From the Mathematical Problematic to the Grounding of Logic

From the Mathematical Problematic to the Grounding of Logic

June 26, 2021 Off By Felso

Husserl’s philosophical journey begins with the philosophy of mathematics.

His doctoral thesis, which he defended in 1887, is on the concept of number. He published his Philosophy of Arithmetic in 1891. In this book, Husserl states that logical analysis is based on some basic propositions, in these propositions some simple, indefinable concepts (such as quantity, density, time and space), simple relations and relational concepts (such as equality, analogy, gradation, whole, part, quantity and unity) it says it’s out.

Since these concepts cannot be defined logically and formally, how can we explain them? According to Husserl, these concepts are abstracted from some concrete phenomena. To “explain” them, then, is to show from which phenomena they are abstracted. Husserl finds the origin of these basic concepts in subjective activity, mental subjective, psychological processes. However, the goal of Husserl’s efforts in the philosophy of arithmetic is to deny that the foundations of arithmetic are found in psychology and to provide objective foundations to mathematics and logic. However, the origin of the basic concepts in subjectivity has led Frege, who evaluated this book, to argue that Husserl fell into a position of psychology. Husserl’s position, however, is more complex. Yes, arithmetic objects are not independent of psychological processes that we can access through reflection, but the laws that govern these objects are not empirical contingencies either. They are objects of a necessary and universal knowledge. Husserl says that concepts can be clarified in two ways. We can explain a concept by defining it logically and formally. However, if we cannot explain a concept like this, it is necessary to think that it emerged with an abstraction made from concrete phenomena. However, in this abstraction, it is necessary to distinguish between the psychological mental process and the a priori relationship that consciousness establishes with being.

Logic and mathematics are also concerned with these formal categories, not with the sensible. Husserl’s aim is to clarify the basic terms of mathematics. Thus, he wants to base the formal structure of mathematics on vision (experience). According to him, philosophy, which is a science, should do this kind of justification. The fact that Husserl found the origin of these concepts in subjectivity drew the reaction of philosophers who were looking for objective foundations for mathematics.

In Logical Studies published in 1901, Husserl’s criticisms of psychology, that is, the view that mathematics and logic can be derived from empirical psychology, were much more extensive and had serious effects on the philosophy of the age. But here too Husserl makes a distinction between the objects of mathematics and logic and the psychological processes that grasp those objects; On the one hand, these objects arise in psychological processes, on the other hand, they differ from those processes in their necessary structure as the object of categorical intuition.

Logical Studies criticized naturalism, which reduces consciousness to nature or nature to consciousness, neglecting to distinguish different ontological regions, psychologism that reduces ideal objects to psychological processes, and naturalism, which tries to explain consciousness as a natural object. developed the theory. We will try to explain them by emphasizing the concepts of “intentionality”, “correctness” and “seeing” in particular.

The meaning given by Husserl to the concept of “intuition” is different from the meaning given by Bergson. For this reason, in Husserl philosophy, the concept of “intuition” was used as the equivalent of the concept of “Intution”.

In Logical Studies, Husserl says that the essence of mental being is intentionality. Every consciousness is consciousness of something. Here we have to understand the concept of “thing” in general, that is, a dream, a number, a table, a memory can also be this “thing”. A mental experience is bipolar, we can say that it consists of a mental act and an intentional one. Thus, an act of remembering leads to a memory, an act of dreaming to a dream, an act of desiring to the desired, an act of criticism to a criticised. Orientation means giving meaning, the directed appears in the light of the meaning given to it. However, this claim is not intended to suggest that the world will appear to it as consciousness tends towards the world. For the truth of our orientation derives from intuition. If my orientation that gives meaning to the thing is filled with an act of vision, then the thing is as I am actually directed. If such a vision is not in question, then my orientation is still meaningful but remains empty.

What vision gives me truth? Husserl argues that there are two kinds of vision: sensory vision and non-sensory a priori vision. In Logical Studies, Husserl distinguishes between meaning and object based on language. There are different types of names in the language. Sometimes names serve to identify a single object, like a property. It’s like “Little Red Riding Hood” denoting a fairy tale hero. Sometimes they refer to a single object even though they have different meanings. “Jena winner” and “