Cálculo del número de strings por inversor

Kant claims that Rational Psychology aims at understanding the subject qua subject (or as an ‘absolute subject’), but that we can only understand subjects by means of predicates (or concepts), never grasp them as they are in-themselves. But when Reason disregards this limitation and tries to reason about the soul, the Paralogisms result.⁷⁹ To better understand the paralogisms, it is necessary to know how the mind generates them. This requires an account of the faculty of reason, which produces Ideas. Kant says, “If the understanding may be a faculty of unity of appearances by means of rules, then reason is the faculty of unity of the rules of

understanding under principles” (Principles are the means by which cognitions can be synthesized, and in general can be considered universal propositions).⁸⁰ An interesting

consequence of this is that reason, unlike the understanding, “never applies directly to experience or to any object, but instead applies to the understanding”.⁸¹ Such an empirical detachment makes any direct application of reason to theoretical speculations problematic, since reason is not bound by the parameters of possible experience, as was previously noted. Oddly enough, this disadvantage is turned on its head by practical reason into a fundamental advantage, since reason appears to be a faculty that is not determined by empirical considerations. Thus, the

independence of reason translates into the independence of the self: the soul’s freedom.

So, granted the transcendental rather than empirical origins of both the concepts of the understanding and principles of reason, it is not difficult to see how the mind not only can but has a pernicious tendency to go beyond the bounds of possible experience and fall into error.

Reason is the faculty which gives “unity a priori through concepts to the understanding’s

79 Kant, Immanuel, Prolegomena to Any Future Metaphysics, trans. James W. Ellington (Indianapolis: Hackett Publishing, 2001), 69-771] [333-335]

80 Kant Critique of Pure Reason 387- 389 [A299-A302/B355-B359]

81 Kant Critique of Pure Reason 389 [A302/B359]

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manifold cognitions, which may be called “the unity of reason.””⁸² In other words, reason unifies what the understanding produces through its own syntheses in an attempt to unify what the latter could not synthesize by means of concepts alone. In itself, as we will see, there isn’t necessarily anything wrong with this impulse to unify cognitions into a coherent system of knowledge since such a system is more useful. The unity of reason ultimately requires the positing of a founding element, referred to by Kant as an Idea, which will provide totality to a series of cognitions. An Idea is “a concept of the understanding [freed] from the unavoidable limitations of a possible experience” in order to ground the conditioned.⁸³ In other words, it is the concept of an ‘unconditioned’ something upon which all cognitions pertaining to a particular field of experience rely that, by necessity, can never be an object of possible experience. An Idea is thus a transfigured concept.

Thus, even at such a preliminary moment of discussion, we can already infer that in some way, the Ideas of the soul, the world, and God will allegedly ground what, for Kant, must

comprise a comprehensive division of the field of knowledge into three possible disciplines:

psychology, cosmology, and theology. Kant lifts this threefold division from Christian Wolff’s major text Rational Thoughts on God, the World, and the Soul of Human Beings, also All Things in General.⁸⁴ But, as we will see, ‘Ideas,’ by nature, if taken as indicative of something real, can produce metaphysical doctrines little better than spooks of the imagination, pied pipers that lead us into intellectual quagmires and squabbles we cannot get out of without critique to declare a ceasefire and draw up an armistice.

82 Ibid 389 [A302/B359].

83 Kant Critique of Pure Reason 461 [A409/B435-B436]

84 Wolff, Christian, “Rational Thoughts on God, the World, and the Soul of Human Beings, also All Things in General,” in Kant’s Critique of Pure Reason: Background Source Materials, ed. Eric Watkins (Cambridge:

Cambridge University Press, 2009), 6.

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But why these three Ideas? To answer this question, we must turn to the two specific ways in which the mind thinks inferentially: by means of inferences of the understanding (or immediate inferences) and syllogisms of reason (or mediate inferences). Immediate inferences, or those inferences in which the conclusion can be derived from a premise without a second, mediating premise, are made by the faculty of the understanding. Thus, we can know that “All cats are mammals” if the statement “Some cats are not mammals” is false, on the basis of the logical rule of contradiction. No secondary premise is necessary to mediate between the premise

‘“Some cats are not mammals” is false’ and ‘“All cats are mammals.”” We can notice that an immediate inference has only two terms; e.g. cats and mammals. It would seem that all immediate inferences must be analytic statements.

