Adaequatio intellectus et rei

Adaequatio intellectus et rei: adequation of the intellect to things (correspondence). Or to paraphrase Hermann Lotze (Logica #130, p. 156), "thought follows reality". A frequent assumption (and fallacy) in science.

Schoolmen

The idea was expressed by William of Auvergne (1190-1249) as 
  • adaequatio intellectus ad rem (adequation of the intellect to things). 
Other versions of the apothegm are:
  • veritas est quod est, enuntiativus est natura veritatis et essentiae ejus (Isaac Israeli 823-932), 
  • veritas est dispositio in re exteriore cum est ei aequalitas (Avicenna), 
  • adequatio intellectus et rei (Aquinas following Israeli), 
  • adequatio rei cum intellectu (Albertus Magnus).
  • veritas transcendentalis significat entitatem rei, connotando cognitionem seu conceptum intellectus, cui talis entitas conformatur vel in quo talis res representatur (Suarez)
  • Ordo et connexio idearum idem est ac ordo et connexio rerum (Spinoza)
Some wording of the schoolmen associated with this concept are:
  • conformitas, correspondentia, convenientia, adaequatio, representatio.

Moderns

  • Veritas auterm enunciationis seu iudicii nihil aliud est quam conformitas ore factae aut iudicii mente peracto cum ipsa enuntiata seu iudicata (Gassendi)
  • ‘truth’, in the strict sense, refers to the conformity of a thought with its object (Descartes, Letter to Mersenne, 16.x.1639) 
  • Idea vera debet convenire cum suo ideato (Spinoza)
  • Let us be content with looking for truth in the correspondence between the •propositions that are in the mind and the things they are about. (Leibniz New Essays, IV, v, 11)

20th Century

Ortega y Gasset in Historia como Sistema argues that:
Image result for ortega y gasset
  • "the world of reality and the world of thought are each a cosmos corresponding one to the other, each compact and continuous, wherein nothing is abrupt, isolated or inaccessible  ...Western man believes, then, that the world possesses a rational structure, that is to say, that reality possesses an organization coincident with the organization of the human intellect, taking this, of course, in its purest form, that of mathematical reason.” - "En los últimos años del siglo XVI y ... primeros del XVII ... cree, pues, el hombre de Occidente que el mundo posee una estructura racional, es decir, que la realidad tiene una organización coincidente con la del intelecto humano, se entiende, con aquella forma del humano intelecto que es le más pura: con la razón matemática."
There's now the issue of whether the human intellect is really capable of grasping the infinite complexity of reality. John Duns Scoto phrases this as an objection:
Atqui impossibilis omnino est talis adaequatio et commesuratio inter potentiam finitam et et obiectum infinitum. Ergo, pariter impossibile est infinitum ab intellecto finiti comprehendi.
And White
...the finite mind is inadequate to grasp the infinite. SC108
And Cusanus
Quoniam ex se manifestum est infiniti ad finitum proportionem non esse (De Docta Ignorantia, Cap iii)
and Trithemius also echoes this argument, having resort to an interesting term "incircumscriptibilem":
Deum igitur nobis credere potius quae scire vel intelligere omnino necessarium fuit: propterea que penitus impossibile sit illam super divinam & incircumscriptibilem maiestatem comprehendi a nobis qui nihil intelligimus sine ministerio sensuum & discursu rationis. (Liber octo quaestionum ad Maximilianum Caesarem de fide et intellectu)
and Lactantius:
incogitabiles... inextricabiles...inaestimabilem potestatem. Dubitet vero aliquis, an quidquam difficile aut impossibile sit Deo, qui tanta tamque mirifica opera providentia excogitavit, virtute constituit, ratione perfecit; nunc autem spiritu sustentet, potestate moderetur, inexcogitabilis, ineffabilis, et nulli alii satis notus quam sibi? (Divinarum Inst., lib i)
But Arthur Eddington introduces a radically different account:
We have learnt that the exploration of the
external world by the methods of physical science leads not to concrete reality, but to a world of symbols.
Along the same lines James Jeans suggests,
The essential fact is simply that all the pictures which science now draws of nature, and which alone seem capable of according with observational fact, are mathematical pictures...They are nothing more than pictures – fictions if you like, if by fiction you mean that science is not yet in contact with ultimate reality.” 


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