Understanding IS vs. OUGHT...

David Hume

 “In every system of morality, which I have hitherto met with [...] the author proceeds for some time in the ordinary way of reasoning, and establishes the being of a God, or makes observations concerning human affairs; when of a sudden I am surpriz’d to find, that instead of the usual copulations of propositions, is, and is not, I meet with no proposition that is not connected with an ought, or an ought not [which] expresses some new relation or affirmation, ’tis necessary that it shou’d be observ’d and explain’d; and at the same time that a reason should be given, for what seems altogether inconceivable, how this new relation can be a deduction from others, which are entirely different from it.”

Hume's fork is often stated in such a way that statements are divided up into two types:
Into the first class fall statements such as "2 + 2 = 4", "all bachelors are unmarried", and truths of mathematics and logic. Into the second class fall statements like "the sun rises in the morning", "the Earth has precisely one moon", and "water freezes at 32 degrees Fahrenheit".

Hume wants to prove that certainty does not exist in science. First, Hume notes that statements of the second type can never be entirely certain, due to the fallibility of our senses, the possibility of deception (see e.g. the modern brain in a vat theory) and other arguments made by philosophical skeptics. It is always logically possible that any given statement about the world is false.

Second, Hume claims that our belief in cause-and-effect relationships between events is not grounded on reason, but rather arises merely by habit or custom. Suppose one states: "Whenever someone on earth lets go of a stone it falls." While we can grant that in every instance thus far when a rock was dropped on Earth it went down, this does not make it logically necessary that in the future rocks will fall when in the same circumstances. Things of this nature rely upon the future conforming to the same principles which governed the past. But that isn't something that we can know based on past experience—all past experience could tell us is that in the past, the future has resembled the past.

Third, Hume notes that relations of ideas can be used only to prove other relations of ideas, and mean nothing outside of the context of how they relate to each other, and therefore tell us nothing about the world. Take the statement "An equilateral triangle has three sides of equal length." While some earlier philosophers (most notably Plato and Descartes) held that logical statements such as these contained the most formal reality, since they are always true and unchanging, Hume held that, while true, they contain no formal reality, because the truth of the statements rests on the definitions of the words involved, and not on actual things in the world, since there is no such thing as a true triangle or exact equality of length in the world. So for this reason, relations of ideas cannot be used to prove matters of fact.

The results claimed by Hume as consequences of his fork are drastic. According to him, relations of ideas can be proved with certainty (by using other relations of ideas), however, they don't really mean anything about the world. Since they don't mean anything about the world, relations of ideas cannot be used to prove matters of fact. Because of this, matters of fact have no certainty and therefore cannot be used to prove anything. Only certain things can be used to prove other things for certain, but only things about the world can be used to prove other things about the world. But since we can't cross the fork, nothing is both certain and about the world, only one or the other, and so it is impossible to prove something about the world with certainty.

http://en.wikipedia.org/wiki/Hume%27s_fork
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Immanuel Kant

Groundwork for the Metaphysics of Morals (1785)

According to Kant, reason tells us what we ought to do, and when we obey our own reason, only then are we truly free.

    Logic cannot have any empirical part; that is, a part in which the universal and necessary laws of thought should rest on grounds     taken from experience; otherwise it would not be logic, i.e., a canon for the understanding or the reason, valid for all thought, and capable of demonstration. Natural and moral philosophy, on the contrary, can each have their empirical part, since the former has to determine the laws of nature as an object of experience; the latter the laws of the human will, so far as it is affected by nature: the former, however, being laws according to which everything does happen; the latter, laws according to which everything ought to happen. Ethics, however, must also consider the conditions under which what ought to happen frequently does not.

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http://www.philosophypages.com/hy/5f.htm ...

Kant's aim was to move beyond the traditional dichotomy between rationalism and empiricism.

[He does this by fusing the two, i.e., we, as human beings, are in (have access to) two possible worlds/standpoints at the same “time”: the sensible world (phenomena - in time and space) and the intelligible world (noumena - which “creates” time and space) J.R.]