The faculty of reason, however, is a faculty of mediate inferences, more commonly referred to as syllogisms.⁸⁵ The inferences reason is capable of making are not implicated within the initial premise and are not analytic like immediate inferences are. Instead, syllogisms require a third term, called the middle term, to link two premises together.

For example,

Quantifier + ‘Middle Term’ are ‘Predicate Term’

Quantifier + ‘Subject Term’ are ‘Middle Term’

Quantifier + ‘Subject Term’ are ‘Predicate Term’

Kant reworks this standard syllogistic form, associating each component with a faculty:

Major premise – a universal rule thought through the understanding Minor premise – the cognition subsumed under the condition of the rule⁸⁶

Conclusion⁸⁷ - “the actual judgment that expresses the assertion of the rule in the subsumed case.”⁸⁸

85 Kant Critique of Pure Reason 389, 403 [A330/B386, A303/B360]

86 Kant Critique of Pure Reason 390 [A304/B360]

87 Ibid 389, 403 [A303/B360-A304/B361], [A330/B387]

88 Ibid

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For the sake of clarity, I will use a straightforward example, since to understand how reason, the faculty of inferences, works, it is best not to jump immediately to an example as complicated as one involving Ideas (the unconditioned). Using a universal proposition as a major premise (which counts as a ‘comparative’ kind of principle, according to Kant):⁸⁹

All bodies are extended entities All heavy things are bodies

Therefore, all heavy things are extended entities

Here the major premise (‘All bodies are extended entities’) is a universal principle applied to a particular class of entities (‘Heavy things’) to produce a conclusion (‘All heavy things are extended entities’). Or, to put it otherwise, we have here an example of an analytic proposition concerning the relationship between all bodies and the attribute of extension. This is then applied to a specific class of entities (‘Heavy things’) to produce a conclusion that connects the two cognitions (A relationship between ‘heavy things’ and ‘extended entities’ is determined).

For Kant, several faculties are in play when constructing the syllogism and deriving a conclusion from the premises. First, a rule is determined by the faculty of understanding, which acts as the major premise of a syllogism. Reason is the faculty which infers a conclusion from the universal rule and a subsumed case (the minor premise). As noted, the minor premise only falls under the major premise (the rule) by means of the power of judgment.⁹⁰ Deleuze, in Kant’s Critical Philosophy refers to the power of judgment as “a complex operation which consists in subsuming the particular under the general.”⁹¹ There are two kinds of judgment: determining judgment and reflective judgment. In determining judgment “the general is already given, known, and all that is required is to apply it, that is to determine the individual thing to which it

89 Ibid 388 [A301/B358.]

90 Ibid.

91 Deleuze Kant’s Critical Philosophy 58

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applies.”⁹² In reflective judgment, however, “the general poses a problem and must itself be found.”⁹³ As Deleuze further points out, judgment is less a faculty than the accord between various faculties: understanding, imagination, and reason.⁹⁴ What faculties are in accord with which depends not only on the kind of judgment (determining or reflective), but also on whether the judgment is theoretical, practical, or aesthetical.

Reason uses syllogisms “to bring the greatest manifold of cognition of the understanding to the smallest number of principles (universal conditions), and thereby to effect the highest unity of that manifold.”⁹⁵ In other words, while the understanding unifies the manifold of intuition, making necessary connections between disparate perceptions by means of concepts (or rules) to yield cognitions, reason seeks to unify the produced manifold of cognitions further by means of principles, and ultimately, by means of Ideas. As John Sallis puts it in The Gathering of Reason,

Ideas serve…as directive unities, that is, they serve to direct the understanding in such a way as to bring the latter “into complete consistency with itself”…Without a directedness toward further unification there would be within understanding an inconsistency between, on the one hand, its character as unifying (gathering) and, on the other hand, the disunity, fragmentation, which remains in the knowledge supplied by understanding alone.⁹⁶

The ultimate aim of reason is to systematize all cognitions, which requires all cognitions to be derived and collected into a totality. Nonetheless, as Kant will observe, and as I have already hinted at, this unifying inclination can produce metaphysical blunders best to be avoided.

