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Francis Bacon. Adam Smith. Robert B. Friedrich D. Johann Gottfried Herder. Home Contact us Help Free delivery worldwide. Free delivery worldwide. Bestselling Series. Harry Potter. Popular Features. New Releases. Kant: Critique of Practical Reason. Description The Critique of Practical Reason is the second of Kant's three Critiques, one of his three major treatises on moral theory, and a seminal text in the history of moral philosophy.

Originally published three years after his Groundwork of the Metaphysics of Morals, the Critique provides further elaboration of the basic themes of Kant's moral theory, gives the most complete statement of his highly original theory of freedom of the will, and develops his practical metaphysics. This revised edition of Kant's Critique of Practical Reason - which contains Mary Gregor's acclaimed translation - is now the authoritative translation of this work.

What's the problem in the second Kritik? Well, there is a problem in the conception of the highest good or Summum Bonum, as Kant calls it. In one sense thesis , the highest good is that which is necessarily required for all the other goods; in another sense antithesis it is the best good of all the goods, even though these goods might not be necessary but contingent. In essence it is a conflict between duty and virtue - should we do our moral duty with the possibiliy of not being rewarded by the world around us, or should we strive for virtue and thereby happiness?

Kant: Critique of practical reason (Summary) - Philosophers

Kant's solution synthesis is very much like his solutions in the first Kritik. He uses the existence of two worlds to do away with the entire problem. We should always do our duty! When this doesn't lead to rewards, in the form of happiness, this is only a phenomenal issue. And this is not a problem anymore, since we exists as noumenal AND phenomenal things. So even though we might not by happy in the phenomenal world when doing our duty, we are happy in the noumenal world. By doing our duty continuously, we progress, as immortal souls, on an infinite road to perfection, which we will never reach, according to Kant, but this doesn't make it less important to strive for this.

As a lucky corollary, for Kant at least, when striving for this highest good ultimate happiness in doing our duty - which, once again, we will never reach, as fallible beings - we need a perfect Supreme Being as a rewarding mechanism and lawmaker. This Being should be omniscient, since it has to know everything about us at any time; this Being should be omnipotent, since it has to be able to make any law that is has to make and to reward us in any way that is demanded; the Being should be be perfectly good, since it has to love justice.

In other words: by trying to find the universal moral law, Kant has ingenuously postively proved the existence of 1 our freedom, 2 the existence of us as immortal souls and 3 the existence of a Supreme Being, God; all three as noumena in the Transcendental World. Three noumena that were only hinted at as possible existing things in the first Kritik! To summarize the whole of Kant's Practical Reason: when we apply Pure Reason to Morality, we find a universal moral law, a categorical imperative, that says that we should act only in such a way that we could want every human being acting thus, without this leading to contradictions.

Our freedom lies in our respect for and our duty towards this moral law, as an autonomous object. When we do our duty, we set out on an infinite road to the highest good i. God, as Supreme Being, necessarily exists as lawmaker and mechanism of reward. These three things, freedom, immortal souls and God, positively exist as noumena - they are needed for a universal moral law. Now, what should we make of all this?

In the first Kritik, I found it very convenient that Kant posits another, unknowable world in which he could deposit all the problems in philosophy. In the second Kritik, this becomes problematical. In the first Kritik, he could get away with saying that immortal souls, human freedom and God might exists - we could not prove or disprove this, but in the second Kritik this is not an option anymore. Kant needs these three things as existing noumena, since they are the building blocks of his Moral Law.

This shows the weakness of the whole system. In my view, he overstretches his method of Pure Reason to acquire synthetic knowledge a priori by wanting say too much. He wants to prove there is a universal moral law the categorical imperative and therefore has to cross his own admitted epistemological boundaries.

He basically contradicts his first Kritik with the publication of the second Kritik. This is problematic. There are, basically, two important problems for Kant as far as I can see. When dealing with the impossibility of positively proving the existence of God, Kant claimed that the existence of God as object could not be proved by predicates.

In other words: trying to prove the existence of noumenal things by using phenomenal things is impossible, by definition. Now, in the second Kritik, Kant seems to prove the existence of immortal souls, freedom and God as noumena by using a very similar argument as the one he criticized earlier.

