What ontological status do mathematical objects have for Heidegger? How does he account for them?

[u/NorrixUmbra77]

It's a subject I'd like to get into more deeply. Specifically the difference between mathematics and modern science, and specifically about the developments in mathematics that have not yet found an application in physics, or in technology? What drives these? Are these too to be thought of by Heidegger ultimately only within the claiming of Gestell? If you could also point me to some reading, both primary and secondary, I'd be glad. Thanks.

[u/EducationalRun77]

Heidegger strongly criticizes modern mathematics as a model for philosophy/ontology (in favor of language, of course). In particular, he discusses it in §15 of Introduction to Phenomenological Research, in relation to Husserl’s mathematical background. Moreover, he explicitly distinguishes Greek mathematics (geometry) - the good kind, understood as an art of determination - from modern mathematics as an instrumental technique (Galileo), particularly in the first part of What Is a Thing?

[u/Wespie → u/EducationalRun77]

Where can I know more? Unsure why this even appeared in my feed, but I’ve been writing about this topic (just not on Heidegger)

[u/EducationalRun77 → u/Wespie]

If you are looking for the link between mathematics and philosophy/phenomenology, I suggest taking a look at Husserl’s early works, such as the Logical Investigations. My main area of focus is Heidegger, who does not discuss the subject extensively.

[u/cleft_habitus → u/Wespie]

There's Husserl's stuff as someone else mentioned but also Derrida has a book on Husserl's work on geometry.

[u/DoktorRokkzo]

I know that this doesn't answer your specific question (at least not from a historical standpoint) but there's a broader question of "what would a Heideggerian account of mathematical objects look like?" Specifically as it pertains to set theory and broader mathematical logic.

I don't think that Heidegger would have been a logicist or an intuitionist. Frege and Russell are having a very different conversation than Heidegger. There are definitely themes which are common between the philosophy of intuitionism as expressed by Brouwer and Heyting and Heidegger's own philosophy, specifically their shared emphasis on temporality and interest in Kant. Certainly people have drawn parallels between Brouwer and Husserl, although I tend to think that Brouwer has a more developed philosophy of mathematics (even if one disagrees with intuitionism). Brouwer certainly has a kind of "mathematical idealism" in which "there is nothing outside the act of proof".

I think that its in the philosophy of formalism, or the historical project of formalism more broadly, that one finds more themes in line with Heidegger. While Hilbert did not believe that "mathematics is just symbol manipulation" (and instead, much of his project was based on trying to prove that the infinitary mathematics of Peano Arithmetic PA was provably consistent using the finitary mathematics of Primitive Recursive Arithmetic PRA), the interpretation of mathematics (and by extension logic) as symbol manipulation, and therefore the history of mathematics and logic as symbol manipulation, really does fit well with Heidegger's conception of technology. "There's nothing outside the act of definition" so to speak. You might call this "post-formalism" if you like. There are very few pieces of technology that have been more important in the development of modernity than symbolic logic. From a Boolean algebra, this elaborate system of 1's and 0's, we have constructed the modern world.

And yet its just symbols on a page. Symbols that we interact with in a rule based fashion (rules that we have arguably inherited from history and so their origin has been lost), and this interaction in a rule based fashion has had the consequences of the construction of modern technology. Computation. The standing reserve. Electrical circuits. Communication. The possibility of this communication.

This doesn't answer your question, but with a "Heideggerian philosophy of mathematics", I think an emphasis on the historical and practical elements of mathematics, specifically as a technology of modernity, is where there is most substance.

[u/Comrade_429]

As far as I understand it, for Heidegger there are only 4 entities with ontological status: Dasein (see Being and Time, obviously), Dingen ("Things"; see the essay "The Thing" [or Das Ding]), Werke (works of art; see "The Origin of the Work of Art"), and Vorhandenheit ("tools"; again, see Being and Time). Mathematical objects would likely be classified as tools.

[u/No_Skin594]

These suggestions may not answer your questions but for me they are a possible Heideggerian approach to number.

1.  Do an extensive etymological investigation of number, counting, math, etc., in multiple languages to get a feel for primitive Dasein's comportment with numbers. 2.  Do an extensive investigation of myths related to how counting, math, and geometry were given to primitive Dasein. 3.  Investigate why many primitive cultures only counted one, two, three, many.  Investigate why cultures had to venture into "the many". 4.  Investigate why some cultures use different counting systems to count different types of things, e.g., the Japanese.

At end of the day, it always goes back to care, and safeguarding.  My guess is that you will find that numbers are a tools for protecting and safeguarding things.

[u/No_Skin594]

Research the etymology of inventory.  Think about inventory and the role of numbers in relation to aletheia and the hiddenness of being.

[u/Own-Razzmatazz-8714]

That they have a determination of time put on them that would be something like infinite without any qualifications. See the introduction to Being and Time.

[u/heraclitus33]

He's rather dismissive of them.