Crítica, Revista Hispanoamericana de Filosofía, Volumen 9, número 26, Agosto 1977
El problema de los universales en Gottlob Frege
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Mauricio Beuchot
Universidad Nacional Autónoma de México

Resumen: This essay intends to elucidate Frege’s solution to the problem of universals, and to point out the fact that it is unsatisfactory. It begins by limiting the meaning of the problem; it deals with the referential or denotata of the terms, in search of their ontological status.
The main approaches to the problem are listed, keeping their traditional nomenclature, i.e., realism and nominalism, together with important intermediate solutions. Here lies the novelty of the approach. The intermediate solutions are rendered important in such a way that we avoid the narrow alternative of Platonism and verbalism.
The intermediate solution, which helps to clarify Frege’s approach (akin to Platonism) is that of Leibniz and Bolzano: the “vérités éternelles” and “Wahrheiten an sich”. The author deplores that neither Leibniz nor Bolzano have been sufficiently clear in the explanation of their theories. They even incur in obvious paradoxes when explaining the relationships between these abstract entities, physical reality and human minds.
The author maintains that Frege’s solution is an extreme realism of the type given by Leibniz and Bolzano.
Before entering into the matter, some recent interpretations such as those of Wells, Quine, Bergmann, Klemke, Grossmann and Thiel are considered. This was necessary to show the difficulty of Frege’s ontological commitment, and avoid simplistic views. Let us note that they are divergent, sometimes contradictory interpretations. Some would declare him a Platonist, some others a nominalist. While the arguments that prove him to be a nominalist are weak, those that prove his Platonism seem to be more plausible. In any case, Frege’s realism could not be termed Platonism as such. This is why his relationship to Leibniz and Bolzano is insisted upon.
The thesis that Frege’s realism is of this type is based upon four points d’appui: (a) his theory of numbers, (b) his semantic theory, (c) his ontological theory and (d) his theory of knowledge.
(a) Frege states that the numbers belong neither to the physical world nor to the mental world. They do not belong to the physical world since they are neither material individuals (in the sense that they are not spatio-temporal), nor are they properties (they are not the result of an abstraction from the individuals as is the case with heat, colour, hardness, etc.). They do not belong to the mental world either, since everything in it is a representation. Number is not a matter of representation but of reasoning; it belongs to a world which, being objective, is not real in the physical sense. This world is apprehended by the faculty of reasoning, which goes beyond representations, and which is not subjective, as they are (e.g., arithmetical theorems are eternal truths).
(b) As far as signs are concerned, they have two aspects: sense and reference. Frege is faced with the problem of the denotation of the very terms “sense” and “reference”: what in fact are senses and references? They cannot be said to pertain to the physical or mental world. Frege goes on to prove it with the same arguments used for numbers. Therefore, senses and references belong to the objective nonreal world mentioned before.
(c) Frege’s ontology accepts, in addition to individual objects belonging to the physical world, other entities pertaining to the objective nonreal world: numbers, truth-values, extensions, concept correlates, functions, characters or properties, concepts, relations, senses and thoughts. He affirms that all of them have their own subsistent and autonomous entity related to the external (physical) and internal (mental) world. That is to say, they belong to this objective nonreal world proposed by him.
(d) Concerning knowledge, Frege distinguishes two cognitive activities: on the one hand, representations, which are subjective and private, cannot be repeated in the same way in different subjects; on the other hand, thoughts, that are objective, can be apprehended in the same manner by all who have them. Progress in science is possible based upon the objectivity of thoughts. Only if everyone has the same understanding of a given geometrical theorem can it be criticized and the truth or falsehood discerned. Representations do not belong to the physical but to the mental world. Thoughts pertain neither to the physical world nor to the mental. They do not belong to the mental world because their objectivity depends on their ability to be understood in the same way by all who are concerned with them. Frege, however, goes beyond this. For him, this objectivity, thus stated, is tantamount to autonomy. For instance, Pythagoras’ theorem is true intemporally, regardless of being thought or not, as is the case with a planet which exerts its interaction with other planets before its discovery by astronomers. This is why thoughts belong to the objective nonreal world.
Therefore, Frege distinguishes three ontological worlds: (i) the mental world, which is internal and subjective, constituted by representations and sense perceptions; (ii) the physical world, that is external, objective and real inasmuch as it is apprehended by the senses; and (iii) the objective nonreal world, independent from the physical and mental worlds, which is neither perceivable by the senses nor representable, but rather is attained by a superior faculty: reason.
This shows that Frege’s solution is an extreme realism, which although not simply reducible to Platonism (since he fails to make explicit the theories of imitation and participation, essential to a Platonist assessment), is an extreme realism very similar to Leibniz’s but rather remote from Bolzano’s.
The essay ends with some reflections on the problems raised by extreme realism and nominalism. With the latter in view, an intermediate solution is proposed: the moderate realism of Aristotle and Aquinas is suggested as a solution, in the hope of providing, on another occasion, the required substantiation.
(Mauricio Beuchot)
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