The infinite exists. Something does not come from nothing and anyone can understand there is something [existence] and that thing has a totality.
Therefore, the infinite exists as distinguished from the successor function.
An infinite predicate is real, Dictum de Omni. {Dasein?}
“We call the predication affirmative when, and only when, there is nothing among the sensational effects that belong universally to the predicate which will not be said to belong to the subject.” EP2: 344.
If we speculate about what Nietzsche meant by “Schopenhauer as Educator” the present interpretation follows.
“His [Kant] object of experience,” of which he is constantly speaking, the proper subject of the categories, is not the representation of perception, nor is it the abstract concept; it is different from both, and yet is both at the same time, and is an utter absurdity and impossibility.
Schopenhauer, Arthur, E F. J. Payne, and Arthur Schopenhauer. The World As Will and Representation. , n.d.. Print.
Nietzsche follows suit:
The extraordinary courage and wisdom of Kant and Schopenhauer have succeeded in gaining the most difficult victory, the victory over the optimism concealed in the essence of logic, - an optimism that is the basis of our culture.
The Birth of Tragedy and the Case of Wagner. New York: Vintage, 1967. Print. ℙ 18
My interpretation of Peirce’s categories, from The One Law of Mind, can simply be stated that Second-ness determines First-ness into Third-ness. It is the second-ness of the Immediate Object that is filtered by Space and Time. Space and Time make possible the indexing of this second-ness. Space and Time may be subjective, but they are necessary conditions not only for the mind to have experience of a mind independent object, but also to formulate a representation that can index that experience to a Final interpretant and be shared with a community of inquirers. Don’t forget the Copernican Revolution!
It is illuminating in that Peirce distinguished three types of Sign: icon, index, and symbol. Peirce’s analysis of Kant’s Critique’s concludes with a type of realism that makes consistent the logic between the Intuition and the Concept, defined by Peirce as the Immediate Object and the Dynamic Object. This allows a community of interpreters to use realism as a guide in their investigations that lead to a Final Interpretant. The object of experience can be indexed in some cases, and is more than a mere icon or a symbol that is deconstructed into absurdity.
As Schopenhauer points out, the object of experience is what is in question. Peirce’s Semiotics composes a set of definitions that make possible the consistent reference to the object of experience. The representation and the two types of objects are elements which the mind synthesizes into meaning from experience of an object. Which object you may ask? Both, which is an intimation to Peirce's solution to the Continuum Hypothesis.
Schopenhauer and Nietzsche seem to be at the level of the Immediate Interpretant, unable to transcend the order of the universe and are thus caught in an eternal return of confusion. Nietzsche may no doubt be an idiot, because he originates deconstruction of experience from the confusion of the work that a sign does. It seems clear he really didn't think there was a solution to Kant's attempt to synthesize the Phenomenon and Noumenon. He is clearly not on the level of Charles Sanders Peirce, who wanted two things in life; to have his name pronounced correctly, and to be known as a logician.
Nietzsche’s philosophy is a political philosophy on the struggle for existence in the presence of pure power. If the world needs unity through revolution, let it be the Copernican Revolution of Kant and Peirce.
Since I penned “G-torr, the anti J-zeus” I have been preoccupied by the power of psychologism, due to life events. I have been reading the Wang text for a while and wondered what Godel thought about psychologism. Searching the index I found one entry on, “Psychologism, 77” which discusses Godel’s outline for a proof of Platonism. By refuting the Creation view, Psychologism, and Aristotelian realism, Godel speculated it was possible to prove the Platonic view of mathematics.
For me this is indicative that Godel instinctively denied the semantic implications of Incompleteness and Undecidability, but the problem was cross referencing “Aristotelian realism,” since the current context didn’t touch on it or “Psychologism.” Again the index refers to “Aristotelian realism (in Mathematics), 77, 223” and when you go to page 223 there is another iteration not just of Aristotelian realism, but Psychologism with no discourse about their semantics.
My intuition is lead to wonder what would cause the subjects of Psychologism and Aristotelian realism be divided by 146 pages of text and only a nominal indication that they are relevant to the topic at hand. Which lead me to think about Platonism and a form of eastern thought that is strongly associated with it, i.e. Chinese thought in general.
