Abstract
Where the logical principles of identity, bivalence and non-contradiction are clarified and consequently justified as transcendental principles related to the intentional constitution of the domain of an objective science in general.
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Notes
- 1.
The relation of logic to experience constitutes an important problem to which Husserl dedicated a reasonable amount of attention. See, for example, his Experience and Judgment, Husserl 1973.
- 2.
Lohmar 2002.
- 3.
Husserl 1969, §76.
- 4.
In truth-logic “the judgments are thought of from the very beginning, not as mere judgments, but as judgments pervaded by a dominant cognitional strive, as meanings that have to become fulfilled, that are not objects by themselves, like the data arising from mere distinctness, but passages to the “truths” themselves that are to be attained” [Husserl 1969, p. 65].
- 5.
For Husserl, transcendental logic “intends to bring to life the system of transcendental principles [my emphasis] that gives to sciences the possible sense of genuine sciences” [Husserl 1969, p. 16]. For him, genuine sciences are those that have overcome their naïve positivity and self-sufficiency by means of philosophical criticism.
- 6.
But – let us make it clear from the start – a justification of bivalence along the lines I will follow here cannot safeguard it against its critics, most notably the intuitionists, on their own terms, for what intuitionists actually contest is the intentional meaning of mathematical reality as posited in classical mathematics. As it will be made clear below, the intuitionist’s denial of bivalence involves a refusal of the thesis of verifiability in principle. They do not accept it as a transcendental principle (which does not mean that they do not endorse transcendental principles of their own, as we will see).
- 7.
This is the objective formulation of the principles, their subjective formulation refer to truth-experiences instead of simply truths. For Husserl, the justification of the objective versions of the principles depends on the justification of the subjective versions, which involves idealizing presuppositions regarding experiences in principle available to the intentional ego.
- 8.
In general, the situation complementary to that expressed by A is not-A. Therefore, the complementary of not-A is not-(not-A). Bivalence, however, identifies not-(not-A) and A as expressing the same situation.
- 9.
Of course, there is more to truth than meaningfulness; the attribution of a definite truth-value to a meaningful assertion requires a truth-experience. Whether this truth-experience must be actually lived or can be only idealized depends on the notion of truth involved. I will argue here that different conceptions of truth are related to different intentional senses of being.
- 10.
Although the investigation of particular ontological types does not belong to formal ontology, they too, of course, must obey general formal laws whose investigation do fall under the scope of formal ontology. The disjunction of the realms of real and ideal objects cannot be accomplished in formal ontology, nor the inclusion of physical objects into the category of real objects. But once these inclusions and exclusions are established it follows from a general formal ontological law that physical objects are not ideal. This law can be expressed thus: if A, B and C are ontological categories (regions), C a subcategory of B, A and B disjoint categories, then A and C are also disjoint. Mereology is an important chapter in formal ontology, which Husserl treated axiomatically in his third Logical Investigation (for Husserl, set theory, arithmetic and all formal mathematical theories are formal ontological sciences).
- 11.
This equivalence highlights the close connections between apophantic and formal-ontology. Determining meaningfulness on the apophantic side is tantamount to determining possibility of being on the ontological side.
- 12.
Husserl 1969, §77.
- 13.
Husserl 1969, chap. 3.
- 14.
ECQ is not necessarily a consequence of the principle of non-contradiction in non-classical logic; in fact, paraconsistent logic admits a form of the principle of non-contradiction (not(not-A&A) is a theorem) but does not admit ECQ. This rule has not always been seen as a valid rule of inference in the history of formal logic.
- 15.
An experience of disconfirmation of not-A, which is an experience of confirmation of not-(not-A) is not necessarily an experience of confirmation of A, unless either A or not-A must be true.
- 16.
