The paper presents an argument against a "metaphysical'* conception of logic according to which logic spells out a specific kind of mathematical structure that is somehow inherently related to our factual reasoning. In contrast, it is argued that it is always an empirical question as to whether a given mathematical structure really does captures a principle of reasoning. lMore generally, it is argued that it is not meaningful to replace an empirical investigation of a thing by an investigation of its (...) a priori analyzable structure without paying due attention to the question of whether it really is the structure of the thing in question.) It is proposed to elucidate the situation by distinguishing two essentially different realms with which our reason must deal: "the realm of the natural'*, constituted by the things of our empirical world, and "the realm of the formal'*, constituted by the structures that we use as "prisms'* to view, to make sense of, and to reconstruct the world. It is suggested that this vantage point may throw light on many foundational problems of logic. (shrink)

We investigate several ideal versions of the pseudointersection number \(\mathfrak {p}\), ideal slalom numbers, and associated topological spaces with the focus on selection principles. However, it turns out that well-known pseudointersection invariant \(\mathtt {cov}^*({\mathcal I})\) has a crucial influence on the studied notions. For an invariant \(\mathfrak {p}_\mathrm {K}({\mathcal J})\) introduced by Borodulin-Nadzieja and Farkas (Arch. Math. Logic 51:187–202, 2012), and an invariant \(\mathfrak {p}_\mathrm {K}({\mathcal I},{\mathcal J})\) introduced by Repický (Real Anal. Exchange 46:367–394, 2021), we have $$\begin{aligned} \min \{\mathfrak (...) {p}_\mathrm {K}({\mathcal I}),\mathtt {cov}^*({\mathcal I})\}=\mathfrak {p},\qquad \min \{\mathfrak {p}_\mathrm {K}({\mathcal I},{\mathcal J}),\mathtt {cov}^*({\mathcal J})\}\le \mathtt {cov}^*({\mathcal I}), \end{aligned}$$ respectively. In addition to the first inequality, for a slalom invariant \(\mathfrak {sl_e}({\mathcal I},{\mathcal J})\) introduced in Šupina (J. Math. Anal. Appl. 434:477–491, 2016), we show that $$\begin{aligned} \min \{\mathfrak {p}_\mathrm {K}({\mathcal I}),\mathfrak {sl_e}({\mathcal I},{\mathcal J}),\mathtt {cov}^*({\mathcal J})\}=\mathfrak {p}. \end{aligned}$$ Finally, we obtain a consistency that ideal versions of the Fréchet–Urysohn property and the strictly Fréchet–Urysohn property are distinguished. (shrink)

In this paper we put forward and defend a view of the nature of logic that we call moderate anti-exceptionalism. In the first part of the paper we focus on the problem of genuine logical validity and consequence. We make use of examples from current debates to show that attempts to pinpoint the one and only authentic logic inevitably either yield irrefutable theories or lead to dead ends. We then outline a thoroughly naturalist account of logical consequence as grounded in (...) rules implicit in human linguistic practices. We insist that there are only two existing kinds of language: natural languages, and artificial languages that have been forged by us. There is thus no room for a "genuine" language and hence for "genuine" logic. We conclude that though logical theories are established—and are liable to criticism—in a similar fashion as those of the sciences, and in this sense logic is not exceptional, to fulfill its mission logic must lay a claim to normative authority over our argumentation and reasoning, which makes its methodology somewhat special. Logical theory is not meant to provide just an explanation, the standards it establishes serve also as a tool, providing for a reinforcement of our rational communication. (shrink)

We know that lots of things are correct. (Helping people in need is correct. Moving the bishop diagonally when playing chess is correct. Adding 7 to 5 to make 12 is correct.) But where does this correctness come from? I argue that correctness is best seen as something we humans created in the process of forming our societies. This, admittedly, is speculative; but aside of this, there are facts that are more than speculations. In particular, I argue that our correctness (...) is based on normative attitudes, though these often determine only the criteria of correctness, letting the criteria to then determine what is correct independently of our will. Thus it holds both that correctness is wholly our creation and that it is independent of us in the sense that things may be correct even if we do not know that they are (or, indeed, think them incorrect). (shrink)

Inferentialism is the conviction that to be meaningful in the distinctively human way, or to have a 'conceptual content', is to be governed by a certain kind of inferential rules. The term was coined by Robert Brandom as a label for his theory of language; however, it is also naturally applicable (and is growing increasingly common) within the philosophy of logic.

A review of deVries' and O'Shea's books, both titled "Wilfrid Sellars". By Jaroslav Peregrin.

