For some contemporary liberal philosophers, a huge concern is liberal neutrality, which is the idea that the state should be neutral among competing conceptions of the moral good pursued by the people. In The Morality of Freedom, Joseph Raz argues that we can neither achieve nor even approximate such neutrality. He shows that neutrality and fairness are different ideas. His notion of neutrality is stricter than John Rawls's and Ronald Dworkin's. Raz shows that both helping and not helping can be (...) neutral or non-neutral, thus neutrality is chimerical. Wojciech Sadurski's appeal to rational expectations does not necessarily tell us which action is neutral. Distinguishing between comprehensive and narrow neutrality, Raz also claims that only the former is a proper response to conflicts. Sadurski criticizes it, claiming that conflicts are comprehensive in a sense which does not deny the adequacy of the narrow neutrality. In reality, however, it is almost impossible to achieve even the narrow neutrality. A theory is presented to explain why political neutrality is almost impossible to achieve. Philosophically, there is no neutral ground for neutral politics. (shrink)
The ability to effectively prevent smallpox was the greatest medical accomplishment of the first half of the 19th century. From 1838 to 1840, half a century after vaccination was introduced but before it became mandatory in England, data about the general population of England and Wales recorded 70 deaths per million from smallpox; only 180, 900 vaccinations were recorded. In London alone from 1848 to 1852, there were 4, 858 youthful deaths from smallpox, 67% of which occurred during the first (...) five years of life (Simon 1857).In a report to the House of Commons in 1802, Edward Jenner (1749-1823) stated that person-to-person vaccination was a basic principle of his procedure. He gained confidence in it from the case .. (shrink)
The main aim of this paper is to challenge the validity of the distinction between legal justice and social justice. It is argued that what we usually call legal justice is either an application of the more fundamental notion of social justice to legal rules and decisions or is not a matter of justice at all. In other words, the only correct uses of the notion of legal justice are derivative from the notion of social justice and, hence, the alleged (...) conflicts between criteria of social and legal justice result from the confusion about the proper relationship between these two concepts. Two views about the social justice/legal justice dichotomy are of particular importance and will provide the focus for the argument: this dichotomy is sometimes identified with a classical distinction between distributive and commutative justice and sometimes with the distinction between substantive and procedural justice. (shrink)
In this paper, a formal theory is presented that describes syntactic and semantic mechanisms of philosophical discourses. They are treated as peculiar language systems possessing deep derivational structures called architectonic forms of philosophical systems, encoded in philosophical mind. Architectonic forms are constituents of more complex structures called architectonic spaces of philosophy. They are understood as formal and algorithmic representations of various philosophical traditions. The formal derivational machinery of a given space determines its class of all possible architectonic forms. Some of (...) them stand under factual historical philosophical systems and they organize processes of doing philosophy within these systems. Many architectonic forms have never been realized in the history of philosophy. The presented theory may be interpreted as falling under Hegel’s paradigm of comprehending cultural texts. This paradigm is enriched and inspired with Propp’s formal, morphological view on texts. The peculiarity of this modification of the Hegel-Propp paradigm consists of the use of algebraic and algorithmic tools of modeling processes of cultural development. To speak metaphorically, the theory is an attempt at the mathematical and logical history of philosophy inspired by the Internet metaphor. And that is why it belongs to the tradition of doing metaphilosophy in The Lvov-Warsaw School, which is continued today mainly by Woleński, Pelc, Perzanowski, and Jadacki. (shrink)
The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...) mind is based on the linear number representation. This classical conception is rejected and a competitive hypothesis is formulated according to which the basic mature representational system of cognitive arithmetic is a structure composed of many numerical axes which possess a common constituent, namely, the numeral zero. Arithmetic of indexed numbers is just a formal tool for modelling the basic mature arithmetic competence. The third task is to develop a standpoint called temporal pluralism, which is motivated by neo-Kantian philosophy of arithmetic. (shrink)
In the paper we discuss criticisms against David Armstrong’s general theory of truthmaking by Gonzalo Rodriguez-Pereyra, Peter Schulte and Benjamin Schnieder, and conclude that Armstrong’s theory survives these criticisms. Special attention is given to the problems concerning Entailment Principle, Conjunction Thesis, Disjunction Thesis and to the notion of explanation.
