Knowledge of Synthetic a Priori Mathematical and Logical Truths - Essay Example

?Kant’s Epistemology: An Essay on the Possibility of Synthetic A Priori Claims By: of Introduction Immanuel Kant made it his task to reconcile two rival traditions, i.e. rationalism and empiricism. In this essay, I shall discuss his attempt to reconcile these two philosophical traditions. In doing so, I shall divide this paper into four main parts. In the first part, I will provide an overview of the rationalist and empiricist tradition, in relation to Kant’s epistemological project. I shall emphasize the relation between David Hume’s empiricism and Kant’s epistemology. The second part will focus on the main features of Kant’s epistemology, which will discuss the distinctions between a posteriori from a priori knowledge, and analytic from synthetic judgments. Afterwards, I shall introduce Kant’s concept of synthetic a priori. The third part will discuss the foundation of Kant’s synthetic a priori. Here, I shall argue for the possibility of attaining such kind of knowledge based on Kant’s analysis of the said matter. Finally, the fourth and last part will consist of my conclusion and summary of the argument. Kant: Rationalism vs. Empiricism The dawn of Kant’s philosophy was dominated by two competing philosophical traditions, namely, rationalism and empiricism. For rationalists, “genuine knowledge about the world, they believe, can only be acquired through the application of reason, and experience in the normal sense is at best misleading, if not irrelevant” (Greetham, 2006, p.58). On the other hand, empiricists accept that all of our knowledge begins with experience, and whose sole basis are our senses. The importance of empiricism was made known by David Hume. Unsatisfied with reason as the sole basis for certainty, Hume devised his own epistemology. For Hume, there are only two kinds of knowledge, i.e. matters of fact and relations of ideas. Propositions about relations of ideas, such as mathematical and logical propositions, give us knowledge, which is absolutely certain, but it does not give us any knowledge or information about reality; these are formal truths, empty and abstract. On the other hand, propositions about matters of fact give us information or knowledge about existing facts, i.e. of reality itself. However, they provide no amount of certainty, not even a basis for probability. A famous example given by Hume (2007, p.156) is the proposition “the sun will rise tomorrow.” How are we so sure that it really will rise tomorrow? There are no such causal laws that guarantee this. Hume responds that it is a mere habit of the mind. It is in matters of fact that Hume defines the limits of our knowledge. For, as far as our knowledge of the world is concerned, we are limited to our sense impressions and their corresponding ideas, which manifest through experience alone. We can reason with mathematics and logic, but we can never gain knowledge of facts herein; for they do not possess any impressions by which we can experience or sense. In other words, knowledge about relation of ideas tells us nothing about matters of fact, while the latter cannot refute the former. Hereafter, Kant’s epistemology comes into play. Kantian Epistemology Relation of ideas which have certainty but no factual content, and matters of fact, which have empirical content but no certainty can be seen analogous to what Kant calls the analytic – synthetic distinction (Lavine, 1985, p.167). The former can be seen analogous to analytic propositions and the latter can be seen analogous to synthetic propositions. Analytic propositions are those in which the predicate is already subsumed in the subject, while synthetic propositions are those in which the predicate is not contained in the subject (Kant, 2005, p.77). Furthermore, Kant distinguishes between 2 types of knowledge, i.e. a priori and a posteriori. Analytic propositions are said to be a priori, for they are self-evident and are universal truths, that is to say, they do not depend on experience to justify their truth-value. While synthetic propositions need validation via experience, and are thus depended on it. Knowledge from sense experience is called a posteriori, as opposed to a priori knowledge. Take for instance the following proposition: the dog is on the mat. This proposition is clearly synthetic because the predicate – is on the mat, is not a necessary quality of the dog. In order to validate the truth of the aforementioned statement, we need to verify it through experience. On the other hand, consider the following proposition: a triangle has three sides. This proposition is analytic. For, the predicate – has three sides, is a necessary quality of all triangles. Now given that analytic statements reflect a priori knowledge, and synthetic statements reflect a posteriori knowledge, is it possible to include a third class of propositions wherein synthetic statements reflect a priori knowledge? Aside from synthetic and analytic propositions, Kant pointed out that there is a third class of propositions or judgments, i.e. synthetic a priori claims. These are claims wherein the predicate is not contained in the subject but satisfies the criteria and nature of a priori knowledge. Take for instance the following, i.e. the mathematical proposition (1 + 2 = 3). This is classified as synthetic a priori. Synthetic because “1”, “+”, and “2” does not contain the idea of “3” in it, and a priori because it necessarily follows that through the relation of 1 + 2, it must then be = 3, and cannot be otherwise, thus it is a universal truth. Another example of Kant’s is: a straight line between two points is the shortest (Gardner, 1999, p.57). This proposition is synthetic because “a straight line” merely implies the quality of “straightness” and a “line”. Thus, it being the “shortest” is not found in the subject. On the other hand, it is a priori because is satisfies the criterion for such, which is necessity and strict universality. Our minds can’t help but accept that the shortest distance between two points is not a curve or any other line, but a straight line. This is, for Kant, what a synthetic a priori claim