Are There Synthetic A-Priori Propositions?
From a logical point of view, the propositions that express human knowledge can be divided according to two distinctions. First is the distinction between propositions that are a priori, in the sense that they are knowable prior to experience, and those that are a posteriori, in the sense that they are knowable only after experience. Second is the distinction between propositions that are analytic, that is, those in which the predicate is included in the subject, and those that are synthetic, that is, those in which the predicate is not included in the subject. Putting the terms of these two distinctions together gives us a ‘fourfold classification’ of propositions. Analytic a-priori propositions include such statements as: ‘All bachelors are unmarried’ and ‘All squares have four sides.’ Analytic a-posteriori propositions do not exist, according to Kant, because, if the predicate is conceptually included in the subject, the need for experience is irrelevant and unnecessary. Also, “the negation of an analytic proposition is a contradiction; but, because any experience is contingent, its opposite is logically possible and hence not contradictory.” Synthetic a-priori propositions include such statements as: ‘Every event has a cause’ and ‘7 + 5 = 12.’ Although it is not part of the concept of an event that it be a cause, it is universally true and necessary that every event has a cause. And, because 12 is a different concept from seven, five, and plus, it does not include any of them singly or jointly as a part of it. Finally, synthetic a-posteriori propositions include such statements as: ‘The cat is on the mat’ and ‘It is raining.’ They are straightforwardly and uncontroversially empirical propositions that are not necessary and are discoverable through observation (perceptions by the senses).
Kant’s view that human experience is bounded by space and time and that it is intelligible only as a system of completely determined causal relations existing between events in the world and not between the world and anything outside of it has the consequence that there can be no knowledge of God, freedom, or human immortality. Each of these ideas exceeds the bounds of empirical experience and so is banished from ‘the realm of reason.’ As he said, he “found it necessary to deny knowledge, in order to make room for faith.”
For Kant, the distinctions between analytic and synthetic and a priori and a posteriori judgments must be kept separate, because it is possible for some judgments to be synthetic and a priori at the same time. What Kant proposes is this: Surely all a posteriori judgments are synthetic judgments, since any judgment based solely on experience cannot be derived merely by understanding the meaning of the subject. But this does not mean that all synthetic judgments are a posteriori judgments, since in mathematical and geometrical judgments, the predicate is not contained in the subject (e.g., the concept 12 is not contained either in 7, 5, +, =, or even in their combination; nor does the concept “shortest distance between two points” contain the idea of a straight line). Such propositions are universal and necessary (and thus a priori ) even though they could not have been known from experience; and they would be synthetic a priori judgments.
If there are such judgments, then how are they possible? Kant’s answer: the rationalists are right in saying that we can know about things in the world with certainty; and the empiricists are right in saying that such knowledge cannot be limited merely to truths by definition nor can it be provided by experience. Instead, we know about the world ‘insofar as we experience it’ according to the unchanging and universally shared structure of mind. All rational beings think the world in terms of space, time, and categories such as cause and effect, substance, unity, plurality, necessity, possibility, and reality. That is, whenever we think about anything, we have to think about it in certain ways (for example, as having causes, as existing or not existing, as being one thing or many things, as being real or imaginary, as being something that has to exist or doesn’t have to exist), not because that is the way the world is, but rather because that is the way that our minds order experience. There can be no knowledge without sensation, but sense data cannot alone provide knowledge either. We can be said to know things about the world, then, not because we somehow step outside of our minds to compare what we experience with some reality outside of it, but rather because the world we know is always already organized according to a certain fixed (innate) pattern that is the mind. Knowledge is possible because it is about how things appear to us, not about how things are in themselves. Reason provides the structure or form of what we know, and the senses provide the content.
Many other philosophers, mainly empiricists, disagree with Kant’s ideas. One major objection is that we can never know anything about things we do not experience and organize in terms of the mind’s structure. For example, we could never know anything about God, soul, and other metaphysical topics. Kant’s solution means that we will never know if our ideas about the world are true; or it means that we have to “redefine reality as that which we experience rather than that which experience represents.” In short, if we are limited to phenomena (things as they appear), either we will never know if our ideas are true or we have to redefine what truth is. If Kant is right, then why do cultures seem to differ on the categories of understanding? One possible answer is that even though the categories seem to vary, such differences are due only to differences in the “surface grammar” of language, the ways in which things are understood as meaningful. When asked why languages are structured in certain ways, some theorists claim that the brain and our neural networks form the “deep grammar” of what things mean.
Though many disagree with these ideas, I believe that synthetic a-priori propositions are indeed possible. Not only that, but I think they are firmly fixed in our minds and thought patterns for example, almost the entire field of mathematics is based on things we can’t actually see and feel in front of us. Yet we base our lives around these systems, and so therefore I would think that by denying the existence of this type of knowledge would also be denying a ‘part’ of our minds, which really have the potential for greatness.