He says we need these three things for the Moral Law, but just because we need them, doesn't prove that they positively exist. Utility is not an argument for existence; I can think of thousands of very useful things, but this doesn't make them exist. It is in broad outlines the same as the ontological argument: existence is part of perfection, but this doesn't prove anything. But let's grant Kant, for the sake of argument, the existence of the three pillars under his Moral Law.

When the moral law, or the categorical imperative, becomes problematic, then the three pillars become superfluous anyway. So what about the categorical imperative? Well, it seems very problematic, to say the least. We should do only the things that we could wish were universal without leading to contradictions. Kant mentions suicide as an example; but if everyone wants to commit suicide, does it lead to a contradiction when we apply it to the categorical test?


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Of course not. If everyone wants to commit suicide, then it doesn't lead to a contradiction when I commit suicide. And it's the same with killing off the whole entire human race. Does it lead to a contradiction when the entire human race wants to kill the whole human race and I do it? Ofcourse not, I would only put in practice what everyone wants anyway. And a thrid and last example: if I should never lie, because it would lead to a contradiction if I should want that everyone lies, should I lie to a murderer who wants to kill my friend and asks for his location which I know?

Kant would say: tell the truth, you will be rewarded as a noumenon. Benjamin Constant offered the last example to show the problems of Kant's categorical imperative, and I think it is convincing. So to conclude: we can think of examples that we would class as immoral acts but that would nonetheless be moral according to the categorical imperative; we can also think of examples that would class as moral acts protecting a friend from a murderer but which are immoral according to the categorical imperative.

So we are back to square one: Kant wanted to find a universal law, but the failure of his categorical imperative leads us to consider every situation as a particular moral instance, which is the one thing Kant wanted to do away with. This makes his three building blocks - which are problematic on their own merits - superfluous oddities in a failing moral theory.

Should we then just ridicule Immanuel Kant for concocting such an arcane idea? Of course we should not. Respect for this moral law which Kant preached is an Enlightenment ideal we should never lose out of out sight. Besides respect for our fellow human beings, Kant learned us that intentions do matter. We should not only focus on consequences of actions - like utilitarians or religious believers who, out of prudence i.

These are two important lessons, never mind the confused philosophy that is attached to it. Jan 17, Dylan O'Brien rated it it was amazing Shelves: favorite-books. Although it is quite slim, Kant's Second Critique packs quite a punch. Picking up where the end of the First Critique left off, it ties up a number of loose ends in Kantian philosophy. Perhaps most importantly, it clearly shows how desire relates to theory. Although most of the first critique would seem to indicate that Kant's system was completely unfit to deal with human desire and aspiration, around the end of that book, one receives the impression that there is something more profound going Although it is quite slim, Kant's Second Critique packs quite a punch.

Although most of the first critique would seem to indicate that Kant's system was completely unfit to deal with human desire and aspiration, around the end of that book, one receives the impression that there is something more profound going on. Kant seems to be attaching a great deal of importance to the desires which lead us beyond what we can experience. It is this discussion which is further, and more systematically elaborated in the second critique. At first these arguments may seem strange, as though Kant were merely encouraging us to willfully construct various ghosts-in-the-machine, in order to modulate our desires more effectively, thereby rendering us more capable of following practical rules that take little stock of our immediate interests.

It is true that this is what Kant is doing, in a way, but he takes a number of subtle turns during the process which, if taken account of, make the entire project seem less contrived. Although I am still trying to figure out precisely how his alternative works, I feel as though he were on to something very important with this manner. It is clear that in his treatment of God, The Soul, and Freedom, Kant is putting forth a profoundly innovative argument, which avoids all of the extremes explored by other philosophers, which even today remain mostly confined to the poles of dogmatic rationalism, nihilistic empiricism, or relativistic pragmatism.

Although his writing style in this book is more consistent, and the subject matter flows more smoothly, one must be more careful while reading it than with the first critique. There are any number of small details, which, if missed, will result in Kant's entire argument seeming vain, and possibly dishonest. I hope to return to this book frequently. Sep 18, ZaRi added it Shelves: philosophy. I have not to search for them and conjecture them as though they were veiled in darkness or were in the transcendent region beyond my horizon; I see them before me and connect them directly with the consciousness of my existence.

