Rozsáhlé dílo obsahující celoživotní práci Karla Engliše nejen z oblasti teorie poznání představuje nikdy nevydaný rukopis s názvem Velká logika. Jedním z výsledků snahy o jeho postupnou publikaci je nyní zveřejněný přepis Englišovy studie „Zeleného kritika mé teleologie“. Přepis části rukopisu je opatřen autorskými vysvětlujícími a obsah doplňujícími poznámkami. Engliš se musel vypořádávat s kritikou svého teleologického přístupu, jež upřednostňoval v ekonomické vědě, stejně jako musel obhajovat své trojí dělení způsobů myšlení (ontologický, teleologický a normologický). Právě Englišovy obhajoby myšlenkových řádů (...) umožňují vyniknout jeho originalitě v axiologické oblasti. (shrink)

The cut and choose game is one of the infinitary games on a complete Boolean algebra B introduced by Jech. We prove that existence of a winning strategy for II in implies semiproperness of B. If the existence of a supercompact cardinal is consistent then so is “for every 1-distributive algebra B II has a winning strategy in ”.

Given a Polish space X and a countable collection of analytic hypergraphs on X, I consider the σ-ideal generated by Borel anticliques for the hypergraphs in the family. It turns out that many of the quotient posets are proper. I investigate the forcing properties of these posets, certain natural operations on them, and prove some related dichotomies.

What is conventionalism in philosophy of science? Basically, it is a thesis about empirical underdetermination. According to Conventionalists, there is “a slack” between our theories and experience that is to be “lined” with conventions. As the experience does not “impose” any theory, scientists are always free to choose a theory on “softer” non-evidential grounds when facing empirical underdetermination. “Conventionalism is a philosophy of freedom,” as Édouard Le Roy put it. Yet the thing to remember is that there is no such (...) a thing as the conventionalism. Reasons for empirical underdetermination that Conventionalists state are not always the same, hence it is more convenient to talk about varieties of conventionalism. The present paper is an attempt to sketch a line between two basic variants of conventionalism which are instrumentalism and constructivism. Co je konvencionalismus? V nejobecnější rovině se jedná o tvrzení o empirické poddeterminovanosti. Podle konvencionalistů existuje "mezera" mezi zkušeností a teoriemi, která může být překonána pouze pomocí konvencí. Vědci si podle konvencionalistů mohou vybrat teorie na základě měkkých kritérií, protože teorie nikdy nejsou předepisovány zkušeností. Konvencionalimus je, jak jednou poznamenal stoupenec jeho radikální varianty, Édouard Le Roy, "filozofii svobody." Konvencionalismus by však neměl být považován za homogenní proud. Konvencionalisté se v podstatných ohledech různí v názorech na příčiny empirické poddeterminovanosti, což je i důvodem, proč je příhodnější hovořit o variantách konvencionalismu. Předložený článek je pokusem vymezit dvě základní varianty konvencionalismu: instrumentalismus a konstruktivismus. (shrink)

Dominantní pozitivistická epistemologie dat v současné vědě, která staví na metafyzickém realismu a ideálu mechanické objektivity, trpí řadou trhlin. Tyto nedostatky byly identifikovány v mnohých kritických ohlasech, které vedou k nové problematizaci ustáleného konceptu dat. Mezi kritizovanými aspekty tohoto konceptu se opakují varování ohledně zasazenosti dat do kontextu jejich tvorby, jejich zprostředkovanost nebo otevřenost manipulacím. Funkce dat v posledních letech nabývá na důležitosti kvůli stoupající datové náročnosti vědy, a proto je dříve neproblematickému konceptu dat věnováno více pozornosti. Objevují se také (...) alternativní přístupy k epistemologii dat, z nichž tato práce představuje směr konstruktivistický a rétorický. Prezentovaný text lze díky své kompilativní povaze, čerpající z kritické literatury zabývající se epistemologií dat, pojmout jako syntézu a rekonfiguraci existujících myšlenek k danému tématu. Je možné ho rovněž přijmout jako jeden z příspěvků k rétorické argumentaci v diskurzu dat současné vědy. (shrink)

Článek srovnává pojetí člověka jako bytosti, situované v celkové souvislosti a vyznačující se otevřeností a sebetranscendencí, v myšlení Jana Patočky a Karla Rahnera, a to se zvláštním zřetelem na interpretaci postavy bohočlověka u obou autorů. Srovnává a dává do souvislosti Patočkův pojem "světa" a pojem "tajemství" u Karla Rahnera, jejich pojetí dějinnosti i radikálního ohrožení člověka. Konečně se zabývá interpretací postavy bohočlověka, kterou můžeme u obou autorů chápat jako klíčovou pro lidskou existenci, a zároveň si můžeme všimnout, že odlišné interpretace (...) tohoto motivu u obou autorů jsou si vnitřně překvapivě blízké. (shrink)

Journal of Mathematical Logic, Volume 24, Issue 03, December 2024. If [math] is a closed Noetherian graph on a [math]-compact Polish space with no infinite cliques, it is consistent with the choiceless set theory ZF[math][math][math]DC that [math] is countably chromatic and there is no Vitali set.

