1. For Kant, it is of the greatest importance that one distinguishes a priori from a posteriori judgments, as well as synthetic from analytic judgments. A priori judgments involve absolute necessity and strict universality, i. e. they are valid without variation for all cognizant beings. A posteriori judgments, on the other hand, are empirical and as such are necessarily synthetic. In the case of synthetic claims, the predicate is not contained in the subject, and are therefore ampliative and augment our knowledge.
For example, the claim “All bodies have weight” is synthetic a posteriori because the concept of weight is not contained within the concept of body. Analytic claims, on the other hand, are such that the predicate is contained in the subject. Such claims may be called “classifying”; for instance, “all triangles have 3 sides” is an a priori analytic claim, because the concept of “having 3 sides” is contained within the subject of triangle. I am not building upon my knowledge of triangles when I consider such a statement.
Analytic judgments are shown to be true directly through the principle of non-contradiction. All a posteriori judgments are synthetic, since it would not make sense to base analytic judgments on our experiences, since their truth value is determined by the meaning or classification of the terms. However, a priori claims may be either synthetic or analytic. An example of a synthetic a priori judgment is any mathematical equation, e. g. “7+5=12. ” Though this is not readily obvious, since many believe such judgments to be analytic and that their validity is determined by the law of non-contradiction.
Kant, however, shows us that such claims are in fact synthetic, because it is not a part of the concept of the summation of 7 and 5 to equal the distinct number 12. Only when we put instances of 7 and 5 together, paired with our intuition, will we discover that 12 is in fact their summation. Any analysis of the distinct concepts of 7, 5, and 12 will never be able to reveal the equality. This seems to be a reasonable, though by no means obvious, account of the synthetic nature of mathematical judgments.
Kant does still maintain the a priori nature of such judgments, since they carry with them necessity. His call to intuition is what enables him to argue that not only mathematical, but also geometrical and metaphysical judgments are possible synthetically a priori. It is impossible for us to operate with concepts per se. We must use our intuition to illustrate and relate the concepts in a systematic manner, and for this reason I believe Kant has done a remarkable job in defending the synthetic nature of a priori mathematical statements. 2.
Synthetic a priori judgments are possible in math and natural sciences because, as Kant writes, such judgments must exhibit their concepts through our intuition. The above example of the equation “7+5=12” reveals how such claims are in fact synthetic, though a priori. Our intuition is a framework through which we intuit the objects we perceive through our senses. This framework is composed of both inner intuition – time – and outer intuition – space. Math relies on our inner intuition since counting depends on the successive nature of mental tasks.
Though we are unable to know things-in-themselves, this fact preserves the possibility of our knowledge of math, geometry, and natural science. Since space and time are the structuring forms of our experiences, we can be sure that the way in which we intuit objects will not change; we can thus have perfect confidence in our experiences of phenomenal activity. In the case of natural science, we can only have knowledge in instances of universal laws, e. g. gravity.
We can understand the way in which bodies tend to gravitate towards one another in a certain relation, and such laws cannot be analytical since it would not be contradictory to deny them; they are not empirical because they encompass all instances which we ourselves have never experienced, and they contain the element of necessity which cannot be known through experience. Again, knowledge of natural science is possible because certain concepts are brought forth into the structuring mind and then projected upon objects of our experience.
Such concepts involve the idea of permanent substance and causal connection (which Hume denied we could know), which are known as categories. Pure intuitions are those which are derived directly from reason, and may be placed into a priori categories such as: distinctions of quantity, quality, relation, and modality; empirical intuitions are derived from our own subjective experiences. They are our permanent framework of intuition. Transcendental judgments reveal our knowledge of the nature of our a priori cognition of objects; it is our understanding of the structuring mind in illustrating and translating what it is we perceive, though not the object-in-itself.
3. For Hume, there are two different forms of reasoning which could be used to justify our causal judgments: demonstrative and probable reasoning. Demonstrative, or deductive reasoning, ultimately fails because it cannot establish the uniformity of nature. We can conceive of chaos, and it is therefore a possibility which would destroy the uniformity of nature. Probable reasoning presupposes uniformity in nature, and is thus circular in its attempt to establish said uniformity. Kant is able to expand upon Hume’s ideas and allows for us to have certainty when it comes to causal reasoning.
His answer to Hume’s problem is the notion of synthetic a priori judgments, which allows for us to know the necessity and universality of things which are not self-evident. Kant answers Hume’s skepticism is that the phenomenal regularity our intuition intuits on objects takes the place of numerical connection which Hume posited. That is, our structuring principles result from our understanding and are prescribed, not derived from nature as a thing-in-itself. Because of synthetic a priori judgments, we are able to point out causal connections between objects through phenomenal properties which our mind perceives in terms of space and time.
These properties are due to intuition and to the categories, which translate the things-in-themselves into understandable phenomena. Everything we perceive, therefore, conforms to our internal structure, i. e. our pure intuitions and the pure categories. This makes Hume’s skepticism obsolete, and gives us justification in our causal reasoning. However, it is important to note that we still do not have certainty, or any knowledge whatsoever, about the noumenal things-in-themselves. I believe this is an outstanding response to Hume, and does well against causal reasoning skepticism.
4. In Kant’s Prolegomena, he writes with the assumption that various forms of knowledge, such as mathematics, natural science, etc. , exist and are possible, and then analytically investigates the requirements which lie at the basis of their existence. However, Kant does in fact prove that experience is generally reliable, in the sense that phenomenal objects necessarily conform to our preexisting mental structure. However, this does not mean that our experience is a reliable indicator of how things really are in and of themselves.
He does not directly address this question, but rather remains agnostic and argues that we cannot know the true nature of how things are outside of space and time (since such concepts are not objective, according to him). Kant inquires as to the extent of our reason, and whether there are bounds or simply limits to our a priori knowledge. Bounds imply a space which exists outside of a definite place, and completely enclosing it so as to make it finite rather than infinite.
Limits, on the other hand, do not presuppose such conditions, and are simply negations which “affect a quantity insofar as it is not absolutely complete. ” Mathematics or natural science, for example, is not bound but is rather limited; it will never reach consummation, a point at which it is completely exhausted. Our a priori concepts of understanding are limited by our sense experience, though our reason seeks to transcend these limitations, and arrive at an unconditioned, essential object. Such is the nature of our transcendental ideas of reason, i. e. the pure concepts of reason.
However, the categories – pure concepts of the understanding – are those which are mentioned previously: quantity, quality, relation, and modality. These categories are involved in our knowledge, and are revealed to us when we examine our own judgments. They are not derived from our experience, but rather are the foundational resources of our intuition. Such distinction is absolutely crucial if we are to address the validity of metaphysical assertions. We may argue that such statements which do not seek to understand the essential nature of an object-in-itself can be validated, while those which do cannot be proved.
However, Kant does remark that it would be absurd to dispense with noumenal objects completely; after all, the phenomenal characteristics we perceive in objects are the result of underlying noumenal existences. Because of these distinctions, and Kant’s truly genius understanding of synthetic a priori possibility, it seems that we finally have an answer to the question, “is metaphysics as a science possible? ” The answer, if we remain in the realm of phenomena, and do not allow reason to seek out unknowable noumenal existence, is a resounding “yes! ”