The former begins from the place I occupy in the external world of sense, and enlarges my co wo things fill the mind with ever new and increasing admiration and awe, the oftener and the more steadily we reflect on them: the starry heavens above and the moral law within. The former begins from the place I occupy in the external world of sense, and enlarges my connection therein to an unbounded extent with worlds upon worlds and systems of systems, and moreover into limitless times of their periodic motion, its beginning and continuance.

The second begins from my invisible self, my personality, and exhibits me in a world which has true infinity, but which is traceable only by the understanding, and with which I discern that I am not in a merely contingent but in a universal and necessary connection, as I am also thereby with all those visible worlds. The former view of a countless multitude of worlds annihilates as it were my importance as an animal creature, which after it has been for a short time provided with vital power, one knows not how, must again give back the matter of which it was formed to the planet it inhabits a mere speck in the universe.

The second, on the contrary, infinitely elevates my worth as an intelligence by my personality, in which the moral law reveals to me a life independent of animality and even of the whole sensible world, at least so far as may be inferred from the destination assigned to my existence by this law, a destination not restricted to conditions and limits of this life, but reaching into the infinite. Aug 29, Diane rated it it was amazing Recommends it for: anyone.

In this book, Kant explores the function of the will, free will, and moral reasoning leading to good done as moral duty. Kant shows that the traditional metaphyiscal proofs for the existence of God have been worthless and misleading, because they misapplied the principles of theoretical reasoning beyond their proper sphere one cannot prove the existence of God using scientific reasoning , thus, giving the impression that theology was a "science" of God.

Instead, Kant argues in this book that li In this book, Kant explores the function of the will, free will, and moral reasoning leading to good done as moral duty. Instead, Kant argues in this book that like the immortal soul, the idea of God should be acknowledged as a postulate of pure practical reason which takes faith to believe. This is one of the more readable Kant treatises which influenced philosophy of religion during the Romantic period and helped spur the Transcedentalist movement in America.

Jan 16, Christos Tsiailis rated it it was amazing. Studied this book at University, simply loved it, unlike some literature books that I studied for my assignments! Nov 23, Dan rated it it was amazing Shelves: philosophy. Excellent book by the german philosopher. This writing addresses metaphysics, reasoning, and nature in general. Nov 24, Henrique Maia rated it liked it. For this is indeed a tough read. Ok, not so tough as the ridiculously difficult Critique of Pure Reason , upon which this book builds upon. So here I again join the choir of all those that before me thought of Kant as an obscure writer.

And be aware that even calling him this is an understatement. And this originality of his was as good an excuse as any to put up with his complete lack of ability in making himself clear by writing. Once established as a great philosopher, the burden of making the message understandable was shifted to his readers. That being so, what can we do about it now? Well, nothing, really. Kant was indeed a lousy writer. Kant himself was very open to the idea of having others translate his thinking to a more clear and understandable language. Imagine yourself climbing Mount Everest; or running a marathon.

You may not be the strongest or the fastest, but completing such a task will inevitably make you a part of a very strict group of people who have achieved something seemingly impossible to do. Kant's works are like this. Well, at least this was my experience now that I have finished this famous second Critique. Maybe with the proper set of mind you can enjoy it too. Nov 09, Arno Mosikyan rated it really liked it Shelves: philosophy. After my cold shower encounter with his two Critiques I just shut up and paste these quotes categorical imperatives : Act only according to that maxim whereby you can at the same time will that it should become a universal law.

Act in such a way that you treat humanity, whether in your own person or in the person of any other, never merely as a means to an end, but always at the same time as an end in itself. Thus the third practical principle follows [from the first two] as the ultimate condition of their harmony with practical reason: the idea of the will of every rational being as a universally legislating will. Oct 12, John Lucy rated it liked it. You might want to read Kant's Critique of Pure Reason first, though it's not absolutely necessary. Kant is famous for the concept of a categorical imperative and, indeed, as he builds his critique of practical reason points out that all reason, including pure reason, is practical in that it points to a human's duty, or sense of obligation, to fulfill and do what is moral.

For Kant, duty is above all other human emotions, if you can label it an emotion. Some of the best discussions in here are on You might want to read Kant's Critique of Pure Reason first, though it's not absolutely necessary. Some of the best discussions in here are on free will. If there is such a thing as inherent morality, if humans do have a duty imparted by nature, or by God, progressing toward a certain end, then how does free will play a part?

