Several Concepts of the Natural World and Geometry - Essay Example

Inference Paper: Transcendental Idealism Introduction In defining a priori knowledge, Kant s that it is held independently of human experience. He also defines synthetic judgments as those that are distinct from their subjective nature, to which they relate due to real connections that exist externally to the concept itself. As a result, these judgments are really informative, although they need reference to outside principles for justification. Synthetic a priori judgments, therefore, provide much of human knowledge’s basis. Applying synthetic a priori judgment to mathematics, Kant claims that: “formal intuition is the essential property of our sensibility by means of which alone objects are given to us, and if this sensibility represents not things in themselves but their appearances, then we shall easily comprehend… that all external objects of our world of sense must necessarily coincide in the most rigorous way with the propositions of geometry.” Kant further claims that this epistemological conclusion implies that objects in space are only representations of human sensuous intuition, as well as that “Pure space is not at all a quality of things in themselves”. This paper will seek to expound on the meaning of Kant’s claim, as well as to offer rejection of this claim. Meaning of the Claim Kant’s arguments are mainly aimed at encouraging an appreciation for the limitations of human knowledge. He argues that it is impossible to have any knowledge beyond the empirical, which means that for human minds, transcendental knowledge is not real but ideal. These constraints to transcendental knowledge, in turn, have two a priori sources, in which the mind possesses sensibility or receptive capacity and understanding or conceptual capacity. Kant notes that sensibility refers to the means through which human understanding accesses objects. He further argues that synthetic a priori judgment in mathematics and geometry is possible because space can be considered as an a priori type of sensibility, which means that the claims of mathematics can be known with a priori certainty only where this experience of objects is our experience’s necessary mode. In addition, Kant also argues that without the ability to represent objects spatially, it is not possible to experience them. In this case, without delineating the space that an object occupies, it is not possible to grasp it. Without spatial representation, human sensations would remain undifferentiated, which would make it impossible to ascribe specific objects with properties. Kant also argues that time is a necessary condition or form in human intuitive ability of objects. In this case, the idea of time is not gatherable from human experience because of the object’s simultaneity and succession, which indicate time’s passage, would be impossible for humans to represent without the capacity to represent the same objects in time. Kant’s claim can also be understood from the perspective that it is not possible for humans to experience objects that do not exist in space and time. In addition, time and space cannot be directly perceived, which means that they must take the form through which the object is experienced. Indeed, Kant says that consciousness that directly apprehends objects as they are, instead of through the means of time and space, is possible but the conditions of sensibility always mediate human apprehension of objects. Thus, any concept or discursive that uses consciousness like that of humans should apprehend objects as occupants of space or regions of space, as well as persisting in this space for a time duration. However, subjection of human senses to a priori conditions of time and space is not adequate, specifically in terms of judging objects as possible. The understanding should provide humans with concepts, which Kant argues are the rules through which objects are identified as universal or common across different representations. Indeed, Kant (p.1) says that no object would be available for man without sensibility and that sans understanding, humans would not think of objects because thoughts that are without content are empty while intuitions that lack concepts are blind. One mistake that humans could make is to believe that the manner in which they sensibly apprehend objects is thinkable, as well as that it reveals the object’s properties themselves. Thus, in order to consider and think about sensibility inputs, it is important that sensations conform to the mind’s conceptual structure of that input. Through the application of concepts, human understanding takes sensations and the particulars they possess and identifies general and common aspects about them. For instance, the concept of shelter would enable an individual to identify general aspects in specific representations of a cave, tent, or house. Understanding mathematics as a synthetic a priori judgment as Kant does allows him to rise above empiricist and rationalist arguments, specifically in relation to the nature of time and space. Whereas rationalists like Leibniz would consider time and space as products of the mind and not intrinsic features of the universe, empiricists like Newton would insist that time and space are absolute rather than a set of temporal and spatial relations. Kant, on the other hand, argues that both empiricists and rationalists are correct because although time and space are absolute, they are also derived from the human mind. Therefore, the truth of mathematics and geometry, as synthetic a priori judgments, are both necessary and informative. This is an instance of Kant’s transcendental argument, which comes from the fact that humans possess knowledge of specific forms where all logical presuppositions possessed by this knowledge should be satisfied. Because mathematics is derived from sensible human intuition, there is absolute surety that it should apply to everything that we perceive. However, for this same reason, there are no assurances that mathematics has much to do with how things are with the exception of how human perceive them. Rejection of Claim So far, Kant’s argument is that synthetic a priori judgments are possible, in this case using mathematics, which is the foundation on which his transcendental philosophy is built. However, Kant’s claim is problematic, especially beginning with his use of synthetic judgment. When Kant refers to the breakup of mathematical judgments into different concepts, this is significantly ambiguous. For instance, arguing that the heavy bag is heavy should be considered an analytical judgment because the concepts of bag and heavy are contained clearly within the ‘heavy bag’. Yet, according to Kant’s claim, the concept of ‘6’ or ‘7’ cannot be contained in the concept ‘13’ using the same reasoning. If a ‘covertly contained’ subject is understood by humans as part of them thinking about whether the predicate is external or internal to the subject’s concept, then the distinction between synthetic and analytic becomes purely and individually introspective. This may lead one to question whether Kant is engaging in psychologism, as well as whether the narrow definition of the concept of ‘covert containment’ means that mathematical judgments may be synthetic or analytic based on the individual. Kant would argue that this is not the case, especially since he considers analytic judgments as providing the basis for how definitions can be constructed, instead of simply presupposing them. In this case, it is Kant’s belief that