There have been some misinterpretations of the thesis of decidability in the literature. Suzanne Bachelard’s classic A Study of Husserl’s “Formal and Transcendental Logic” (Bachelard 1968) contains one. For her, decidability means effective decidability. Jacques Derrida in his introduction to Husserl’s “Origin of Geometry” has an interesting discussion on how Husserl’s notion of decidability, which is closely related to his idea of a complete – or definite – theory, as Derrida correctly remarks, need not be read as effective decidability. According to Derrida, the notion of decidability, correctly understood, must be conceived in terms of the horizon of science in general, and mathematics in particular, thus saving Husserl’s idea of a nomological mathematical theory from the limitations imposed by Gödel’s theorem. Derrida correctly notices that “[g]eometrical determinability in the broad sense [as opposed to decidability in strict sense, that is effective decidability – my note] would only be the regional and abstract form of an infinite determinability of being in general, which Husserl so often called the ultimate horizon for every theoretical attitude and for all philosophy.” (Derrida 1989, p. 55, n. 51).
- 17.
A science is positive if it presupposes the existence in itself of its domain of interest as an objectively complete and in principle completely determinable domain of knowledge; the role of the principle of bivalence is to grant “positivity” to the science that embraces it. This is true even for objective logic itself: “…logic, by its relation to a real world, presupposes not only a real world’s being-in-itself but also the possibility, existing “in itself”, of acquiring cognition of a world as genuine knowledge, genuine science, either empirically or a priori. This implies: Just as the realities belonging to the world are what they are, in and for themselves, so also they are substrates for truths that are validated in themselves – “truths in themselves”” [Husserl 1969, p. 225]. “Thus logic, as Objective in this new sense, as the formal logic of a possible world, finds a place for itself in the multiplicity of “positive” sciences …” [Husserl 1969, p. 227].
- 18.
Husserl 1973, p. 297.
- 19.
Husserl 1969, §79.
- 20.
Husserl himself was bewildered by this presupposition: “[judgments are supposed to be decided ‘in themselves’]. That surely signifies: by a ‘method’, by a course of cognitive thinking, a course existing in itself and intrinsically pursuable, which leads immediately or mediately to an adequation, a making evident of either the truth or the falsity of any judgment. All this imputes an astonishing a priori to every subject of possible judgment and therefore to every actual or conceivable human being – astonishing: for how can we know a priori that courses of thinking with certain final results ‘exist in themselves’; paths that can be, but never have been, trod; actions of thinking that have unknown subjective forms and that can be, though never have been, carried out?” [FTL, p. 175/197–98].
- 21.
The classical expression of this is Hilbert’s famous “wir müssen wissen, wir werden wissen!” uttered in a conference in Bologna in 1928.
- 22.
See note 9.
- 23.
Husserl 1969, p. 229.
- 24.
Husserl 1969, p. 173.
- 25.
For Husserl, transcendental logic, “intends to bring to life the system of transcendental principles that gives to sciences the possible sense of genuine sciences” [Husserl 1969, p. 16]. A genuine science is, for him, one that overcomes, by means of philosophical criticism, its naïve positivity and self-sufficiency.
- 26.
This is why Husserl can say that “no ordinary ‘realist’ has ever been as realist and as concrete as I, the phenomenological ‘idealist’” [letter to Abbé Baudin, 1934].
References
Bachelard, S. (1968). A study of Husserl’s “Formal and transcendental logic”. Evanston: Northwestern University Press.
Derrida, J. (1989). Edmund Husserl’s “Origin of Geometry”: An introduction. Lincoln/London: University of Nebraska Press.
Husserl, E. (1969). Formal and transcendental logic. The Hague: M. Nijhoff.
Husserl, E. (1973). Experience and judgment. Evanston: Northwestern University Press. Trans. of Erfahrung und Urteil: Untersuchungen zur Genalogie der Logik. Hamburg: Classen & Goverts, 1948. New edition, Hamburg: Felix Meiner Verlag, 1972.
Lohmar, D. (2002). Elements of a phenomenological justification of logical principles. Philosophia Mathematica, 3(10), 227–250.
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da Silva, J.J. (2017). Logic. In: Mathematics and Its Applications. Synthese Library, vol 385. Springer, Cham. https://doi.org/10.1007/978-3-319-63073-1_3
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