There are two ways inferences can be used to derive a totality of cognitions; the first is an open-ended derivation of conditioned elements by means of assumed conditions (Assuming that

“All matter is composed of atoms,” I can then say, “A chair is composed of atoms,” a dining

92 Ibid 58

93 Ibid. This discussion of judgment prefigures the discussion of aesthetics in the Critique of Judgment.

94 Ibid 59

95 Ibid 390 [A305/B361]

96 Sallis, John, The Gathering of Reason. (Athens, Ohio: Ohio University Press, 1980), 62

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room set is composed of four chairs, etc). Kant refers to the movement from conditions to the conditioned as a descending series, or episyllogism. The conditioned elements that can be determined by means of a given condition are theoretically endless since the series does not trace backwards but opens up as a “potential progression…that becomes.”⁹⁷ Kant mentions this kind of syllogistic reasoning only to dismiss it, since it cannot ground all possible conditioned elements. In other words, a descending series can never be totalized, which leaves reason constantly frustrated in its efforts to totalize cognitions. The language of episyllogisms isn’t commonly used by Kant, even though it seems to play a fundamental role in practical reasoning, particularly in regards to the argument for the justified belief in the immortality of the soul (more on this argument in Chapter Six). In other words, Kant provides grounds for believing that the soul is immortal based on a descending series – the open-ended, asymptotic attempt for the will to comply with the moral law – for example (it is only on the basis of Divine intuition that such an infinite series can be grasped as a totality). Cast in another light, the ascetic practice of freedom by means of compliance with the universal law depends on episyllogistic reasoning.

On the other hand, reason can attempt to derive a condition by means of a conditioned element. The ascending series that results is referred to as a prosyllogism. As Kant points out,

“only under [the] presupposition…that all members of the series are given on the side of the conditions…is the judgment [i.e. the conclusion] before us possible a priori.”⁹⁸ The fewer principles which cognitions can fall under, the more unified the manifold of cognitions becomes.

The ultimate aim of this unification is to produce a totality of cognitions, otherwise known as a system of knowledge.

97 Kant Critique of Pure Reason 404 [A331/B388]

98 Ibid 404 [A331/B388]

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The only way such a totality of cognitions, collected under the fewest principles, is possible is if the unconditioned element that conditions all other (possible) conditions in a series is derived. In the Paralogisms and the Ideal (concerning the soul and God, respectively), reason posits a necessary unconditioned element by means of two forms of syllogistic reasoning (the categorical syllogism and disjunctive syllogism, respectively). The Antinomies of reason are different.⁹⁹ In the Antinomies, concerning cosmological Ideas, the unconditioned element can either be a preceding element or the total series of conditions.¹⁰⁰ This has to do with the peculiar nature of the hypothetical syllogism. Returning to my previous example, either an atomic unit will condition all other aggregates of matter, or the infinite series of conditioned aggregates will do so. This distinction will play a significant role in the Antinomies, wherein one side of an antinomy will claim the unconditioned element to be an element, or part that precedes a series of conditioned elements, while the other side of the antinomy will claim the total series of

conditioned elements to be the unconditioned element. The former is the dogmatic rationalist response, since it refers to an unconditioned element that can in no way be an object of possible experience. The latter is the empiricist response, since it refers to an unconditioned series that is theoretically observable.¹⁰¹ In either case, the unconditioned element is meant to act as a

unifying principle for the series under consideration (Whether it can be proven to do so or should