is. By Kant’s analysis and presentation of synthetic a priori claims, it enabled him to justify mathematical and scientific principles, which can give us knowledge with certainty and thereby further extending our knowledge of the world. Hence, it follows then to ask, how are synthetic a priori judgments possible? What are its foundations so as to claim that there must be some? Herein, we move on to Kant’s view of the mind and its two a priori structures. Kant’s Defense for The Possibility of Synthetic A Priori Claims Kant’s view of the mind is that the mind is an active lawgiver. This implies that the mind organizes and synthesizes the manifold of our experiences according to its own inherent laws. So based on this, everything we experience in this world is based on the innate structures of our minds. It is like seeing things through the lens of a pair of sunglasses. Aside from the active nature of the mind, Kant tells us of 2 major faculties of the mind, namely: sensibility and the understanding. The sensibility is the ability of the mind to receive objects through sense perception. Herein, we have 2 a priori structures, which accompany our faculty of the senses. These are the forms of intuition, which are space and time (Morisson, 2011). So when we perceive of a thing, our minds cannot help but perceive it spatially and temporally existing. These concepts of space and time, says Kant, are a priori for it is not possible to perceive of an object without it occupying space and time, but it is possible to conceive of space and time without objects. The understanding on the other hand is the ability of the mind to make judgments about things. This can also be described as the faculty of reasoning or judging. Furthermore, the a priori structures that belong to this faculty are known as the categories of the mind (Morisson, 2011). They are grouped into four main categories, and subdivided further for each category, which amount to twelve categories all in all. These are as follows: “Of Quantity – unity, plurality, totality; Of Quality – reality, negation, limitation; Of relation – of inherence and substinence, of causality and dependence, of community; Of Modality – possibility-impossibility, existence-nonexistence, necessity-contingence” (Kant, 1943, p.80). According to Kant, when we perceive the world and its objects, all our impressions will be defined according to these twelve categories. And in this manner, we shall thus secure accurate knowledge. But what is its relevance to synthetic a priori claims? Herein, I shall offer Kant’s argument in defense of the possibility and necessity of synthetic a priori claims. Kant’s only argument for claiming that there are synthetic a priori judgments or claims is through his examples from mathematics. Kant uses the example: 7 +5 = 12. I quote, “the concept of 12 is by no means already thought in merely thinking this union of 7 and 5; and I may analyse my concept of such a possible sum as long as I please, still I shall never find the 12 in it” (Kant, 2002, p.148). In other words, this proposition is necessarily true, i.e. a priori. But it also cannot be known to be true based on mathematics and logic alone, i.e. synthetic. For, we would need to solve it to know that it is true. So there must be such synthetic a priori claims. The point of Kant’s defense here is grounded upon his categories of the mind. 7 + 5 = 12 is a priori for the concept of summation is rooted upon a category of the mind: Of Quantity – Totality. Furthermore, through the help of another category of the mind, i.e. Of Causality and Dependence, we arrive at the sum, 12. For, the causal relation of 5 and 7 leads us to the sum of 12. Another example is scientific laws of nature. Take for instance the following principle of motion: there is an equal and opposite reaction for every action. This proposition is synthetic for its validity is based on experimentation. It is a priori because of our concept Of Causality and Dependence, which is an a priori category of the mind. Hence, when we observe an object in motion, we cannot help but do so causally. Furthermore, as mentioned above, sensibility is the ability of the mind to receive objects through sense perception. Thus, when we perceive objects in motion, we cannot help but do so under the influence of space and time. The categories of the mind can be seen analogous to looking through a pair of sunglasses, for as we look through the lens, our vision is filtered with the tint. Similarly, when we perceive objects, we cannot help but do so under the influence of space and time and the twelve categories of the mind. Thus, upon constructing synthetic a priori claims, we realize that it is rooted from our mind and from our senses. For, if no part of our knowledge comes from our mind then knowledge would be purely empirical, i.e. all claims would be a posteriori. So it seems that for knowledge to be possible, the senses and reason are both necessary. As Kant would put it: Neither of these faculties has a priority over the other. Without the senses, no object would be given to us, and without the understanding no object could be thought. Thoughts without content are empty, awareness without concepts is blind . . .The understanding is aware of nothing, the senses can think nothing. Only through their union can knowledge arise (Kenny, 2006, p.158). Conclusion Given our analysis of Kant’s method and solution to his problem, we can now outline his argument as follows and assess its validity. As mentioned earlier, if no part of our knowledge was derived from the categories of mind, then knowledge would be purely a posteriori. However, it is not the case knowledge is purely a posteriori, for we do have a priori knowledge. Therefore, It is also not the case that no part of our knowledge was derived from the categories of mind. In short, if we can claim to know something without validating its truth via experience, then knowledge of synthetic a priori claims is possible. Indeed, we can have knowledge independent of experience, i.e. mathematical and logical truths. Therefore, knowledge of synthetic a priori claims is possible. 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