A conceptual representation

we introduce here a multi-level conceptual representation, based on two morphisms : 'is linked to' and 'opposes' :
a. \( \rightarrow \) ,\( \Rightarrow \), \( \Rrightarrow \), \( \rightarrow_4 \)... : 'is linked to', level (n+)1, (n+)2, (n+)3,...
b. \( \vdash \),\( \Vdash \),\( \Vvdash \),\( \vdash_4 \)... : 'opposes', level (n+)1, (n+)2, (n+)3,...
[optional :
c.  \(\circ \),\(\circ_2\),...: 'equivalence' or 'opposition', level (n+)1, (n+)2,...
d. \(. \) : under category
e. \( \leadsto\), \( \leadsto_2 \), : to, level (n+)1, (n+)2,...]

Let us give an example of implementation of this representation, in a philosophical context. (we are not trying to 'demonstrate' anything). Let Mr. X has these initial representations:
1. "Science is interested only in the reproducible : \( science \rightarrow reproductible \)
2. Moreover, science often appears as a model of truth : \(science \rightarrow truth \) (for example to people like Jacques Bouveresse)
3. The reproducible thus ends up appearing as an essential criterion of truth: \(reproducible \rightarrow truth \)
In reality the search for truth is not even a goal of science, which swears only by the reproducible. And to bring science and truth closer together is very reductive (for the concept of truth). It can be said that the metaphysical trace of science holds in the de-cision of the symmetry (i.e. its breaking):
$$ truth \rightarrow reproducible \Vdash truth \vdash reproducible "$$
Suppose now that X reads Heiddeger, in particular this passage from 'Introduction to metaphysik' [translation Fried and Polt]:
"For it cannot be decided so readily whether logic and its fundamental rules can provide any measure for the question about beings as such. It could be the other way around, that the whole logic that we know and that we treat like a gift from heaven is grounded in a very definite answer to the question about beings, and that consequently any thinking that simply follows the laws of thought of established logic is intrinsically incapable of even beginning to understand the question about beings, much less of actually unfolding it and leading it toward an answer. In truth, it is only an illusion of rigor and scientificity when one appeals to the principle of contradiction, and to logic in general, in order to prove that all thinking and talk about Nothing is contradictory and therefore senseless."

If X has the following representations on Heidegger:
\(truth \rightarrow question \, about \, beings \)
\(Logik \rightarrow science \)
\(science \vdash philosophy / poetry \)
and link his concept of reproducibility to Heidegger's Gestell (essence of technique / science)
\( Heidegger.science/Gestell \rightarrow X.reproducible \)
And if X retains his view that \(science \rightarrow reproducible \), it seems possible that he enriches his representation with:
\begin{array}{r c l}
truth \rightarrow reproducible & \Vdash & truth \vdash reproducible \\
 & \Rrightarrow & \\
science & \Vdash & philosophy / poetry
\end{array}
The relative link between Heidegger concept of philosophy / poetry and X's concept of reproducibility is not necessarily a view of Heidegger, so that this link is a creative -and subjective-one (which may be ultimately true or not [or 'interesting' or not]). (We may note that if poetry is talking about Nothing (last sentence of the text above), it might appear plausible that poetry is not X.reproducible...)

Let us suppose finally that X reads Stuart Kauffman, in particular 'Investigations' and 'Humanity in a creative world'.
If X admits that his concept of \( reproducible \vdash noreproducible \) (as part of the subjective 'ecosystem' of X's thought) is close to Kauffman's \( ergodic \vdash noergodic \) $$reproducible \rightarrow ergodic$$ and if X represents core Kauffman's idea as : \( noergodic \vdash ergodic \Rightarrow physics \vdash biology / complex \)
then X can further enriched his concept of reproducibility:
\begin{array}{r c l}
noergodic \vdash ergodic & \Rightarrow & physics \vdash biology / complex \\
 & \Rrightarrow & \\
noreproducible \vdash reproducible & \Rightarrow & physics \vdash biology / complex \\
\end{array}

So that X's concept of reproducibility allows X to create a link between his 'Heidegger's (thought) ecosystem' and his 'Kauffman's (thought) ecosystem' :
\begin{array}{r c l}
Heidegger & \Rrightarrow & Kauffman \\
 & \rightarrow_4 & \\
norepro \vdash repro \Rightarrow philo \vdash science & \Rrightarrow & noergodic \vdash ergodic \Rightarrow bio/ complex \vdash physics
\end{array}
Obviously all X morphisms presented above are debatable. But the purpose of this example is to sketch a plausible (necessarily subjective) learning experience. The question is less to ask the objective reality of \( P = [Heidegger.science/Gestell \rightarrow X.reproducible] \) or \( P' = [reproducible \rightarrow ergodic] \) than to help X to be creative. Specifically, could it be possible to (automatically) suggest \( P \) to X ? \( P \) contribute to make X build a bridge between (his) Heidegger and (his) Kauffman through is repro concept : could this drive an Assistant algorithm to suggest \( P \) (and \( P' \) and so on) to X ?
Its not too much difficult to trace the path
\( Bergson \leadsto Whitehead \leadsto Wittgenstein \leadsto Kauffman  \)
as Kauffman give (verly light) mention of Whitehead, and then if you google \( Whitehead \circ Kauffman \) you get
\( Whitehead \circ Kauffman \leadsto Shaviro \)
and Prof. Shaviro site give typically more plausible '\( \leadsto \)' genealogy as above (Bergson...)
But maybe X would have more interest in a (hidden) \( Heidegger \leadsto Kauffman  \) story ?