In order to fulfil their essential roles as the bearers of truth and the relata of logical relations, propositions must be public and shareable. That requirement has favoured Platonist and other non-mental views of them, despite the well-known problems of Platonism in general. Views that propositions are mental entities have correspondingly fallen out of favour, as they have difficulty in explaining how propositions could have shareable, objective properties. We revive a mentalist view of propositions, inspired by Artificial Intelligence work on perceptual algorithms, which shows how perception causes persistent mental entities with shareable properties that allow them to fulfil the traditional roles of (one core kind of) propositions. The clustering algorithms implemented in perception produce outputs which are (implicit) atomic propositions in different minds. Coordination of them across minds proceeds by game-theoretic processes of communication. The account does not rely on any unexplained notions such as mental content, representation, or correspondence (although those notions are applicable in philosophical analysis of the result).
The contemporary Platonists in the philosophy of mathematics argue that mathematical objects exist. One of the arguments by which they support this standpoint is the so-called Enhanced Indispensability Argument (EIA). This paper aims at pointing out the difficulties inherent to the EIA. The first is contained in the vague formulation of the Argument, which is the reason why not even an approximate scope of the set objects whose existence is stated by the Argument can be established. The second problem is reflected in the vagueness of the very term indispensability, which is essential to the Argument. The paper will remind of a recent definition of the concept of indispensability of a mathematical object, reveal its deficiency and propose an improvement of this definition. Following this, we will deal with one of the consequences of the arbitrary employment of the concept of indispensability of a mathematical theory. We will propose a definition of this concept as well, in accordance with the common intuition about it. Eventually, on the basis of these two definitions, the paper will describe the relation between these two concepts, in the attempt to clarify the conceptual apparatus of the EIA., Současní platonisté ve filozofii matematiky argumentují, že matematické objekty existují. Jedním z argumentů, které toto stanovisko podporují, je tzv. Enhanced Indispensability Argument (EIA). Cílem tohoto příspěvku je poukázat na obtíže spojené s EIA. První z nich je obsažena v vágní formulaci Argumentu, což je důvod, proč nelze stanovit ani přibližný rozsah nastavených objektů, jejichž existence je uvedena argumentem. Druhý problém se odráží v neurčitosti samotného pojmu nepostradatelnost, která je pro argument nezbytná. Příspěvek bude připomínat nedávnou definici pojmu nepostradatelnost matematického objektu, odhalit jeho nedostatek a navrhnout zlepšení této definice. Poté budeme se zabývat jedním z důsledků svévolného zaměstnávání konceptu nepostradatelnosti matematické teorie. Navrhneme také definici této koncepce v souladu se společnou intuicí. Nakonec, na základě těchto dvou definic, bude článek popsat vztah mezi těmito dvěma pojmy, ve snaze objasnit koncepční aparát EIA., and Vladimir Drekalović