It would seem that Kant believes that individual humans are free but humanity generally is not. Working that out, I think, is unsatisfactory, but certainly interesting. A necessary read for any student of deontological or Kantian ethics. Most notably, this work elaborates on the proper object of the will, especially the will qua an object of intelligent respect: the moral 'feeling' brought about.

Kant’s Account of Reason

The same way that he did with critique of pure reason, he makes a jump to talking about religion that I don't feel like I totally understand. I feel like I understand his personal motives for it, but I'm not totally sure I agree with the jump. Either way, I thought the sort of let's call it a "reason hierarchy" was interesting. Although I had heard the idea of axiomatic law countless times in schools, understanding Kant's actual reasoning behind the argument was interesting.

I read this book qu The same way that he did with critique of pure reason, he makes a jump to talking about religion that I don't feel like I totally understand. I read this book quickly. I hope I understood it reasonably well. It was less complicated than the critique of pure reason. A bit of a disappointment.

Of course this is an important work, of course everybody should read it. There are gems of moral philosophy in it, but the part where he tried two times to define freedom seems lacking. Then later, when he tries to lie the foundations of his practical philosophy in God, Immortality and Freedom, I was really disappointed in how artificial this construction seemed to me. He tries to save these core concepts but in my opinion and with what we know now, he fails.

Thats a s A bit of a disappointment. Thats a shame. Dec 16, Nick Bond rated it it was ok. While Critique of Pure Reason had a lot of brilliant insights that made me rethink the way I look at major philosophical questions, I was much less impressed with this critique. There were some interesting ideas the categorical imperative stands out , but it felt mostly like an elaborate rationalization of Christianity, with a noticeably pre-Darwin take on the conscience and moral law.

Add onto that Kant's characteristically obscure writing style and you're left with something less than a page- While Critique of Pure Reason had a lot of brilliant insights that made me rethink the way I look at major philosophical questions, I was much less impressed with this critique. Add onto that Kant's characteristically obscure writing style and you're left with something less than a page-turner. Recommended only to dedicated students of Kant or moral philosophy.

This means that both sensibility and understanding must work in cooperation for knowledge to be possible. There are two other important cognitive faculties that must be mentioned. Kant says that we can at least know that it is responsible for forming intuitions in such a way that it is possible for the understanding to apply concepts to them. Reason is not satisfied with mere disconnected bits of knowledge.

Reason wants all knowledge to form a system of knowledge. Transcendental idealism is a theory about the relation between the mind and its objects. Three fundamental theses make up this theory: first, there is a distinction between appearances things as they appear and things as they are in themselves. Second, space and time are a priori , subjective conditions on the possibility of experience, and hence they pertain only to appearances, not to things in themselves.

Third, we can have determinate cognition of only of things that can be experienced, hence only of appearances, not things in themselves. Hence, transcendental idealism is the theory that it is a condition on the possibility of experience that the objects of experience be in some sense mind-dependent. Kant argues that space and time are a priori , subjective conditions on the possibility of experience, that is, that they are transcendentally ideal. Kant grounds the distinction between appearances and things in themselves on the realization that, as subjective conditions on experience, space and time could only characterize things as they appear, not as they are in themselves.

Further, the claim that we can only know appearances not things in themselves is a consequence of the claims that we can only know objects that conform to the conditions of experience, and that only spatiotemporal appearances conform to these conditions. One argument has to do with the relation between sensations and space.


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  6. Hence, the ability to sense objects in space presupposes the a priori representation of space, which entails that space is merely ideal, hence not a property of things in themselves. If geometry, which is the study of the structure of space, is synthetic a priori , then its object — space — must be a mere a priori representation and not something that pertains to things in themselves. Many commentators have found these arguments less than satisfying because they depend on the questionable assumption that if the representations of space and time are a priori they thereby cannot be properties of things in themselves.

    There Kant argues that if space and time were things in themselves or even properties of things in themselves, then one could prove that space and time both are and are not infinitely large, and that matter in space both is and is not infinitely divisible. In other words, the assumption that space and time are transcendentally real instead of transcendentally ideal leads to a contradiction, and thus space and time must be transcendentally ideal. It is a question of central importance because how one understands this distinction determines how one will understand the entire nature of Kantian idealism.

