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## Tue, Dec. 26th, 2006, 06:46 pm mostconducive: What is Surjectivity? Superjectivity? and Subjectivity, mathematically?

From the Wikipedia page http://en.wikipedia.org/wiki/Surjection I find the definition of Surjection, Surjectivity, Superjectivity but it is in mathematical language I don't understand, all these symbols of 'functions' I don't get.

I take it to be pure or transcendental (abstract) objectivity, abstracting from Alfred North Whitehead's metaphysics, where the (perhaps now unfortunately outdated) term 'Superject' means object, to Whitehead, 'eternal object' (a Subject or 'subjective form' being process, I take the other to be the product.) Is the object, using the term superject, the 'product' as in multiplication?

Superjectivity, or surjectivity seems to me to have a very precise mathematical definition, just like the differences between injectivity and bijectivity, and subjectivity.

My question, precisely put, is whether there is a more precise definition of subjectivity and superjectivity (certainly the one is just as precise as the other) from mathematics?

What is Surjectivity? Superjectivity? and Subjectivity, mathematically?
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### Wed, Dec. 27th, 2006 05:35 am (UTC)mostconducive

So "Epimorphism" is synonymous in reference to categories of sets... I'm not a mathematician, more a philosopher, so in attempting to gain insight from a different term with the same meaning, I wonder if the object as superject (as in Alfred North Whitehead's use of 'subject-superject' as the intercoherent actual entity) is an object by virtue of its self-mapping?

I'd refer you to Whitehead, him being the "real man of mathematics" behind Principia Mathematica, Rusell's extrovertedness seeing the project to completion and assuring the reification of his God-as-logic by outlawing self-reference (subjectivity) in mathematics. Whitehead's metaphysical treatise "Process and Reality" describes the usual use of "subject" as one-sided, for often is meant the actual entity, the abbreviated "subject-superject."

The truth of "philosophical constructions" isn't foreign to the truth of mathematics, just as truth itself is wholly independent upon any realm of discourse. My question regards the unity of these usages to reveal the true meaning beyond the appearances which the appearances indicate.

Just because "surjectivity" is mentioned as the title of an encyclopedic entry, and "superjectivity" isn't, many responders at this forum and others overlook the terms obvious identity, and so disregard what I inform following Whitehead's usage, and so also overlook the transference of meaning to the other -jectivity function I refer to, "subjectivity." It just shows how the followers (rather than authorities) are blinded to the truth (of objectivity as superjectivity in this case) by the manifestation of consensus (objectivity.)

Outside mathematical analysis, and mathematics is not limited to quantity (number,) for instance in synthesis, integration (of the integer) and particularly to the quality of semantics (a very unfortunately neglected part of mathematics,) analogy would clarify what the tendencies of analysis "sever and mutilate" (to paraphrase Spencer-Brown.) So for the semantics of the foundations of mathematics, I pursue a consensus of "superjectivity" in mathematics (in the minds of mathematically inclined individuals) unified with objectivity abstracted from the form of the object or objects we are familiar with, and it would be the infinity which pours meaninig and value from the Spirit (as the infinitesimal singularity, as a constant) to animate the life-world by filling the cups that are forms with the full void which is the absolute infinite.
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### Thu, Aug. 23rd, 2007 02:07 am (UTC)earthyspirit

all language is math.

p as push or ADD or "to"
al as mt or "all empty" or "a" linear sense of "the" "to" to be "of"
in as on or "to"
and mt as the "meet"in(g)

### Thu, Aug. 23rd, 2007 01:59 am (UTC)earthyspirit

Comprehensibility of sets in terms of words means seeking the substantial meaning of individual alphabetic symbols, the LETTERS.

the morpheme in the words consistently is "ject" now as english has degenerated pejoratively ever since switching from latin, one will find it hard to find much on the morpheme "ject" unless they are willing to play set theory with words.

This means taking as many words containing the morpheme as possible, lining them up and looking at the patterns, the pointings of them, so in an effort to clarify, lets do a bit of that now.

eject - to..out - expel
[Middle English ejecten, from Latin eicere, eiect- : -, ex-, ex- + iacere, to throw; see ye- in Indo-European roots.]

object
deject
reject
abject
inject

OK I've seen enough as I've been studying language as a set theory for two years now, most in the last few months, the utilization of EX as the similar in the eject footnote shows that ject is a synonym for "OF".

ex from latin

ex-
pref.
1. Outside; out of; away from: exodontia.
2. Not; without: excaudate.
3. Former: ex-president.

[Middle English, from Old French, from Latin and Greek; see eghs in Indo-European roots.]

eghs as a stem for ex... interesting, haven't seen this before, have to dig into the old dictionary at home later on it, lets see what we can dig up tho still...

ENTRY: eghs
DEFINITION: Out. Oldest form *ehs, becoming *eghs in centum languages.

Most of humanities language has been befuddles by a lack of a set theory for the alphabet outside the scope of phonetics, people are taught to believe that the alphabet means sounds but in truth the mathematics of creation are embedded into the symbols.

### Thu, Aug. 23rd, 2007 02:01 am (UTC)earthyspirit

the entire language of humanity can be honed down to two simple concepts..

though once simplified they become relatively more complex..

"to" and "of"