It is consistent with ZF $\mathsf {ZF}$ set theory that the Euclidean topology on R $\mathbb {R}$ is not sequential, yet every infinite set of reals contains a countably infinite subset. This answers a question of Gutierres.

There is an optimal way of increasing certain cardinal invariants of the continuum.

We study a generalization of the splitting number s to uncountable cardinals. We prove that $\mathfrak{s}(\kappa) > \kappa^+$ for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption $\mathfrak{s}(\aleph_\omega) > \aleph_{\omega + 1}$ has a considerable large cardinal strength as well.

Open peer commentary on the article “The Autopoiesis of Social Systems and its Criticisms” by Hugo Cadenas & Marcelo Arnold. Upshot: I reaffirm and extend the notion of social autopoiesis away from mere labels and descriptions to acting physical components of social systems and societies, ranging from subcellular to biological and human. All self-producing biological organisms are essentially societies of interacting components and therefore notions of autopoiesis and social systems are fundamentally, if not definitionally, interrelated. Some examples of real-life applications (...) of social autopoiesis are also given. Future generations of scientists might even find the qualifier “social” redundant because there is no other autopoiesis than “social.”. (shrink)

Turtles are among the most intriguing amniotes but their communication and signaling have rarely been studied. Traditionally, they have been seen as basically just silent armored ‘walking stones’ with complex physiology but no altruism, maternal care, or aesthetic perception. Recently, however, we have witnessed a radical change in the perception of turtle behavioral and cognitive skills. In our study, we start by reviewing some recent findings pertaining to various highly developed behavioral and cognitive patterns with special emphasis on turtles. Then (...) we focus on freshwater turtles and use data about their sexual behavior and size sexual dimorphism to test whether conspicuous coloration of the head is in these animals related to sexual processes. We found that absence of aggressive mating behavior is statistically associated with the presence of conspicuous coloration on turtles’ heads. It also seems that while species with female-biased SSD are characterised by conspicuously colored head ornaments, in species with male-biased SSD conspicuous coloration is absent. Unlike large females, males thus seem to be under pressure to develop conspicuous coloration and engage in non-aggressive behavior using signaling to succeed in courtship. And finally, we discuss possible roles of head color patterns in turtle communication during mating. (shrink)

I describe several ways in which forcing arguments can be used to yield clean and conceptual proofs of nonreducibility, ergodicity and other results in the theory of analytic equivalence relations. In particular, I present simple Borel equivalence relationsE, Fsuch that a natural proof of nonreducibility ofEtoFuses the independence of the Singular Cardinal Hypothesis at ℵω.

Appearance of Old world vipers of genus Vipera serves various purposes including crypsis and aposematism. Recent research showed that the zigzag pattern represents strong signal to predators to avoid vipers as a prey. It is also possible that vipers function within ecological community as Batesian model for numerous mimics, including other reptiles, birds, and invertebrates. It is then showed that Batesian models need to have prominent features to sustain the mimicry system. The main modulation of this system is presented here (...) as iconicity. Iconicity is treated as quantitative variable resulting from open dynamic process with multiple inputs, also including iconicity of previous states of system. Batesian mimicry is based on mimics adopting the iconicity of the model. It is an example of ecological facilitation, and as such, it is part of niche construction. Since Batesian mimicry is based on semiotic processes, it is a special case of ecological facilitation, namely semiotic facilitation. (shrink)

Kant treats the problem of a philosophical theory of God in two basic steps. First he develops his own understanding of the notion of God by providing the doctrine of the transcendental ideal. Then he proceeds to a critique of three types of the proof of God’s existence. Thus, Kant’s „deconstruction“ of philosophical theology has a positive and a negative part. The present contribution analyses the positive part only, with the aim to supply a detailed reconstruction of Kant’s procedure here. (...) The reconstruction proceeds in the following steps. First we have to elucidate Kant’s notion of ideal. Following Wolff’s differentiation of the three kinds of special metaphysics, Kant distinguishes three basic types of those notions of pure reason which, in an explicit reference to Plato, he names „ideas“. It must then be explained why Kant calls the theological idea, unlike the psychological and the cosmological ones, an ideal. My claim is that the difficulty of the chapter on the transcendental ideal derives from the fact that Kant, without adverting to it explicitly yet in accordance with his own methodology, develops one by one three alternative suggestions of how the notion of the transcendental ideal can be approached. These three suggestions are then investigated in three sections where I also attempt to answer the question as to why Kant defines the theological idea to be not only an ideal but also a transcendental one. In conclusion, I provide a reconstruction of Kantʼs explanation of the origin of the notion of the transcendental ideal in pure reason. (shrink)

The relationship between killing ideals and adding reals by forcings is analysed.

It is proved consistent that there be a proper σ-ideal ℑ on ω 1 and an ℵ 1 -preserving poset P such that $\mathbb{P} \Vdash$ the σ-ideal generated by ℑ̌ is not proper.

We show that all posets of uniform density ℵ 1 may have to add a Cohen real and develop some forcing machinery for obtaining this sort of result.

In mathematical practice certain formulas φ are believed to essentially decide all other natural properties of the object x. The purpose of this paper is to exactly quantify such a belief for four formulas φ, namely “x is a Ramsey ultrafilter”, “x is a free Souslin tree”, “x is an extendible strong Lusin set” and “x is a good diamond sequence”.