    The following briefly summarizes the main interpretive options, but it does not take a stand on which is correct. Appearances and hence the entire physical world that we experience comprise one set of entities, and things in themselves are an ontologically distinct set of entities. Although things in themselves may somehow cause us to have experience of appearances, the appearances we experience are not things in themselves.

    There have been attempts at interpretations that are intermediate between these two options. After establishing the ideality of space and time and the distinction between appearances and things in themselves, Kant goes on to show how it is possible to have a priori cognition of the necessary features of appearances. Cognizing appearances requires more than mere knowledge of their sensible form space and time ; it also requires that we be able to apply certain concepts for example, the concept of causation to appearances.

    The argument of the Transcendental Deduction is one of the most important moments in the Critique , but it is also one of the most difficult, complex, and controversial arguments in the book. Hence, it will not be possible to reconstruct the argument in any detail here. Kant takes it to be uncontroversial that we can be aware of our representations as our representations. Further, we are also able to recognize that it is the same I that does the thinking in both cases. In general, all of our experience is unified because it can be ascribed to the one and same I, and so this unity of experience depends on the unity of the self-conscious I.

    Kant next asks what conditions must obtain in order for this unity of self-consciousness to be possible. His answer is that we must be able to differentiate between the I that does the thinking and the object that we think about. That is, we must be able to distinguish between subjective and objective elements in our experience. So next Kant needs to explain how we are able to differentiate between the subjective and objective elements of experience. His answer is that a representation is objective when the subject is necessitated in representing the object in a certain way, that is, when it is not up to the free associative powers of my imagination to determine how I represent it.

    For instance, whether I think a painting is attractive or whether it calls to mind an instance from childhood depends on the associative activity of my own imagination; but the size of the canvas and the chemical composition of the pigments is not up to me: insofar as I represent these as objective features of the painting, I am necessitated in representing them in a certain way. Kant assumed that we have a unified experience of the many objects populating the world.

    This unified experience depends on the unity of apperception. The unity of apperception enables the subject to distinguish between subjective and objective elements in experience. This ability, in turn, depends on representing objects in accordance with rules, and the rules in question are the categories.

    Hence, the only way we can explain the fact that we have experience at all is by appeal to the fact that the categories apply to the objects of experience. It is worth emphasizing how truly radical the conclusion of the Transcendental Deduction is. Kant takes himself to have shown that all of nature is subject to the rules laid down by the categories.

    But these categories are a priori : they originate in the mind. Thus the conclusion of the Transcendental Deduction parallels the conclusion of the Transcendental Aesthetic: where the latter had shown that the forms of sensibility space and time originate in the mind and are imposed on the world, the former shows that the forms of understanding the categories also originate in the mind and are imposed on the world. The Transcendental Deduction showed that it is necessary for us to make use of the categories in experience, but also that we are justified in making use of them.

    In the following series of chapters together labeled the Analytic of Principles Kant attempts to leverage the results of the Deduction and prove that there are transcendentally necessary laws that every possible object of experience must obey. The first two principles correspond to the categories of quantity and quality. First, Kant argues that every object of experience must have a determinate spatial shape and size and a determinate temporal duration except mental objects, which have no spatial determinations.

    The next three principles are discussed in an important, lengthy chapter called the Analogies of Experience. They derive from the relational categories: substance, causality, and community. According to the First Analogy, experience will always involve objects that must be represented as substances. One event is said to be the cause of another when the second event follows the first in accordance with a rule.

    And according to the Third Analogy which presupposes the first two , all substances stand in relations of reciprocal interaction with each other. That is, any two pieces of material substance will effect some degree of causal influence on each other, even if they are far apart.

    The First Analogy is a form of the principle of the conservation of matter: it shows that matter can never be created or annihilated by natural means, it can only be altered. Hume had argued that we can never have knowledge of necessary connections between events; rather, we can only perceive certain types of events to be constantly conjoined with other types of events. In arguing that events follow each other in accordance with rules , Kant has shown how we can have knowledge of necessary connections between events above and beyond their mere constant conjunction.