knowledge about the content of human concepts would be impossible unless these concepts consist of core elements. This would seem to be a counter-argument against any accusation of psychologism in Kant’s claims. However, this arouses another accusation that Kant seems to be confusing the different versions of synthetic and analytic judgment distinctions, especially as he brings in the concept of synthetic a priori knowledge. The synthetic aspect in Kant’s claim advances two differing criteria for one concept, the first of which is that mathematical judgments are synthetic if their truth is ascertained through the conceptual meanings of involved terms. Another criteria proposed by Kant’s claim is that the truth of mathematical judgments is evident, although it does not extend into the knowledge of humans. There is an obvious difference between the two conceptions, specifically because mathematical judgments can be conceptually true in the absence of self-evident truth. Therefore, Kant’s synthetic a priori judgments according to his own reasoning would be analytic. This idea of synthetic a priori mathematical judgment may also be criticized on the basis that every form of empiricism agrees on one thing; the repudiation of synthetic a priori knowledge’s existence. This problem may even be considered one of the most pertinent in philosophy, especially as it sets out to investigate whether the empiricist classification that there are no a priori synthetic propositions is, in itself, a posteriori or a priori. In this case, Kant notes that logical empiricists could argue that the statement is a posteriori. As a result, this would mean that it would take on the form of an empirical hypothesis, which would be disprovable through empirical evidence, especially using the a priori statement. However, a question arises as to whether this would really act to disconfirm the claim and statements. Drawing on the empirical hypothesis that all lions are brown, such a hypothesis would be immediately disconfirmed if a gray or non-brown lion were discovered, which would echo the induction problem introduced by Hume. In addition, if the contention that a priori judgment is not synthetic was to be considered as a posteriori, the contention must be in a position to be disconfirmed theoretically using sense data, similar to the example using the brown lion. Another question that arises from Kant’s claim is whether it is possible to discover empirically that synthetic mathematical judgments are also a priori. This inference from Kant’s claim should be rejected because the a priori notion is not observable. Indeed, if synthetic a priori exists as Kant’s assumes, then it would be easy to observe and know them. All that would be required is for an individual to come up with a synthetic a priori statement, write it down, and allow other people to look at it. Therefore, Kant’s claim that infers that synthetic judgments are a priori should be provable as a posteriori using theoretical capabilities, which would make it a posteriori. As a result, although a mathematical statement should be empirically expressed in order for its meaning to be communicated, this does not mean that the two concepts should be considered as the same thing. The observations of geometry on a piece of paper would only act to disconfirm the judgment that no synthetic a priori judgment is written down on paper. However, a question arises as to whether the individual who drew mathematical and geometrical statements on a piece of paper would consider it as synthetic a priori. If this is true, it would be expected that their judgment would only be heard along with reading the mathematical statements written on the piece of paper. It is impossible to observe that synthetic mathematical statements are a priori, as well as whether synthetic a priori judgments are actually propositions at all. It emerges that the reason for this is because prepositions are unobservable due to their intricate nature, which means that the creation of synthetic a priori mathematical judgments will not empirically disconfirm the fact that synthetic judgments can never be a priori. This is because one of the necessary conditions for a posteriori judgments is that they must have the ability to disconfirm. Mathematical and geometric statements, therefore, cannot be a priori on the basis of Kant’s reasoning and must be a posteriori in conclusion. Therefore, this counters Kant’s claim that all external objects of our world of sense must necessarily coincide in the most rigorous way with the propositions of geometry. However, Kant’s concept of synthetic a priori statements, especially in mathematics, is significant for Kant’s holistic philosophy. It does provide an important bridge between empiricist and rationalist epistemology, in which it also gives the best defense of metaphysical knowledge’s plausibility, especially in light of its repudiations by Hume and other skeptics. However, it is also important to consider replacing Kant’s overarching theme of the possibility of synthetic a priori judgments by asking whether it is really necessary to have belief in such judgments. Possible Response to this Rejection Kant, however, would respond to this rejection based on empiricism and rationalism by also rejecting their contention that humans have only one basic faculty for cognition, which are sense perception and reason respectively. Taking the position that the human mind is dual in nature and has two basic faculties for cognition, i.e. understanding and sensibility, Kant would argue that humans have faculties for intuitions and faculties for concepts. The difference between sensibility and understanding faculties in mathematics, as well as the difference between intuitions and concepts, as distinct cognition forms is an essential part of Kantian philosophy. Kant would argue that concepts are general representations that possess universality in logical form, as well as discursive representations that express pure forms of logic. In addition, concepts, Kant would note, are also indirect representations of objects in time and space, while they also organize or classify perceptions of an object in time and space. On the other hand, intuitions are singular, sense-related, object-dependent, and non-conceptual conscious object-directed representations. Therefore, Kant would explicitly hold that synthetic a priori judgment, as it exists in legitimate or transcendental idealistic metaphysics; it should also exist in mathematics. Conclusion In conclusion, it is inferable from Kant’s claim that human conviction, especially concerning the natural world and geometry, can be derived from several concepts. Indeed, the most basic principles in mathematics are not empirical generalizations in relation to what humans experience but are, instead, synthetic a priori judgments that humans can experience and where the mentioned concepts offer the critical connectives. This is a transcendental argument, which Kant uses to reason on the basis that humans possess knowledge to a conclusion that it is essential to satisfy all logical assumptions of this knowledge. However, this claim can be rejected because of the certainty that humans would attain in using such reasoning. Because mathematics is derived from human sensible intuition, humans can believe with surety that mathematics applies to all that they see, although the same reasoning means that there are no assurances that mathematics has anything to do with how things appear with the exception of how humans perceive them. Read More