The presentation of the formal conception of noemata is the main aim of the article. In the first section, three informal approaches to noemata are discussed. The goal of this chapter is specifying main controversies and their sources concerned with different ways of the understanding of noemata. In the second section, basic assumptions determining the proposed way of understanding noemata are presented. The third section is devoted to the formal set-theoretic construction needed for the formal comprehension of noemata. In the (...) fourth section, definitions of noemata and their various kinds, as well as definitions of other phenomenological notions are formulated. In the last section, possibilities of further developing the proposed formal conception are indicated. (shrink)
Both the defenders and critics of judicial review assume tacitly that there is a special moral capacity needed for a correct articulation of constitutional (explicit or implied) rights, and they only disagree about who is likely to possess this moral capacity to a higher degree. In this working paper I challenge this unstated assumption. It is not the case that the reasoning oriented towards rights articulation is more moral than many non-rights-oriented authoritative public decisions in the society. Further, I suggest (...) that rights-related reasoning cannot be shown to be differently moral in a way which would support the idea that this relevant difference may justify why some political agents (such as judges) may be more suited to performing this particular type of moral reasoning than others (such as legislators). The best argument for such a distinction refers to the opportunity for and habit of conducting "moral thought experiments" which is what, as part of their professional duties, judges normally do, and which they can therefore instinctively do also when they engage in a "concrete" judicial review of a statute. But there is no good moral reason to believe that "moral thought experiments" triggered by specific fact-situations should be privileged as a method of moral reasoning, compared to an unashamedly abstract, principle-based moral reasoning. If anything, a good case may be made (referring to the need to openly acknowledge moral conflict, secure impartiality, equality and legitimacy) for deliberately abstracting from specific cases and focusing on the abstract and general level, only modifying it later, if one is compelled to such modifications by considering evidence from specific instances. Not even one half (the bottom-up half) of the Rawlsian famous "reflective equilibrium" apparatus can be of help in this regard. (shrink)
We provide an algorithm for determining a categorial grammar from linguistic data that essentially uses unification of type-schemes assigned to atoms. The algorithm presented here extends an earlier one restricted to rigid categorial grammars, introduced in  and , by admitting non-rigid outputs. The key innovation is the notion of an optimal unifier, a natural generalization of that of a most general unifier.
Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely (...) connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent’s mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties. (shrink)
The equivalence of (classical) categorial grammars and context-free grammars, proved by Gaifman , is a very basic result of the theory of formal grammars (an essentially equivalent result is known as the Greibach normal form theorem , ). We analyse the contents of Gaifman's theorem within the framework of structure and type transformations. We give a new proof of this theorem which relies on the algebra of phrase structures and exhibit a possibility to justify the key construction used in Gaifman's (...) proof by means of the Lambek calculus of syntactic types . (shrink)
We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and (...) equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages. (shrink)
In the paper there is presented the semantic interpretation of idealism/ realism controversy which is one of the most essential issues in Ingarden’s phenomenological project of ontology. The procedure of semantic paraphrase which is contemporary developed by Wolen´ ski, is the main interpretative tool. In the central part of the paper, there is formulated the formal theory of the semantic framework underlying idealism/realism discourse. Finally, there are formulated some notes showing that intentional conception of negation may be used for defending (...) various idealistic positions. (shrink)
Legal philosophy must be based on a set of substantive political values about such fundamental matters as the nature of the political community and the meaning of human freedom. This general thesis is illustrated by the analysis of moral discourse about the justification and limits of liberty-rights and equality-rights.The most effective way of arguing about the liberal conception of individual liberties (consistent with the Millian Harm Principle) is by recourse to the priority of the right over the good. But this (...) conception is little more than a restatement of the Harm Principle itself hence, a more fundamental justification for it is required. This can be provided by a substantive conception of equality of individuals as moral agents who are capable of choosing, pursuing and changing their own conceptions of the good, within the parameters of avoiding harm to others. (shrink)
Action logic of Pratt  can be presented as Full Lambek Calculus FL [14, 17] enriched with Kleene star *; it is equivalent to the equational theory of residuated Kleene algebras (lattices). Some results on axiom systems, complexity and models of this logic were obtained in [4, 3, 18]. Here we prove a stronger form of *-elimination for the logic of *-continuous action lattices and the –completeness of the equational theories of action lattices of subsets of a finite monoid and (...) action lattices of binary relations on a finite universe. We also discuss possible applications in linguistics. (shrink)
We discuss the logic of pregroups, introduced by Lambek , and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid.
