A scientific community cannot practice its trade without some set of received beliefs. These beliefs form the foundation of the "educational initiation that prepares and licenses the student for professional practice". The nature of the "rigorous and rigid" preparation helps ensure that the received beliefs are firmly fixed in the student's mind. Scientists take great pains to defend the assumption that scientists know what the world is like...To this end, "normal science" will often suppress novelties which undermine its foundations. Research (...) is therefore not about discovering the unknown, but rather "a strenuous and devoted attempt to force nature into the conceptual boxes supplied by professional education". (shrink)

Thomas S. Kuhn's classic book is now available with a new index.

Feyerabrend argues that intellectual progress relies on the creativity of the scientist, against the authority of science.

Quel est le rôle de Galilée dans la naissance séculaire de la science moderne? Je réponds à la question ci-dessus à la lumière de deux nouveaux éléments. Dès le xvie siècle, Nicolas de Cues, quoiqu’il ne pratiquât pas la science expérimentale, a anticipé une partie substantielle de la révolution copernicienne et de la naissance de la méthodologie galiléenne. Le deuxième élément est l’introduction d’une nouvelle conception des fondements de la science ; ils sont définis comme constitués de trois dialectiques. Après (...) cette définition, la naissance de la science moderne correspond à un très long processus historique qui se conclut à notre époque. Sur cette longue période, Galilée ne fut pas seulement le premier à recourir à une méthodologie scientifique, mais aussi presque le seul à jamais avoir été conscient de l’ampleur des enjeux intellectuels de l’entreprise scientifique. (shrink)

In the present paper Peirce’s inferential processes are accurately defined against the background of the four ways of reasoning in Computability theory, i.e. general recursion, unbounded minimalization, oracle and undecidabilities. It is shown that Peirce anticipated almost all them.

MethodologyA new hypothesis on the basic features characterizing the Foundations of Mathematics is suggested.Application of the methodBy means of it, the several proposals, launched around the year 1900, for discovering the FoM are characterized. It is well known that the historical evolution of these proposals was marked by some notorious failures and conflicts. Particular attention is given to Cantor's programme and its improvements. Its merits and insufficiencies are characterized in the light of the new conception of the FoM. After the (...) failures of Frege's and Cantor's programmes owing to the discoveries of an antinomy and internal contradictions, respectively, the two remaining, more radical programmes, i.e. Hilbert's and Brouwer's, generated a great debate; the explanation given here is their mutual incommensurability, defined by means of the differences in their foundational features.ResultsThe ignorance of this phenomenon explains the inconclusiveness of a century-long debate between the advocates of these two proposals. Which however have been so greatly improved as to closely approach or even recognize some basic features of the FoM.Discussion on the resultsYet, no proposal has recognized the alternative basic feature to Hilbert's main one, the deductive organization of a theory, although already half a century before the births of all the programmes this alternative was substantially instantiated by Lobachevsky's theory on parallel lines. Some conclusive considerations of a historical and philosophical nature are offered. In particular, the conclusive birth of a pluralism in the FoM is stressed. (shrink)

Stephen George Simpson. with definition 1.2.3 and the discussion following it. For example, taking 90(n) to be the formula n §E Y, we have an instance of comprehension, VYEIXVn(n€X<—>n¢Y), asserting that for any given set Y there exists a ...

I characterize Bishop's constructive mathematics as an alternative to classical mathematics, which makes use of the actual infinity. From the history an accurate investigation of past physical theories I obtianed some ones - mainly Lazare Carnot's mechanics and Sadi Carnot's thermodynamics - which are alternative to the dominant theories - e.g. Newtopn's mechanics. The way to link together mathematics to theoretical physics is generalized and some general considerations, in particualr on the geoemtry in theoretical physics, are obtained.that.