If a firm provides incentives by promoting those who have performed well in a job, it may transfer them to a job to which they are not well suited and agents are promoted to their levels of incompetence. Tournaments are an alternative to reputation as a means of ensuring that firms reward good performance when performance is unverifiable.

The question how to turn the principles implicitly governing the concept of truth into an explicit definition of the concept hence coalesced with the question how to get a finite grip on the infinity of T-sentences. Tarski's famous and ingenious move was to introduce a new concept, satisfaction, which could be, on the one hand, recursively defined, and which, on the other hand, straightforwardly yielded an explication of truth. A surprising 'by-product' of Tarski's effort to bring truth under control was (...) the breathtaking finding that truth is in a precisely defined sense ineffable, that no non trivial language can contain a truth-predicate which would be adequate for the very 4 language. This implied that truth proved itself to be strangely 'language-dependent': we can have a concept of truth-in-L for any language L, but we cannot have a concept of truth applicable to every language. In a sense, this means, as Quine put it, that truth belongs to "transcendental metaphysics", and Tarski's 'scientific' investigations seem to lead us back towards a surprising proximity of some more traditional philosophical views on truth. 3. TARSKI'S THEORY AS A PARADIGM So far Tarski himself. Subsequent philosophers then had to find out what his considerations of the concept of truth really mean and what are their consequences; and this now seems to be an almost interminable task. (shrink)

Recent decades are marked by the upswing of the use of the term “normativity“ not only in philosophical discussions, but increasingly also within reports of empirical scientists. This may invoke the question how far these developments overlap and in how far they go past each other. A significant overlap might lead to an interesting coalescence of the two approaches to norms, which may provide for a ”naturalization” of some philosophical speculations about normativity, putting them on a firmer foundation, while offering (...) the empirical scientists some new impulses for directing their research. In this paper I give an overview of some recent empirical results concerning human normativity and I point out a certain philosophical tradition, rooted especially in the works of Wittgenstein, Sellars and Brandom, which treats normativity so that it becomes more or less compatible with these results. (shrink)

In this paper I put forward a thesis regarding the anatomy of “cultural evolution”, in particular the way the “cultural” transmission of behavioral patterns came to piggyback, through us humans, on the transmission effected by genetic evolution. I claim that what grounds and supports this new kind of transmission is a complex behavioral “meta-pattern” that makes it possible to grasp a pattern as something that “ought to be”, i.e. that transforms the pattern into what we can call a rule. (Here (...) I draw especially on the philosophical insights of Wilfrid Sellars.) In this way I interlink empirical research done in evolution theory with some more speculative philosophical theories, thus shedding new light on the former and adding an empirical footing to the latter. (shrink)

?lánok sa sústre?uje na Antisthenovo chápanie výchovy, ktoré bolo nepochybne inšpirované Sókratom. K?ú?ový zlomok – „po?iatkom výchovy je skúmanie mien“ – je dokladom o úzkom spojení logiky a etiky, aké môžeme nájs? aj v Platónových a Xenofóntových dialógoch. Autor ?lánku porovnáva Antisthenov koncept paideie s Isokratovým rétorickým ideálom a poukazuje na variácie sókratovského modelu výchovy u významných predstavite?ov Sókratovho krúžku . Na rozdiel od Platóna Antisthenés neprejavuje záujem o metafyzické rozvinutie náuky svojho u?ite?a, ale ponúka pozitívny etický ideál, ktorý treba (...) nasledova?. Práve v tomto bode neskôr na sókratovskú tradíciu nadviazali kynici a stoici, pri?om kynici kládli vä?ší dôraz na osobnú etiku, zatia? ?o stoici ju dop??ali aj logickými skúmaniami. (shrink)

Cieľom článku je nanovo reflektovať činnosť jednej z najslávnejších ženských filozofiek, Hip­parchie z Maróneie. Naším zámerom je ukázať, prečo sa stala v porovnaní s inými ženami antiky taká významná a v mnohom signifikantná pre ďalší vývoj procesu ženskej eman­cipácie. Hlavným svedectvom je pre nás fragment SSR V I 1 od Diogena Laertského, ktorý kladieme do súvislosti s ďalšími antickými správami o Antisthenovi a raných kynikoch. Dve hlavné témy Diogenovho svedectva sú Kratétova svadba s Hipparchiou a spor Hipparchie s Theodórom. Vo (...) výklade poukazujeme na momenty, v ktorých je filozofická osobnosť Hip­parchie nadčasová a inšpiratívna aj pre súčasnosť. (shrink)

