Second nature (from L. secundum naturam, "according to nature," lit. "following nature")

Logics: a reminder

a. Deduction allows deriving b as a consequence of a (deriving the consequences of what is assumed [synagögé or anagögé]) = applying a law

b. Induction allows inferring a from multiple instantiations of b when a entails b (inferring probable antecedents as a result of observing multiple consequents [epagögé, "bringing in"]) = inferring a law


c. Abduction allows inferring a as an explanation of b (inferring the precondition a from the consequence b [apagögé—note that Peirce translates this term as retroduction]), a.k.a. "inference to the best explanation" = assuming a law (i.e. a hypothesis)

Peirce's definition of abduction differs: it is "the inference of the truth of the minor premiss of a syllogism of which the major premiss is selected as known already to be true while the conclusion is found to be true," i.e. it supplies the middle premise of an enthymeme. What is called abduction above, Peirce calls . . .

d. Retroduction, which is "reasoning from consequent to [hypothetical] antecedent" (C. S. Peirce, "A Neglected Argument for the Reality of God" [1908], CP 6.469-70). Peirce sometimes calls it "Hypothetic Inference." It "depends on our hope, sooner or later, to guess at the conditions under which a given kind of phenomenon will present itself" (Letter to F. A. Woods [1913], CP 8.385-88). Cf. the fallacy of post hoc ergo propter hoc.

Thus, we can infer the conditions of possibility of a state of affairs, e.g. a problem in argumentation, existing.

Cybersemiotics

Topoi 2: strange logics/hypertopias

The panoply of possibilities (truths, many worlds, the field of argument) > a reality (Truth, the world, an argument).

= the collapse of the wave-function in observation—or in writing, the assumption that you must reduce your argument to a singular position.

Cf. Kochen & Specker (1967): every statement about a quantum system must
a. rely on a host of assumptions, and/or
b. refuse to obey the standard rules of logic (which are distributive and use the Boolean operators "and," "or," and "not").

Standard logic and mathematics fit the topos of set theory. (They are straight.)

Quantum logics do not. (They are fuzzy and strange.)

Isham has identified the topos of quantum theory, the logic of which serves for the quantum and real worlds, i.e. it is distributive (C. J. Isham and J. Butterfield, "Some Possible Roles for Topos Theory in Quantum Theory and Quantum Gravity," Found. Phys. 30.10 (2000): 1707-35).

But, rather than finding a topos that fits (inductively [yields a law]), we can also opt for a certain topos (abductively [yields a hypothesis or possibility]). (See Robert Matthews, "Impossible Things for Breakfast, at the Logic Café," New Scientist [14 April 2007], online at <http://fastblogit.com/media/logic_cafe.html>.)

That would allow us to assume a partial truth to be true—or a hypertopia to exist as a genuine possibility.

Topoi

Topos (Gk "place"; i.e. "place to find ['invent'] something") referred in classical Greek rhetoric to a standardised method of constructing or treating an argument, i.e. categories that help delineate the relationships among ideas (i.e. stock predicates), and stock concepts. The arguments based on these topoi were divided by Aristotle into "common" and "special" groups:

a. common (categories): laws, witnesses, contracts, oaths, comparisons of similarity, difference, or degree, definitions of things, division of things (whole/parts, for instance), cause and effect, and other items that could be analyzed, researched or documented;

b. special (concepts): justice or injustice, virtue, good, and worthiness.

Curtius expanded this concept in studying topoi as commonplaces: reworkings of traditional material, particularly the descriptions of standardised settings, but extended to almost any literary meme. They might be more-or-less stock characters (ethoi), topics (topoi), settings (kairoi), argument strategies (like types of exposition [logoi] or narratives [mythoi]), etc.

In physics, a topos is something a little different . . .

Escribir Es Nacer

Hijo de la oraciòn,
cada mañana
dejo el seno del cántico,
me desnudo del himno que se eleva
a la gloria de Dios
y desde el polvo
me atrevo a murmurar
tristes palabras.

