Tuesday, February 15, 2022

B vii-ix, ¶ 2-3


[¶2] That from the earliest times logic has traveled this secure course can be seen from the fact that since the time of Aristotle it has not had to go a single step backwards, unless we count the abolition of a few dispensable subtleties or the more distinct determination of its presentation, which improvements belong more to the elegance than to the security of that science. What is further remarkable about logic is that until now it has also been unable to take a single step forward, and therefore seems to all appearance to be finished and complete. For if some moderns have thought to enlarge it by interpolating psychological chapters about our different cognitive powers (about imagination, wit), or metaphysical chapters about the origin of cognition or the different kinds of certainty in accordance with the diversity of objects (about idealism, skepticism, etc.), or anthropological chapters about our prejudice (about their causes and remedies), then this proceeds only from their ignorance of the peculiar nature of this science. It is not an improvement but a deformation of the sciences when their boundaries are allowed to run over into one another; the boundaries of logic, however, are determined quite precisely by the fact that logic is the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking (whether this thinking be empirical or a priori, whatever origin or object it may have, and whatever contingent or natural obstacles it may meet within our minds).
[¶3] For the advantage that has made it so successful logic has solely its own limitation to thank, since it is thereby justified in abstracting - is indeed obliged to abstract - from all objects of cognition and all the distinctions between them; and in logic, therefore, the understanding has to do with nothing further than itself and its own form. How much more difficult, naturally, must it be for reason to enter upon the secure path of a science if it does not have to do merely with itself, but has to deal with objects too; hence logic as a propadeutic constitutes only the outer courtyard, as it were, to the sciences; and when it comes to information, a logic may indeed be presupposed in judging about the latter, but its acquisition must be sought in the sciences properly and objectively so called.


Logic is a science that can stand as an exemplar of secure sciences: we observe that it has not needed to seek out new foundations and that it seems to be complete. Many presumed advances are actually deformities as they miss the fact that logic's security is due precisely to the way it has limited itself. Logic stands as a condition for all sciences.


Logic is the first of three sciences Kant will reflect on to draw out why they have attained security. In logic's case, it attained not only security but completeness early on. Logic's clear limits and formal nature were important for its success but the central feature Kant will focus on regards the limits restricting the field of logic to the rules of any and all thinking.
The limits of a science are established by principles that frame the object of that science and allow us to anticipate what is inside or outside of those boundaries thereby allowing us to anticipate something about all objects we may encounter. Were one to lose this capacity to anticipate the object, then special consideration or observation would be impossible since one wouldn't know what to look at and in which manner it was to be appraised.
Having no limit simply makes science impossible. However, having a limit is not itself sufficient unless this limit is maintained. If a science had now this boundary and then later another, the relationship between the various items of knowledge contained therein would become dubious. Across Kant's work, there are many occasions where he emphasizes the confusion that results in metaphysics from not recognizing its limits and the critique is itself an attempt to establish these limits. One such example that we will spend time with later is how confusing appearances and things in themselves leads to a conflation of logic and ontology.
Before moving on to the completeness logic has attained, it is significant to note that all science should be considered as a priori in this respect: they all employ limitations to guide their investigations in advance of experience or otherwise provide themselves with their object a priori. These frames being employed a priori does not prevent them from having been developed out of empirical concepts, as with natural science, but is enough to allow us to abstract from experience and deal with the objects of a science a priori (without looking directly at them). This also does not mean that natural sciences, such as physics, do not make empirical observations but that these observations require an a priori framing, and also that we can employ our scientific examples on questions we construct and not only on phenomena we directly observe. More will be said on this when we discuss natural science as secure science.
The completeness that logic has attained is not possible for all sciences, but due to logic's formal nature, it attained this completeness early on. Natural science, since it deals with the material of experience, has an inexhaustible field to study, and so could never attain completeness. On the other hand, logic deals only with the form of thinking, and so as long as one has even a single thought to study whatever is essential to the form of thinking is already in reach.
Kant mentions that logic is the outer courtyard of the sciences. This does not concern the same topic of its security but is a reflection on logic's relation to other sciences. Logic is completely formal and contains principles that apply to all thought; this means that when applying it to some thought you can abstract from the material involved and only look at the structure. As the outer courtyard of science, logic is a condition for all thinking in the sciences (i.e., a negative condition) while not contributing any material for sciences to study; it is not an organon but a canon.


Does the existence of the mathematical logic of today contradict Kant?

What the word 'logic' evokes has not remained stable, but if we distinguish classical logic from mathematical logic we may find that we can have our cake and eat it, too. It doesn't seem that mathematical logic must be seen as extending or altering classical logic as a science of the rules of all thinking which Kant had in mind. Mathematical logic does investigate relations between propositions within a system, but these structures seem like they can be treated separately and perhaps suggest a subtly different object of study, but on this topic, I would hope for some help from my reader.


logic (logik), secure (sichern), science (Wissenschaft)

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