RI Kant and the objective construction of Math 2023

RJC KI JC1 Math JJL 1 Is Math invented or discovered? Is Math objective or subjective? The Kantian way Usually, in attempting to answer the question “Is Math invented or discovered?”, a simple way to go about this is to simply try and show that Math is either objective or subjective (and not both). The reasoning behind this is clear enough: if objective, it seems to point to the fact that Math is discovered while if subjective, it seems to point to the fact that Math is invented. This dichotomy, while simple and useful in preventing any confusion, is unfortunately, a false one. This is because there is at least one more possible position – the middle path – posited no less by Immanuel Kant. To understand this position fully, we must keep Kant’s project in mind. Recall that Kant thought that the epistemologies posited by the Rationalists and the Empiricists were both flawed. This was essentially because in order to have meaningful and contentful thinking, one must have both content and concepts where the concepts are applied to the content to make sense of it. Hence, for the Rationalist, Kant thought that though the mind does indeed require concepts and understanding to make sense of data, the main problem was where the data comes from if it did not come from the external world. In other words, concepts without any content are empty. For the Empiricist, Kant thought that the blank slate theory was wrong; one can have data but if one does not have the concepts to make sense of the data, then the data would just be a mish-mash of content. Since our knowledge is not a mish-mash of content but content that has been meaningfully arranged and classified, then it necessarily means that our content has had concepts applied to it by the mind. In other words, content without concepts is ‘blind’ or just ‘noise’. Keeping this in mind, Kant posited his famous filters of consciousness. Previously, we learnt that these filters of consciousness included space, time and causality. While this is correct, it over-simplifies Kant’s thinking. Here is (hopefully) a more accurate version of Kant’s argument. Kant thought that there were 2 kinds of filters of consciousness: the Forms of Sensibilities and the Forms of Understanding. The Forms of Sensibilities are what allows the mind to receive data from the Noumenal World. There are only 2 forms of sensibilities: Space and Time (Causality is a Form of Understanding). In essence, these forms of sensibilities are what provide the mind with content. The Forms of Understanding are what allows the mind to make sense of the data that it receives from the Noumenal World. There is no need to know what these are (there are altogether 12 here, of which Causality is one of them). The most important thing to take note of is that these Forms of Understanding fall into 3 kinds of categories: Dynamic, Mathematics, and the last which is a combination of the 2 (no name was given in th