    The Postulates of Empirical Thinking in General contains the final set of principles of pure understanding and they derive from the modal categories possibility, actuality, necessity. The Postulates define the different ways to represent the modal status of objects, that is, what it is for an object of experience to be possible, actual, or necessary. The most important passage from the Postulates chapter is the Refutation of Idealism, which is a refutation of external world skepticism that Kant added to the edition of the Critique.

    In the Refutation, Kant argues that his system entails not just that an external that is, spatial world is possible which Berkeley denied , but that we can know it is real which Descartes and others questioned. Where the skeptics assume that we have knowledge of the states of our own minds, but say that we cannot be certain that an external world corresponds to these states, Kant turns the tables and argues that we would not have knowledge of the states of our own minds specifically, the temporal order in which our ideas occur if we were not simultaneously aware of permanent substances in space, outside of the mind.

    Accordingly, Kant holds that there can be knowledge of an object only if it is possible for that object to be given in an experience. This aspect of the epistemological condition of the human subject entails that there are important areas of inquiry about which we would like to have knowledge, but cannot. The three most important ideas with which Kant is concerned in the Transcendental Dialectic are the soul, the world considered as a totality , and God. The peculiar thing about these ideas of reason is that reason is led by its very structure to posit objects corresponding to these ideas.

    Kant argues that such reasoning is the result of transcendental illusion. A cognition involves both intuition and concept, while a mere thought involves only concept. For instance, consider the question whether we can cognize the I as a substance that is, as a soul. On the one hand, something is cognized as a substance when it is represented only as the subject of predication and is never itself the predicate of some other subject.

    On the other hand, something can only be cognized as a substance when it is given as a persistent object in an intuition see 2f above , and there can be no intuition of the I itself. Hence although we cannot help but think of the I as a substantial soul, we can never have cognition of the I as a substance, and hence knowledge of the existence and nature of the soul is impossible. Antinomies arise when reason seems to be able to prove two opposed and mutually contradictory propositions with apparent certainty. Kant discusses four antinomies in the first Critique he uncovers other antinomies in later writings as well.

    The First Antinomy shows that reason seems to be able to prove that the universe is both finite and infinite in space and time. The Second Antinomy shows that reason seems to be able to prove that matter both is and is not infinitely divisible into ever smaller parts.

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    The Third Antinomy shows that reason seems to be able to prove that free will cannot be a causally efficacious part of the world because all of nature is deterministic and yet that it must be such a cause. And the Fourth Antinomy shows that reason seems to be able to prove that there is and there is not a necessary being which some would identify with God. In all four cases, Kant attempts to resolve these conflicts of reason with itself by appeal to transcendental idealism.

    The claim that space and time are not features of things in themselves is used to resolve the First and Second Antinomies. Since the empirical world in space and time is identified with appearances, and since the world as a totality can never itself be given as a single appearance, there is no determinate fact of the matter regarding the size of the universe: It is neither determinately finite nor determinately infinite; rather, it is indefinitely large. The distinction between appearances and things in themselves is used to resolve the Third and Fourth Antinomies.

    Although every empirical event experienced within the realm of appearance has a deterministic natural cause, it is at least logically possible that freedom can be a causally efficacious power at the level of things in themselves. And although every empirical object experienced within the realm of appearance is a contingently existing entity, it is logically possible that there is a necessary being outside the realm of appearance which grounds the existence of the contingent beings within the realm of appearance.

    It must be kept in mind that Kant has not claimed to demonstrate the existence of a transcendent free will or a transcendent necessary being: Kant denies the possibility of knowledge of things in themselves. Instead, Kant only takes himself to have shown that the existence of such entities is logically possible. In his moral theory, however, Kant will offer an argument for the actuality of freedom see 5c below. The Ideal of Pure Reason addresses the idea of God and argues that it is impossible to prove the existence of God.

    Reason is led to posit the idea of such a being when it reflects on its conceptions of finite beings with limited reality and infers that the reality of finite beings must derive from and depend on the reality of the most infinitely perfect being. Of course, the fact that reason necessarily thinks of a most real, necessary being does not entail that such a being exists.

    Kant argues that there are only three possible arguments for the existence of such a being, and that none is successful. According to the ontological argument for the existence of God versions of which were proposed by St. Anselm and Descartes , among others , God is the only being whose essence entails its existence. Kant argues that both of these implicitly depend on the argumentation of the ontological argument pertaining to necessary existence, and since it fails, they fail as well.