The rationalists had tried to show that we can understand the world by careful use of reason; this guarantees the indubitability of our knowledge but leaves serious questions about its practical content. The empiricists, on the other hand, had argued that all of our knowledge must be firmly grounded in experience; practical content is thus secured, but it turns out that we can be certain of very little. Both approaches have failed, Kant supposed, because both are premised on the same mistaken assumption.

Progress in philosophy, according to Kant, requires that we frame the epistemological problem in an entirely different way. The crucial question is not how we can bring ourselves to understand the world, but how the world comes to be understood by us. Instead of trying, by reason or experience, to make our concepts match the nature of objects, Kant held, we must allow the structure of our concepts shape our experience of objects. This is the purpose of Kant's Critique of Pure Reason (1781, 1787): to show how reason determines the conditions under which experience and knowledge are possible.

Varieties of Judgment

In the Prolegomena to any Future Metaphysic (1783) Kant presented the central themes of the first Critique in a somewhat different manner, starting from instances in which we do appear to have achieved knowledge and asking under what conditions each case becomes possible. So he began by carefully drawing a pair of crucial distinctions among the judgments we do actually make.

The first distinction separates a priori from a posteriori judgments by reference to the origin of our knowledge of them. A priori judgments are based upon reason alone, independently of all sensory experience, and therefore apply with strict universality. A posteriori judgments, on the other hand, must be grounded upon experience and are consequently limited and uncertain in their application to specific cases.

Thus, this distinction also marks the difference traditionally noted in logic between necessary and contingent truths.

But Kant also made a less familiar distinction between analytic and synthetic judgments, according to the information conveyed as their content. Analytic judgments are those whose predicates are wholly contained in their subjects; since they add nothing to our concept of the subject, such judgments are purely explicative and can be deduced from the principle of non-contradiction. Synthetic judgments, on the other hand, are those whose predicates are wholly distinct from their subjects, to which they must be shown to relate because of some real connection external to the concepts themselves. Hence, synthetic judgments are genuinely informative but require justification by reference to some outside principle.

Kant supposed that previous philosophers had failed to differentiate properly between these two distinctions. Both Leibniz and Hume had made just one distinction, between matters of fact based on sensory experience and the uninformative truths of pure reason. In fact, Kant held, the two distinctions are not entirely coextensive; we need at least to consider all four of their logically possible combinations:
Unlike his predecessors, Kant maintained that synthetic a priori judgments not only are possible but actually provide the basis for significant portions of human knowledge. In fact, he supposed (pace Hume) that arithmetic and geometry comprise such judgments and that natural science depends on them for its power to explain and predict events. What is more, metaphysics—if it turns out to be possible at all—must rest upon synthetic a priori judgments, since anything else would be either uninformative or unjustifiable. But how are synthetic a priori judgments possible at all? This is the central question Kant sought to answer.
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        I have therefore found it necessary to deny knowledge in order to make room for faith.
        Ich musste das Wissen aufheben, um zum Glauben Platz zu bekommen.
        (Critique of Pure Reason, Preface to 2nd edition, B xxx)

[By this,] Kant did not mean to return to the sceptical fideism of earlier thinkers such as Pierre Bayle , who simply substituted religious belief for theoretical ignorance. Instead, Kant argues first that the human mind supplies necessary principles of sensibility and understanding, or perception and conception; [but] if human reason tries to extend the fundamental concepts and principles of thought beyond the limits of perception for purposes of theoretical knowledge, it yields only illusion; [and] finally, there is another use of reason, a practical use in which it constructs universal laws and ideals of human conduct and postulates the fulfilment of the conditions necessary to make such conduct rational, including the freedom of the will, the existence of God, and the immortality of the soul. This use of reason does not challenge the limits of theoretical reason but is legitimate and necessary in its own right.

( http://www.rep.routledge.com/article/DB047SECT4 )

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1) David Hume is famous for saying “we cannot derive an ought from an is.” What did he mean by this?

2) How did Kant overcome the is - ought distinction of Hume, while still allowing that there will be an “infinite gap” between the two?

3) Does Kant solve the problem of certainty? Or does he not merely illustrate why our knowledge of anything is uncertain (in an absolute, universal sense) – though “true” - within the framework of understanding “we” ourselves (as rational beings) have constructed? [relate to mythos-logos...]