There are the old schools of philosophy of mathematics: Logicism, formalism and intuitionism. These have been developed into e.g. Realism, Fictionalism, structuralism, etc.
There was the linguistic turn, and recently the cognitive turn. There was the Cartesian Dualism ("inside" vs. "outside"), Critical philosophy of Kant, Husserl, Heidegger, Postmodernism, etc.
In my view I find that the best position is Dalielle Macbeth, Realizing Reason, Which is based on mathematical practice and regaining meaning. Meaning is not reductive, Frege was ill conceived, ampliative proofs should be diagrammatic instead of mechanistic, etc.
My philosophical position is based on:
1. Experience
2. Should be conceptional.
3. Foundations is derived by examining historical events in depth and by ”concentrate the essence of practice and in turn use the result to guide practice”. I do not support the reduction of all mathematics e.g. to Set theory and Mathematical Logic, although it seems that in some cases is working.
4. Pragmatism, diagrammatic reasoning, and conceptual approach, seems to be the philosophy of Category Theory.
All these are nicely expressed in the following two books:
- Danielle Macbeth Realizing Reason A Narrative of Truth and Knowing. Oxford 2014.
- Ralf Krömer, Tool And Object, Birkhäuser, 2007.
My philosophical position is based on:
1. Experience
2. Should be conceptional.
3. Foundations is derived by examining historical events in depth and by ”concentrate the essence of practice and in turn use the result to guide practice”. I do not support the reduction of all mathematics e.g. to Set theory and Mathematical Logic, although it seems that in some cases is working.
4. Pragmatism, diagrammatic reasoning, and conceptual approach, seems to be the philosophy of Category Theory.
All these are nicely expressed in the following two books:
- Danielle Macbeth Realizing Reason A Narrative of Truth and Knowing. Oxford 2014.
- Ralf Krömer, Tool And Object, Birkhäuser, 2007.
"Briefly, my position – called “Triple Aspect Monism” (TAM) – is that conscious experience is a fundamental aspect of reality, neither separable from nor reducible to the other two aspects (namely, the physical-chemical-biological – in short, “physical” – and the informational). In the presentation of TAM, I take into account concepts used in current scientific practice. The physical and the informational aspects are composed of entities and processes described in the context of their respective scientific disciplines. The third aspect, conscious experience, is united to the others and would hopefully be treated scientifically, besides the existing philosophical, religious, and artistic approaches. According to TAM, the three aspects belong to one large dynamical system covering the totality of existence which Spinoza and other philosophers have called Nature. It evolves in time and progressively manifests the three aspects, beginning with the physical, unfolding into the informational and finally, under certain circumstances, into conscious activities"
Pereira Jr., A. (2013). Triple-Aspect Monism: A Conceptual Framework for the Science of Human Consciousness. In A. Pereira Jr. & D. Lehmann (Eds.), The Unity of Mind, Brain and World: Current Perspectives on a Science of Consciousness (pp. 299-337). Cambridge, UK: Cambridge University Press.
Dear Costas, if you have time and interest could you please suggest me an adequate way of formalizing TAM using category theory or a similar approach? My best attempt was the diagram "Three layered cake in Nature's box" (Figure 1 of the attached paper).
Dear Alfredo,
I have your books. right now I have to write a book review and I am a little busy. Give me some time to understand you TAM, and I will be back! Mean while you can have a look at the book of Danielle Macbeth, realising Reason.
Realism based on science and invention bridging the gap between fantasy and realism.
Dear Bend,
I like that! "Eleatic Buddist"!
Since some they do not remember the definition of Eleaticism:
Eleaticism, one of the principal schools of ancient pre-Socratic philosophy, so called from its seat in the Greek colony of Elea (or Velia) in southern Italy. This school, which flourished in the 5th century bce, was distinguished by its radical monism—i.e., its doctrine of the One, according to which all that exists (or is really true) is a static plenum of Being as such, and nothing exists that stands either in contrast or in contradiction to Being. Thus, all differentiation, motion, and change must be illusory. This monism is also reflected in its view that existence, thought, and expression coalesce into one.
On the other hand Bend, I think there is an antiphrasis in saying Eleatic and Buddhist. Buddisms is rathe a dialectical philosophy, and thus a duality is around. On the other you are an extremist monists!
With a third moment, the dual phase of dialectics recovers the Monist unity, but an unity in diversity. The Eleatic Monism is sterile, it is unicity without diversity.
Dear Bernd, I am defending my Triple Aspect Monist (TAM) position. It is related to Aristotle, Hegel and Peirce. In Aristotle the third term is the middle. In Hegel, it is "Aufhebung". In Peirce it is the Thirdness that accounts for the pragmatic dimension (and convergence to the truth in the long run). In TAM, it is consciousness - the third aspect that emerges from the first two (matter/energy and form/information) and recovers the unity of reality.
Love and respect.
(this is my shortest answer. I don't know if it is religious or philosophical... sorry ! )
Love is nothing without respect, dear Bernd !
(That is my thesis. Your antithesis would be to choose Love. My synthesis is that Respect is the Mother of Love ... KKKK!)
Kostas asked for short answers...
With Love having a Father and a Mother a new triad is formed...
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