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    Although Kant argues in the Transcendental Dialectic that we cannot have cognition of the soul, of freedom of the will, nor of God, in his ethical writings he will complicate this story and argue that we are justified in believing in these things see 5c below. Recall that an analytic judgment is one where the truth of the judgment depends only on the relation between the concepts used in the judgment.

    Kant, by contrast argued that mathematical knowledge is synthetic. Recall, however, that a judgment can be both synthetic yet a priori. Like the judgments of the necessary structures of experience, mathematics is also synthetic a priori according to Kant. Surely, this proposition is a priori : I can know its truth without doing empirical experiments to see what happens when I put seven things next to five other things.

    If mathematical knowledge is synthetic, then it depends on objects being given in sensibility. And if it is a priori , then these objects must be non-empirical objects. What sort of objects does Kant have in mind here? Recall that an intuition is a singular, immediate representation of an individual object see 2c above. Empirical intuitions represent sensible objects through sensation, but pure intuitions are a priori representations of space and time as such.

    These pure constructions in intuition can be used to arrive at synthetic, a priori mathematical knowledge. And this will be true irrespective of what particular triangle I constructed isosceles, scalene, and so forth. Kant holds that all mathematical knowledge is derived in this fashion: I take a concept, construct it in pure intuition, and then determine what features of the constructed intuition are necessarily true of it. In addition to his work in pure theoretical philosophy, Kant displayed an active interest in the natural sciences throughout his career.

    Most of his important scientific contributions were in the physical sciences including not just physics proper, but also earth sciences and cosmology. In Critique of the Power of Judgment he also presented a lengthy discussion of the philosophical basis of the study of biological entities. Hence, Kant was pessimistic about the possibility of empirical psychology ever amounting to a true science. A few years later, Kant wrote the Physical Monadology , which dealt with other foundational questions in physics see 2a above. This theory can be understood as an outgrowth and consequence of the transcendental theory of experience articulated in Critique of Pure Reason see 2f above.

    Where the Critique had shown the necessary conceptual forms to which all possible objects of experience must conform, the Metaphysical Foundations specifies in greater detail what exactly the physical constitution of these objects must be like. The continuity with the theory of experience from the Critique is implicit in the very structure of the Metaphysical Foundations. The basic idea is that each volume of material substance possesses a brute tendency to expand and push away other volumes of substance this is repulsive force and each volume of substance possesses a brute tendency to contract and to attract other volumes of substance this is attractive force.

    The repulsive force explains the solidity and impenetrability of bodies while the attractive force explains gravitation and presumably also phenomena such as magnetic attraction. Further, any given volume of substance will possess these forces to a determinate degree : the matter in a volume can be more or less repulsive and more or less attractive. The ratio of attractive and repulsive force in a substance will determine how dense the body is. Mechanists believed that all physical phenomena could be explained by appeal to the sizes, shapes, and velocities of material bodies. The Cartesians thought that there is no true difference in density and that the appearance of differences in density could be explained by appeal to porosity in the body.

    Similarly, the atomists thought that density could be explained by differences in the ratio of atoms to void in any given volume. Thus for both of these theories, any time there was a volume completely filled in with material substance no pores, no void , there could only be one possible value for mass divided by volume. The Cartesians and atomists took this to be impossible. At the end of his career, Kant worked on a project that was supposed to complete the connection between the transcendental philosophy and physics.

    Although Kant never completed a manuscript for this project due primarily to the deterioration of his mental faculties at the end of his life , he did leave behind many notes and partial drafts. Many of these notes and drafts have been edited and published under the title Opus Postumum. In addition to his major contributions to physics, Kant published various writings addressing different issues in the natural sciences. There he argued, against the Cartesian mechanists, that physical phenomena such as fire can only be explained by appeal to elastic that is, compressible matter, which anticipated the mature physics of his Metaphysical Foundations see 4a above.

    In his Universal Natural History and Theory of the Heavens , Kant gave a mechanical explanation of the formation of the solar system and the galaxies in terms of the principles of Newtonian physics. He proposed that at the beginning of creation, all matter was spread out more or less evenly and randomly in a kind of nebula. Since the various bits of matter all attracted each other through gravitation, bodies would move towards each other within local regions to form larger bodies.