The Mathematical Paradigm in Philosophy: On Frege's Concept‐Script 

18:10 .. the article by Jan Westerhoff on Trede is *_Ars Characteristica Kantiana: Ludwig Benedict Trede’s Forgotten Necessary Grammar_* from 2003 in Kant-Studien 94

Mathematics as a level of reality (Secondness) in platonic physics The three levels of reality in platonic physics are given below. Mathematics, like ideas in general -- that is to say, mental objects-- is a form of Secondness, which in turn is an object of Mind or Firstness. Mind is the timeless, spaceless central domain of Plato's metaphysics, containing a priori certainties such as necessary logic, arithmetic and numbers, as well as Leibniz's pre-established harmony. It does all of the thinking, controlling and perceiving of the universe. Nothing is done without it and its control is cybernetic. Mathematics, as Secondness, is simply a mental object nlike monads are, but it is not monadic in that it has no correponding physical bodies. Insterad, it is a special language with a special grammar, in particular arithmetic and logic, but on its own can do nothing, create nothing, or achieve anything anymore than a human can using mathematics as a tool of thought. Or Shakespeare could with the english language. This is in line, if we consider mathematics as a language, with the idea of computationalism en.wikipedia.org/wiki/Computational_theory_of_mind " In philosophy, a computational theory of mind names a view that the human mind or the human brain (or both) is an information processing system and that thinking is a form of computing." which unfortunately has been construed by some to give anthropomorphic or god-like powers to mathematics. The universe was not constructed by mathematics alone, as it is mental, not physical. While this passivity may seem to some to diminish the power of mathematics, it in fact frees it from the limitations of the outer world, such as the limitations of Leibniz's pre-established harmony, and limits it only to its inherent logic and arithmetical constraints. This is particularly useful in abstract mathematics. In addition, due to what has been referred to as "the unreasonable effectiveness" of mathematics in the world, it appears that mathematics is predominantly the language of the pre-established harmony of Leibniz. In addition, all of Plato's philosophy of mathematics should hold. plato.stanford.edu/entries/platonism-mathematics/ ------------------------------------------------------------------------------------------------------------------------------------------------------------ The three levels of reality in platonic physics FIRSTNESS -FIRST PERSON (I) -Mind- The One, the Monarch- this is the realm of Plato's Mind. It is life itself, pure nonphysical intelligence. Purely subjective, timeless and spaceless - with innate knowledge and a priori memory, containing the pre-established harmony, necessary logic, numbers - the womb of the WHAT. Mind creates all, perceives all, controls all. Thus the individual mind controls the brain, not the reverse. Mind plays the brain like a violin. SECONDNESS - SECOND PERSON (YOU RIGHT HERE) ental objects so both subjective +objective- The Many. In this, the WHAT separates from Mind and becomes a HERE. Accordingly. Heidegger referred to existence as "dasein". "Being here." Some of these objects, such as ideas, or mathematics, are not monads, since they have no corresponding physical bodies. According to Leibniz, all monads are alive to various degrees. There are of three gradations of life in these, according to Leibniz: a) Bare, naked monads, which we can think of as purely physical ( Eg, a fundamental particle). b) Animal and vegetative monads, which Leibniz calls souls, which can have feelings, but little intellect. c) Spirits (corresponding to humans), which have, in addition, intellectual capacities. Mind transforms physical signals in nerves and neurons into experiences. If Mind then reperceives or reflects on these experiences, they are said to be thoughgt or apperceived. To be apperceived is to be made conscious. Thus consciousness is the product of thought. Intentions are also made in the same way, so that we caqn say that thoughts are intentions by Mind. The human brain is a monad which contains as subsets, mental capacities. Neuroscience tells us that there is binding between monads for parts and functions of the brain, but since monads cannot act directly on each other, this binding must be indirect, through the sequential updates of the perceptions and appetites of the subfunction monads. These must be made by Mind, either directly or through the preestablished harmony PEH). Unfortunately the Stanford Leibniz site on Leibniz makes no mention of the action of Mind on the individual mind, IMHO a gross shortcoming. Sensory signals and signals for feelings must also go through such a binding process. In a sense, the binding process plays the role of a self, but in conventional neuroscience self is a function of the brain, rather than the other way round, as common sense suggests and the intentionality of self or mind proves, along with the need for a PEH. This shortcoming in conventional understanding of the brain becomes all the more nagging if we consider thinking, which is closely related to apperception, because it must be conscious.Thinking, we submit, consists of consciously manipulating and comparing such apperceptions. Through Mind, with its potentially infinite wisdom and intelligence, intuitions and thoughts can arise spontaneously in the individual mind. If these are to be immediate and/or original, it is reasonable to believe that they originate in Mind, rather than indirectly through separate although bound parts of the brain. Anyone who has experienced a vocal duet in which the vibratos are in phase should become convinced of this. Mind is the monarch of the intelligent mind, which controls the brain. Mind plays the brain like a violin. Mind is also is able to focus on a thought for a brief period, within the context of one's memory and universal memory, for purposes of thinking an comparison, making the biological brain and its complex bindings seem hopelessly indirect and subject to confusion. THIRDNESS - THIRD PERSON (IT OVER THERE) Corresponding physical objects as is appropriate- -here the object is born or emittted from the monad--and emerges into spacetime as a particle, becoming completely objective, a WHAT+ HERE +WHEN., In addition the Thirdness of a private thought or experience is its public expression in some appropriate form. 3. Conclusions This format allows us to examine quantum phenomena from inside out and perception, thinking and consciousness ontologically- from physical nerve signals to mental experiences such as thought, consciousness, and cognition. It also avoids problem encountered in “bottom-up” science, such as complexity and emergence, if for no other reason than there is no apparent way of conceiving of a singular control point at the bottom. -- Dr. Roger B Clough NIST (retired, 2000). See my Leibniz site: rclough@verizon.academia.edu/RogerClough For personal messages use rclough@verizon.net