Now it is entirely possible to let the incomplete index on the second instance of “Psychologism” slip by without a trace of suspicion, however, what about no semantic discourse on their relevance? Perhaps I should thank Strauss for his work on esotericism and the use of indices to throw you off the trace, unless you devote the whole text to a complete analysis. But then, that would make this a political text and not a text on Formal Science.
I wanted to do a presentation in graduate school on using Peirce’s Semiotic Grammar to counterexample the Gettier Problem, but things took another course. I believe I can formulate the counter example by pointing out the functional difference between a Rhematic Indexical Legisign, which is a demonstrative pronoun: this, that, these, those (those ten coins in anyone's pocket), and a Dicent Indexical Sinsign (an actual and determinate pocket of a correlating job recipient).
The ambiguity comes in the form of justification allowed: he who has ten coins. To allow a Rheme to do the work of a Dicent is obviously invalid, and thus unsound. It compels one to wonder what the academy is up too.
Another thread pulled Peirce and Jung’s work together for me, their understanding of the self as a symbol (233).
Symbols grow. They come into being by development out of other signs, particularly from likenesses or from mixed signs partaking of the nature of likenesses and symbols. We think only in signs. These mental signs are of mixed nature; the symbol-parts of them are called concepts. If a man makes a new symbol, it is by thoughts involving concepts. So it is only out of symbols that a new symbol can grow. Omne symbolum de symbolo. A symbol, once in being, spreads among the peoples. In use and in experience, its meaning grows. Such words as force, law, wealth, marriage, bear for us very different meanings from those they bore to our barbarous ancestors. The symbol may, with Emerson’s sphynx, say to man,
Of thine eye I am eyebeam.
In all reasoning, we have to use a mixture of likenesses, indices, and symbols. We cannot dispense with any of them. The complex whole may be called a symbol; for its symbolic, living character is the prevailing one. A metaphor is not always to be despised: though a man may be said to be composed of living tissues, yet portions of his nails, teeth, hair, and bones, which are most necessary to him, have ceased to undergo the metabolic processes which constitute life, and there are liquids in his body which are not alive. Now, we may liken the indices we use in reasoning to the hard parts of the body, and the likenesses we use to the blood: the one holds us stiffly up to the realities, the other with its swift changes supplies the nutriment for the main body of thought.
Peirce, C. S., Houser, N., Eller, J. R., Lewis, A. C., De, T. A., Clark, C. L., Davis, D. B., ... Peirce Edition Project. (1998). The essential Peirce: Selected philosophical writings. Volume 2, 1893-1913. Bloomington: Indiana University Press.
"In order to orient ourselves, we must have a function which ascertains that something is there (sensation); a second function which establishes what it is (thinking); a third function which states whether it suits us or not, whether we wish to accept it or not (feeling); and a fourth function which indicates where it came from and where it is going (intuition)."
Jung, Carl. Collected works, Vol. 11, Part IV, "The Problem of the Fourth."
Jung Aristotle
Sensation ≡ Material Cause
Thinking ≡ Formal Cause
Feeling ≡ Efficient Cause
Intuition ≡ Final Cause
N.B. In Peirce’s The Doctrine of Necessity Examined, he is describing how Democritus is thinking about one cause, but the pre-Socratic philosophers were thinking about three causes, pre Aristotle. He links Democritus’ understanding of efficient cause with external compulsion; without any notion of material cause: the main association (unnecessarily) with scientific determinism. This notion, analogously, of Feeling with an external compulsion seems particularly relevant to modern notions justice, which ironically Peirce indicates with his remarks on Stoicism.
Rhematic iconic qualisign (111)
Rhematic iconic sinsign (112)
Rhematic iconic legisign (113)
Rhematic indexical sinsign (122)
Rhematic indexical legisign (123)
Rhematic symbolic legisign (133)
Dicent indexical sinsign (222)
Dicent indexical legisign (223)
Dicent symbolic legisign (233)
Note on 111, 222, 223:
It is beyond the scope of Peirce’s analysis that 111, 222 and 223 should be represented together as I have them, except within the scope of Existential Graphs. This is not an Existential Graph, however Existential Graph theory, as I came to understand Peirce, was used to derive the order of Peirce's Categories, which are represented in this depiction.
