The Synthetic a Priori
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Subject and predicate, individual and property
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We will now suppose that we are dealing with sentences that are (grammatically) atomic sentences, such as, "Moses crossed the Red Sea." In this sentence we recognise two parts. The sentence works by saying something about "Moses", so Moses is the subject of the sentence. What is said about Moses is called the predicate of the sentence. The terms subject and predicate are grammatical terms. They refer to parts of an atomic sentence. Sentences are things that are written down on sheets of paper, or spoken between people or thought in one's head. However, sentences refer to people and things in the real world. Some people dispute whether the grammatical parts of a sentence, subject and predicate refer to real (logical) parts of reality. However, supposing that they do, then we would say that the subject of a sentence refers to an object or individual in the real world, and the predicate of a sentence refers to a property of that object or individual or relationship between objects or individuals. Let us represent this diagrammatically. ... There might be more than one way to analyse a sentence; we might say, for example, that this sentence expresses a relationship (of crossing over) between two objects (Moses and the Red Sea); however, for the present we will keep things simple and regard this as a sentence attributing a property (crossing the Red Sea) to an individual (Moses). We can represent any atomic sentence in the following way. ... Some comments on terminology. Subjects of sentences refer to objects in the real world. We might also use the term "thing" in place of object. The term "individual" is a technical world used by logicians and is preferred by them. As a logical term it means any object, living or not, that can be regarded as a thing in the real world. The relationship between language and reality is generally known as reference. Thus subjects refer to individuals and predicates refer to properties. However, the term denotation is also used specifically for the relationship between the subject and individual. Thus, we say the name "Peter" denotes the man (individual) Peter in the real world. What we are trying to capture here is the intuitively plausible idea that our language mirrors reality in someway; that since we utter sentences in order to describe the real world, there is some detailed relationship between the constituents of sentences and parts of the real world. There is a further point of clarification that is useful here. The terms subject and predicate are grammatical parts of a sentence. The terms object (individual) and property (and relation) are real parts of the real world. However, not all sentences succeed in referring. For example, some people do not think there was a person called Moses, or if there was, they might disagree as to whether he crossed the Red Sea or not. Here is a sentence which, whilst meaningful, clearly cannot actually refer to anything in the real world. "The unicorn jumped over the Moon." Since this sentence is meaningful but also since it cannot refer to anything real in the world, there must be a third component in the analysis of an atomic sentence. This component is the meaning that people who use the sentences grasp when they use them. The logician and philosopher Gottlob Frege called this component sense. We could also use the term concept; so here meaning, sense and/or concept will all denote the same idea – that is, what it is that is grasped by people when they use a subject or predicate in a sentence. The sense (meaning or concept) of a unicorn is the idea of a horse with a horn. There are, actually, no such animals, but this does not affect our ability to understand the term, since understanding a term requires not that terms must have a reference, but only that they must have a sense (or meaning). Likewise, the sense of the predicate "…jumped over the Moon" is captured possible by a picture in our minds of something jumping over something else, and that something else looking like the Moon. The picture is comical and absurd, and this absurdity captures our awareness that no such action is really possible, but does not prevent it from having sense.
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Contents of
The Synthetic a Priori
1 Empiricism, Platonism, Innate Ideas and the A Priori
2 Analytic a priori
3 Kant and the synthetic a priori
4 Compound (molecular) and atomic sentences
5 Logically atomic sentences and the philosophy of logical atomism
6 Complex sentences and attitudes
7 Subject and predicate, individual and property
8 Synthetic and analytic, definitions offered by Kant
9 A priori and a posteriori
10 The synthetic a priori in Kant - the Critique of Pure Reason
11 Kant, The Critique of Pure Reason, the self and transcendental apperception
12 Empiricist philosophies of mathematics - conventionalism (formalism)
13 Empiricist philosophies of mathematics - the empiricism of J.S. Mill
14 Hybrid empiricist philosophies of mathematics
15 Empiricist philosophies of mathematics - Wittgenstein and non-cognitivism
16 A.J. Ayer and conventionalism - his reply to Kant
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