Escribir es nacer,
dejar la cristalina
morada de inocencia
donde ya no estoy.

Mi verso tiene formas maternales;
es nube sobre el mar
y una gota de lluvia,
es niño que en la arena se entretiene
con las espumas y las caracolas
Mi padre está en los cielos
y yo me siento alegre,
nacido de su Verbo,
de donde salgo cada día.

http://en.wikipedia.org/wiki/Manuel_Altolaguirre

Snowflakes and Icebergs

= a. isomorphic form in writing, b. deep learning

The snowflake

There is an isomorphic, even fractal (especially, perhaps, when the isomorphism is more than merely structural, i.e., when it's semantically loaded), relationship between the structure of the sentence, paragraph and essay, viz.

a. essay: intro (with TS), body (with aspects of the T in the t-s's), and conclusion (returning to the TS)

b. paragraph: t-s (intro), evidence (body) and argumentation (conclusion)

c. sentence: S + P

Or you might say that it is a structure-preserving mapping relation.

[T(S) = thesis(-statement)
t-s = topic-sentence
S= subject
P = predicate

An isomorphic (ἴσος isos "equal" + μορφή morphe "shape") structure is structurally identical, i.e., if two objects are isomorphic, then any property which is preserved by an isomorphism and which is true of one of the objects is also true of the other.
A fractal (L fractus, "broken" or "fractured") is "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity (B. B. Mandelbrot, The Fractal Geometry of Nature [W.H. Freeman and Company, 1982]). A mathematical fractal is based on an equation that undergoes iteration (recursive feedback).]

The iceberg

a. Deep and shallow learning are not attributes of individuals: one person may use both approaches at different times, although he or she may have a preference for one or the other.

b. They correlate fairly closely with motivation: "deep" with intrinsic motivation and "surface" with extrinsic, but they are not necessarily the same thing; either approach can be adopted by a person with either motivation.

(There is a third form, known as the “achieving” or strategic approach, which can be summarised as a very well-organised form of surface approach, and in which the motivation is to get good marks. Learning is construed as a game, so that acquisition of technique improves performance.)

The features of deep and surface approaches can be summarised thus:

Deep	Surface
Focus is on “what is signified”	Focus is on the “signs” (or on the learning as a signifier of something else)
Relates previous knowledge to new knowledge	Focus on unrelated parts of the task
Relates knowledge from different courses	Information for assessment is simply memorised
Relates theoretical ideas to everyday experience	Facts and concepts are associated unreflectively
Relates and distinguishes evidence and argument	Principles are not distinguished from examples
Organises and structures content into coherent whole	Task is treated as an external imposition
Emphasis is internal, from within the student	Emphasis is external, from demands of assessment

(based on Ramsden 1988)

(See F. Marton and Säljö, "On Qualitative Differences in Learning—1: Outcome and Process," Brit. J. Educ. Psych. 46 (1976): 4-11; "On Qualitative Differences in Learning—2: Outcome as a function of the learner's conception of the task" Brit. J. Educ. Psych. 46 (1976): 115-27.)

The Surface learner is trying to "suss out" what the teacher wants and to provide it, and is likely to be motivated primarily by fear of failure. One study has suggested that efforts by teachers to convey that what they want is deep learning only succeeds in getting surface learners to engage in ever more complex contextualising exercises, trying to reproduce the features of the deep approach from a surface basis (P. Ramsden, D. Beswick and J. Bowden, "Effects of Learning Skills Intervention on First Year Students' Learning," Human Learning 5 [1986]: 151-64).

[James Atherton, http://www.learningandteaching.info/learning/deepsurf.htm]

Or you can look at it slightly differently: deep learning is something you deliver sotto voce—or sotto agua, to use the iceberg metaphor—along with the surface learning (which should be strategically, rather than extrinsically, motivated): modelling, reflecting, critically reading, in a way that is charitable, positional and "de-authorising," i.e. contextual and co-constructed.