

  4 Why does Kant build his philosophy upon the logical form, S is P?

  5 Kant believes that humans are essentially rational beings. He has, however, a very specific way to understand the idea of ‘rational’. What is this specific way?

  6 Would you expect Kant’s theory of knowledge to be sensitive to the differences between older and younger people, or between ancient and modern people, or between men and wome
n? If not, why not?

  7 A thought experiment: consider any item in your immediate surroundings, (e.g., a cup, a table, a tree, etc.) and analyse it carefully according to its shape, its colour and the kind of thing that it is.

  8 What is a presupposition? How is the practice of drawing logical implications different from that of revealing presuppositions?

  9 How can the activity of revealing presuppositions sometimes yield uncertain results?

  10 Using the same object from question 7, now ask about the object in the Kantian style, ‘How is it (e.g., the cup, or table, etc.) possible?’

  Section Two:

  What can we know?

  3

  Kant’s theory of knowledge

  We see the blue sky, the green light, the white clouds, the red flag, and make elementary judgements. Kant identifies the abstract form of these judgements, where we apprehend some thing and ascribe a particular quality to it, as S is P. He then reflects upon this basic logical form to develop a theory of knowledge.

  In this chapter, we will consider Kant’s critique of the British empiricist understanding of the concept of causality. This critique is based on the interrelationship between two distinctions: (1) analytic judgements versus synthetic judgements, and (2) judgements known to be true a priori versus those known to be true a posteriori. Emerging from this interrelationship is Kant’s famous recognition of a special kind of judgement, namely, one that is synthetic, but known also to be true a priori. The chapter concludes by showing how Kant used the abstract form of elementary judgements, S is P, to develop an account of how our mental faculties interact when we make judgements.