V tomto článku se zabývám konceptem SI (superinteligence) a s ní spojeným problémem kontroly. Podle určité skupiny teoretiků umělé inteligence stojíme na prahu události, která může radikálně změnit povahu technologického pokroku a lidské společnosti obecně. Touto událostí má být takzvaná technologická singularita, která je často spojována se vznikem první větší než lidské inteligence. Lidé jako Nick Bostrom varují před nebezpečím, které pro nás vznik SI znamená a upozorňují, že musíme co nejdříve najít metody kontroly této inteligence. Podle Bostroma a dalších (...) nebezpečí SI vyplývá z její povahy. Já na jedné straně posuzuji, jak SI může vzniknout, a na druhé straně soudím smysluplnost problému kontroly. Vznik SI vyplývá ze vzniku umělé inteligence. Proto soustřeďuji podstatnou část textu argumentům pro její vznik. Ukazují jak se Bostrom a další nechávají unést jedním problematickým argumentem. Dále podrobuji jejich pozici klasické kritice umělé inteligence. Prezentuji, jak stále lpí na problematických domněnkách svých předchůdců. Zejména soustřeďuji svoji kritiku na tvrzení, že SI bude mít jeden konečný cíl, který bude interpretovat. Toto tvrzení označuji jako antitetické, a to představě, že SI bude obecnou inteligencí. V závěru z mojí argumentace vyvozuji, že problém kontroly zaměňuje dva jiné různé problémy „kontroly.“. (shrink)

This paper is a follow up of the author’s programme of characterizing Ramsey classes of structures by a combination of model theory and combinatorics. This relates the classification programme for countable homogeneous structures to the proof techniques of the structural Ramsey theory. Here we consider the classes of topological and metric spaces which recently were studied in the context of extremally amenable groups and of the Urysohn space. We show that Ramsey classes are essentially classes of finite objects only. While (...) for Ramsey classes of topological spaces we achieve a full characterization, for metric spaces this seems to be at present an intractable problem. (shrink)

The topic of this paper is the question whether there is a logic which could be justly called the logic of inference. It may seem that at least since Prawitz, Dummett and others demonstrated the proof-theoretical prominency of intuitionistic logic, the forthcoming answer is that it is this logic that is the obvious choice for the accolade. Though there is little doubt that this choice is correct (provided that inference is construed as inherently single-conclusion and complying with the Gentzenian structural (...) rules), I do not think that the usual justification of it is satisfactory. Therefore, I will first try to clarify what exactly is meant by the question, and then sketch a conceptual framework in which it can be reasonably handled. I will introduce the concept of 'inferentially native' logical operators (those which explicate inferential properties) and I will show that the axiomatization of these operators leads to the axiomatic system of intuitionistic logic. Finally, I will discuss what modifications of this answer enter the picture when more general notions of inference are considered. (shrink)

The article addresses two closely related questions: What are the criteria of adequacy of logical formalization of natural language arguments, and what gives logic the authority to decide which arguments are good and which are bad? Our point of departure is the criticism of the conception of logical formalization put forth, in a recent paper, by M. Baumgartner and T. Lampert. We argue that their account of formalization as a kind of semantic analysis brings about more problems than it solves. (...) We also argue that the criteria of adequate formalization need not be based on truth conditions associated with logical formulas; in our view, they are better based on structural (inferential) grounds. We then put forward our own version of the criteria. The upshot of the discussion that follows is that the quest for an adequate formalization in a suitable logical language is best conceived of as the search for a Goodmanian reflective equilibrium. (shrink)

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new (...) realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of prooftheoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones. (shrink)

In a remarkable early paper, Wilfrid Sellars warned us that if we cease to recognize rules, we may well find ourselves walking on four feet; and it is obvious that within human communities, the phenomenon of rules is ubiquitous. Yet from the viewpoint of the sciences, rules cannot be easily accounted for. Sellars himself, during his later years, managed to put a lot of flesh on the normative bones from which he assembled the remarkable skeleton of the early paper; and (...) his followers too. However, what they say is somewhat divergent; and therefore my aim in this paper is to concentrate on the very concept of rule and analyse it in the context of the question what it is about us humans that makes us special. (shrink)

