mathematical

is a project of thing-ness which skips over things. The project first opens a domain where things, i.e., facts show themselves. This project posits that which things are taken as, what and how they are to be evaluated beforehand.

1. The mathematical is, as mente concipere, a project of thing-ness which, as it were, skips over the things. The project first opens a domain where things-i.e.,facts-show themselves.2. In this projection is posited that which. things are taken as, what and how they are to be evaluated beforehand. Such evaluation and taking-for is called in Greek axio6. The anticipating determinations and assertions in the project are axi6mata. Newton therefore entitles the section in which he presents the fundamental determinations about things as moved Axiomata, sive leges motus[The Axioms or Laws of Motion]. The project is axiomatic. Insofar as every science and cognition is expressed in propositions, the,cognition which is taken and posited in the mathematical project is of such a kind as to set things upon their foundation in advance. T h e axioms are fundamental propositions. (heidegger 'modern science' .. 268) is not a thing in itself, nor is it any objective determination pertaining to, or inherent in things. (KANT CPR 46)

is, in the sense of learning what one already knows, the fundamental presupposition of 'academic' work. Plato's words over the academy are nothing but a hard condition and clear circumscription of work.

A knowledge which does not build its foundation knowledgeably, and thereby takes its limits, is not knowledge but mere opinion. The mathematical, in the original sense of learning what one already knows, is the fundamental presupposition of 'academic' work. This saying over the Academy thus contains nothing more than a hard condition and a clear circumscription of work. Both have had the consequence that we today, after two thousand years, are still not through with this academic work and never will be as long as we take ourselves seriously. (heidegger 'modern science' 254)

is that 'about' things which we really already know (i.e.) the body as bodily, the plant-like of the plant, the animal-like of the animal, the thingness of the thing. We do not first get something out of things, but, in a certain way, we bring it already within us.

The mathemata are the things insofar as we take cognizance of them as what we already know them to be in advance, the body as the bodily, the plant-like of the plant, the animal-like of the animal, the thingness of the thing, and so on. This genuine learning is therefore an extremely peculiar taking, a taking where he who takes only takes what he basically already has. (heidegger 'modern science' : 251) . . . . The matheata, the mathematical, is that 'about' things which we really already know. Therefore we do not first get it out of things, but, in a certain way, we bring it already with us. (heidegger 'modern science' 252)

is the idea that, for example, in grasping the number three (as in the recognition of their being 3 chairs over there) as such, we only expressly recognize something which, in some way, we already have. This recognition is genuine learning.

In thus grasping the number three as such, we only expressly recognize something which, in some way, we already have. This recognition is genuine learning. (heidegger 'modern science' 252)

mathematical, n.Definitions

mathematical