HFD Zagreb 1993. |

FILOZOFIJA MATEMATIKE

Stav o realizmu u matematici u svjetlu Putnamovog općeg stanovišta o realizmu u znanosti

Problem istine

Spoznajni položaj matematičkig teorija

Mogućnost i nužnost

Problem matematičkih entiteta

Modalna slika matematike kao zamjena za matematičku objek-sliku

Putnamov odnos prema suvremenim matematičkim teorijama (matematički 'izmi', filozofske pretpostavke, zasnivanja)

Konvencionalizam kao oblik filozofije znanosti

Konvencionalizam kao matematički 'izam'

Reichenbachova nekonvencionalistička jezgra geometrije

Grübaumov konvencionalizam u filozofiji primijenjene geometrije

ZNAČENJE, FUNKCIONALIZAM, KORESPODENCIJA

Značenje

Funkcionalizam

Slaganje teorije psihološkog funkcionalizma s proturedukcionističkim filozofijama znanosti

Dokazi u prilog psihološkom funkcionalizmu

Značajke uobičajene materijalističke tvrdnje, protudokazivanje na osnovama psihološkoga funkcionalizma

Korespodencija

UNUTARTEORIJSKI DOSEG, REFERENCIJA, A PRIORI

Zaokret k unutarteorijskom »realizmu«

Značenje, referencija

Problem

*aprioria*Prigovori zasnivanju područja matematike na vitgenštajnovskoj postavci o prirodnoj sposobnosti ili obliku života

ODGOVORI I PRIJEDLOZI

LITERATURA

KAZALO IMENA

**THE PHILOSOPHY OF SCIENCE OF HILARY PUTNAM**

This book represents an attempt at a critical analysis of the philosophy of Hilary Putnam. Particular accent is given to Putnam's philosophy of mathematics, while the discussion includes only those sections of his philosophy of language, philosophy of the natural sciences and the philosophy of psychology to the extent to which they influenced his standpoint on the philosophy of mathematics. Given that the concept of realism in the philosophy of science is one of the key epistemic problems, the realistic core of Putnam's philosophy is analysed. His 'turnabout' towards anti-realism was needed as such to expressly recognise it as scientific anti-realism. This is the extent, therefore, of what this 'turning-point' meant for his own critical standpoints.

Generally, criticism is undertaken with standpoints contrary to Putnam's philosophy and includes: mathematical a priori of a genetic type, the concept of scientific realism which includes external (extra-theoretical) cause in the confirmation of scientific theories, correspondence theory as an acceptable theory of truth, the rejection of functionalism, decisiveness about the truthfulness of mathematical propositions from exclusively intra-mathematical reasons, the concept of mathematical possibility as the property of mathematically demonstrated true mathematical models, the concept of mathematical necessity as the property of the whole of researched mathematical possibilities, the conception of mathematics as an epistemically fruitful science which reveals the logical/mathematical struc-turality of the 'computing' part of the mind, the understanding of contemporary computers as contingent technological identification with a part of the human mind/brain. The undertaken criticism agrees in everything with Putnam's analysis and rejection of contemporary conventionalism.

Problematically, Putnam's philosopy of mathematics is critically analysed through his conception of scientitiflc realism, the problem of truth, the problem of abstract mathematical entities, the problem of conventionalism. Especially emphasised is the problem of the epistemological status of mathematical theories. As the central problem, we attempt to answer the question: Of what do mathematical theories speak? What reality do they reveal? And according to what is mathematics a science at all? Putnam's solution, according to which mathematical theories are given an epistemic status just changed to mathematical content, the criticism from the opposing a priori non-Platonic standpoint is subjugated. Putnam's proof through the functioning of Turing's machines in contributing to the assertion of the non-necessity of abstract mathematical entities is slowed down through the concept of self-reference with abstract mathematical entities and the assertion of the impossibility of the conception of mathematical formulas as a series of entries without significance. It is established that neither Hilbert's mathematical demonstration and formalistic formation of mathematics follows the claim of the series of signs absolutely without significance.

In opposition, Putnam's viewpoint on conventionalism as essentialistic negativism is maintained and additionally substantiated with examples from applied geometries.

The classical 'Twin Earth' problem is quasi-formalistically analysed together with the dispute over the conclusion according to which the significance of concepts cannot be the product of the mind, and that through the meaning of the concept of self-reference with abstract mathematical entities.

Special attention is devoted to the problem of the a priori, given that the standpoint on this observes that the conception of scientific knowledge is foundationally linked with the type of philosophy of science we can represent. Putnam's standpoint is analysed in the sense of excluding reasons, on account of which he changed his viewpoint several times on the problem of a priori knowledge.