Logic is usually considered to be the study of logical consequence – of the most basic laws governing how a statement’s truth depends on the truth of other statements. Some of the pioneers of modern formal logic, notably Hilbert and Carnap, assumed that the only way to get hold of the relation of consequence was to reconstruct it as a relation of inference within a formal system built upon explicit inferential rules. Even Alfred Tarski in 1930 seemed to foresee no (...) kind of consequence other than one induced by a set of inference rules: "Let A be an arbitrary set of sentences of a particular discipline. With the help of certain operations, the so-called rules of inference , new sentences are derived from the set A , called the consequences of the set A . To establish these rules of inference, and with their help to define exactly the concept of consequence, is again a task of special metadisciplines; in the usual terminology of set theory the schema of such definition can be formulated as follows: The set of all consequences of the set A is the intersection of all sets which contain the set A and are closed under the given rules of inference." (p. 63) Thereby also the concept of truth came to be reconstructed as inferability from the empty set of premises. (More precisely, this holds only for non-empirical, necessary truth; but of course logic never set itself the task of studying empirical truth.) From this viewpoint, logic came to look as the enterprise of explication of consequence in terms of inference. (shrink)

Logic is usually presented as a tool of rational inquiry; however, many logicians in fact treat logic so that it does not serve us, but rather governs us – as rational beings we are subordinated to the logical laws we aspire to disclose. We denote the view that logic primarily serves us as logica serviens, while denoting the thesis that it primarily governs our reasoning as logica dominans. We argue that treating logic as logica dominans is misguided, for it leads (...) to the idea of a “genuine” logic within a “genuine” language. Instead of this, we offer a naturalistic picture, according to which the only languages that exist are the natural languages and the artificial languages logicians have built. There is, we argue, no language beyond these, especially none that would be a wholesome vehicle of reasoning like the natural languages and yet be transparently rigorous like the artificial ones. Logic is a matter of using the artificial languages as idealized models of the natural ones, whereby we pinpoint the laws of logic by means of zooming in on a reflective equilibrium. (shrink)

The followers of Wilfrid Sellars are often divided into “right” and “left” Sellarsians, according to whether they believe, in Mark Lance's words, that “linguistic roles constitutive of meaning and captured by dot quoted words are ‘normative all the way down.’” The present article anatomizes this division and argues that it is not easy to give it a nontrivial sense. In particular, the article argues that it is not really possible to construe it as a controversy related to ontology, and goes (...) on to argue that it is also not easy to construe it as one concerning the translatability of the normative idiom into the non-normative one. The conclusion is that the only coherent interpretation of this disagreement is as a disagreement about the possibility and desirability of assuming a standpoint “inside” our linguistic practices. (shrink)

In this study two strands of inferentialism are brought together: the philosophical doctrine of Brandom, according to which meanings are generally inferential roles, and the logical doctrine prioritizing proof-theory over model theory and approaching meaning in logical, especially proof-theoretical terms.

My study cannot give more than some comments on a very extensive theme that requires a number of studies which have not even been precisely formulated, as yet. I should like to show that the specific thought pattern, the specific perception of reality, intrinsic to a specific cultural category—that which is the predominant one in the given cultural complex—influences all other categories and determines their nature. I want to illustrate my thesis on the relationship between literature and history. With some (...) exaggeration I would formulate my thesis as follows : as literature is, so is history; the same perception of reality is in the background of both and determines their form. I will limit myself to this theme and I will not deal with the causes determining the differences of pattern in various fields of a certain culture; I will not attempt to solve the philosophical and sociological problems, neither will I seek for further connections in the total cultural complex, with which I illustrate my thesis, that is the Chinese cultural complex, although it would not be too difficult. (shrink)

Growth modelling is of interest to scientists in various disciplines. In our article, we will collect 17 models designed for growth modelling, appraise these models and contribute to the discussion of their applicability. The merit of the paper lies in studying the convergence properties of nonlinear regression in selected models. Our studies will be performed mainly concerning the quality of the obtained estimates, which are closely related to the intrinsic curvature of the model according to Bates and Watts. This curvature (...) determines the size of the linearization domains. Only if the initial solution is in this domain, then the convergence of the estimate in nonlinear regression is guaranteed. The primary goal is to design a methodology for selecting a growth model. We will demonstrate fruitfulness of our methodology on the weight measurements of 10 calves under 25 months of age from cowsheds in the village Záluží in the Czech Republic. Estimated parameters of growth curves, sizes of linearization domain, calculated residues and coefficients of determination indices will be the subject of discussion. (shrink)

Tomáš Marvan Otázka významu: Cesty analytické filosofie jazyka. 1. vyd. Praha: Togga, 2010, ISBN 978-80-87258-33-0, 150 stran.