99 “Here a new phenomenon of human reason shows itself, namely a wholly natural antithetic…it guards reason against the slumber of an imagined conviction, such as a merely one-sided illusion produces [i.e. the Paralogisms], but at the same time leads reason into the temptation either to surrender itself to a skeptical hopelessness or else to assume an attitude of dogmatic stubbornness, setting its mind rigidly to certain assertions without giving a fair hearing to the grounds for the opposite, Ibid 460 [A407/B433-B434]

100 Now one can think of this unconditioned either as subsisting merely in the whole series, in which every member without exception is conditioned, and only their whole is absolutely unconditioned, or else the absolutely

unconditioned is only a part of the series, to which the remaining members of the series are subordinated but that itself stands under no condition…The absolute whole of the series of conditions for a given conditioned is always unconditioned, because outside of it there are no more conditions regarding which it could be conditioned.” Ibid 465 [A417-8/B445]

101 Ibid 497-498 [A465/B493 – A466/B494]

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just be pragmatically assumed in order to better organize cognitions will be a question addressed later in the chapter).

Neither the faculty of sensibility, nor the faculty of understanding, is capable of

discovering these unconditioned elements, precisely because they cannot be ‘discovered.’ They are neither perceived, nor concepts fitted for union with anything sensible. Thus, these elements, be they a part that conditions all intuitions of a specific kind, or the synthesized totality of all intuitions of a specific kind, lie outside the bounds of possible experience. Nonetheless, reason is intrinsically compelled to hypothesize the existence of these unconditioned elements in order to unify the manifold of cognitions, since unity does not seem to be possible in any other way.

As I already noted, the hypothesized concepts reason attempts to infer in order to unify the manifold of cognitions are called Ideas. The three unconditioned elements, or Ideas, are the Soul, the World, and God. Thus, we now have a general account as to why and how reason produces Ideas, but I have yet to provide specific accounts of how each Idea is generated. It is to that task I now turn.

Just as the logical judgments provide a clue for the deduction of the categories,¹⁰² the logical syllogisms associated with the categories of Relation will provide a clue as to how the Ideas can be deduced. This makes sense since reason infers by means of syllogisms and the three syllogisms associated with each category of Relation respectively make up a

comprehensive list of possible syllogisms, or mediate inferences that reason can use. Thus reason operates in three ways, depending on “the relation of cognition to the understanding:” by

102 At Ibid 459 [A406/B432], Kant calls these clues “logical schema.”

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means of categorical, hypothetical, and disjunctive syllogisms.¹⁰³ “What is universal in every relation that our representations can have”¹⁰⁴ is presented below:

I. The relation to the subject

a. Corresponds to the categorical syllogism, which concerns the relationship between a subject and its predicates

b. E.g. All M are P All S are M All S are P

II. The relation to the manifold of the object in appearance

a. Corresponds to the hypothetical syllogism, which concerns the relationship between a ground and its consequence

b. E.g. If p, then q p

q

III. The relation to all things in general

a. Corresponds to the disjunctive syllogism, which concerns the relationship

“between the cognition that is to be divided and all of the members of the division.”¹⁰⁵

b. E.g. Either A or B ~B

A

Each syllogism will have a different class of unconditioned element underlying it, and each has a rational¹⁰⁶ science that attempts to take up that unconditioned element as an object guaranteed a priori, without appeal to empirical evidence. As is shown below, each syllogism ultimately concerns a kind of relation that a specific science addresses, and can allegedly be grounded in a unique way: For example, categorical syllogisms (which concern the relationship between subject and predicate) ultimately seek a subject that cannot be a predicate: the soul, or bearer of

103 Ibid 390 A304/B361

104 Ibid 405-406 [A333/B390 – A334/B391]

105 Ibid 208 A73/B98

106 ‘Rational’ in this context refers to ‘rationalism,’ an epistemological position I noted above which reasons by means of the logical implications of ideas rather than empirical observation.

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all self-predicates. Here is the comprehensive list of each rational science as well as its corresponding Idea, each corresponding to 1, 2, and 3 above, respectively:¹⁰⁷

In document Diseño de un huerto solar fotovoltaico de 1 MW en la zona de Yecla (página 96-101)