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 ?

Learning Fallacy II

In 'Learning Fallacy' LF we began the reflexion on the model / data duality :
a. what kind of data are relevant for my problem - i.e. am I not typically biased towards over-reducing/localising the problem ?
b. how much specific is my model - that is am I not typically biased towards overfiting, i.e. under-symmetrising my model ?

We call the corresponding heuristic :
a. Data Expansion
b. Large Symmetry

The data expansion heuristic is not a more-data-is-better tale. Here we are talking of perspective on 'reality' [recall that your reality is a work-in-progress...] : what kind of implicit (over-simplifying) hypothesis am I doing by leaving seemingly not relevant data ?

Ex a : We already mentioned the RFIM hypothesis on Finance, which precisely is considered to be relevant more broadly for social domain.
The transdisciplinary (or not) paradigm is one manifestation of the Data Expansion problem : a typical example is given in 'Natural language / neuro economics II'.

Ex b : recall the paradoxical behavior of Markowitz in FL : the Portfolio theoretician adopts a fully symmetrised approach for his skin-in-the-game private financial strategy...
'Learning as categorification IV' propose simple examples where symmetries are explicitly declared the essential part of the problem.

Natural language / neuro economics II

we had a first round over NL in the post NL / neuro economics [NLNE]. Curiously, at that time our (rapid) web foraging missed the important "faculty of language" Hauser et al. 2002 paper [FL]. We will go further in the subject with the 2016 Hauser Watumull 'UGF' and 2014 'On recusion' papers.
FL is interesting for us for two reasons :
a. it links to Learning Fallacy II [LF]
b. it links with NLNE and A Conceptual Representation CR


FL has a clear comparative approach, and its semantics fields builds on the Data Expandion DE  Large Symmetry LS tradeoff of LF :  'compar' : 39, 'analog' : 10, 'homolog' 12, specif : 18, uniq : 30.
$$FL \rightarrow Data \,Expansion / Large \, Symmetry$$
In detail :

a. "We hypothesize that FLN only includes recursion and is the only uniquely human component of the faculty of language".
$$FL.animals \rightarrow DE $$"Although scholars interested in language evolution have often ignored comparative data altogether or focused narrowly on data from nonhuman primates, current thinking in neuroscience, molecular biology, and developmental biology indicates that many aspects of neural and developmental function are highly conserved, encouraging the extension of the comparative method to all vertebrates (and perhaps beyond) ."
"Although this line of reasoning may appear obvious, it is surprisingly common for a trait to be held up as uniquely human before any appropriate comparative data are available."

b. "We further argue that FLN may have evolved for reasons other than language, hence comparative studies might look for evidence of such computations outside of the domain of communication (for example, number, navigation, and social relations)."
"We consider the possibility that certain specific aspects of the faculty of language are “spandrels”—by-products of preexisting constraints rather than end products of a history of natural selection (39). This possibility, which opens the door to other empirical lines of inquiry, is perfectly compatible with our firm support of the adaptationist program. Indeed, it follows directly from the foundational notion that adaptation is an “onerous concept” to be invoked only when alternative explanations fail."$$FL.(bio)functions \rightarrow LS$$ in more detail:
$$communication, number, navigation, social \, relations \rightarrow FLN \\  \Rightarrow universal \, constraint \,(computational \, and \, biological) \\ \Rrightarrow LS $$ (it should be read recursively : \( [[x \rightarrow y] \Rightarrow z] \Rrightarrow u \)
This reasoning line dwells on the computational perspective of our NLNE: the problem of NL is a computational one, then a simplicity / creativity one, so essentially - as much as we learnt from Nature eons trial and error 'foraging', recursion is 'nearly optimal'. FL makes clear reference to the Minimalist program : "Recent work on FLN (4, 41–43) suggests the possibility that at least the narrow-syntactic component satisfies conditions of highly efficient computation to an extent previously unsuspected."
$$FL \rightarrow recursion$$
As already mentioned in NLNE, First Order Logic expressiveness is not enough, your need more 'deepness'. The 2-Cat concept in category theory is not proper neither for a conceptual representation, and CR is a tentative trial to a general Creative Assistant.