Although the change of beliefs in the face of new information has been widely studied with some success, the revision of other mental states has received little attention from the theoretical perspective. In particular, intentions are widely recognised as being a key attitude for rational agents, and while several formal theories of intention have been proposed in the literature, the logic of intention revision has been hardly considered. There are several reasons for this: perhaps most importantly, intentions are very closely (...) connected with other mental states—in particular, beliefs about the future and the abilities of the agent. So, we cannot study them in isolation. We must consider the interplay between intention revision and the revision of other mental states, which complicates the picture considerably. In this paper, we present some first steps towards a theory of intention revision. We develop a simple model of an agent's mental states, and define intention revision operators. Using this model, we develop a logic of intention dynamics, and then investigate some of its properties. (shrink)
Review of two books in Polish: -/- Between Monism and Pluralism. A Study of the Genesis and Foundations of John Dewey’s Philosophy. -/- Concepts of Ch. S. Peirce’s Pragmatism and their Revival in 20th-Century Philosophy of Language.
In , Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen  proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz . For the reasons which will be discussed in the last section, (...) Cohen's proof seems to be at least incomplete. This paper yields a direct proof of the equivalence ofFCGs andSPGs. (shrink)
Some notions of the logic of questions (presupposition of a question, validation, entailment) are used for defining certain kinds of completeness of elementary theories. Presuppositional completeness, closely related to -completeness (, ), is shown to be fulfilled by strong elementary theories like Peano arithmetic.
In , I proved that the product-free fragment L of Lambek's syntactic calculus (cf. Lambek ) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut-rule. The proof (which is rather complicated and roundabout) was subsequently adapted by Kandulski  to the non-associative variant NL of L (cf. Lambek ). It turns out, however, that there exists an extremely simple method of non-finite-axiomatizability proofs which works uniformly for different subsystems of L (in particular, for NL). We (...) present it below to the use of those who refer to the results of  and . (shrink)
In Zielonka (1981a, 1989), I found an axiomatics for the product-free calculus L of Lambek whose only rule is the cut rule. Following Buszkowski (1987), we shall call such an axiomatics linear. It was proved that there is no finite axiomatics of that kind. In Lambek's original version of the calculus (cf. Lambek, 1958), sequent antecedents are non empty. By dropping this restriction, we obtain the variant L 0 of L. This modification, introduced in the early 1980s (see, e.g., Buszkowski, (...) 1985; Zielonka, 1981b), did not gain much popularity initially; a more common use of L 0 has only occurred within the last few years (cf. Roorda, 1991: 29). In Zielonka (1988), I established analogous results for the restriction of L 0 to sequents without left (or, equivalently, right) division. Here, I present a similar (cut-rule) axiomatics for the whole of L 0. This paper is an extended, corrected, and completed version of Zielonka (1997). Unlike in Zielonka (1997), the notion of rank of an axiom is introduced which, although inessential for the results given below, may be useful for the expected non-finite-axiomatizability proof. (shrink)
Pentus (1992) proves the equivalence of LCG's and CFG's, and CFG's are equivalent to BCG's by the Gaifman theorem (Bar-Hillel et al., 1960). This paper provides a procedure to extend any LCG to an equivalent BCG by affixing new types to the lexicon; a procedure of that kind was proposed as early, as Cohen (1967), but it was deficient (Buszkowski, 1985). We use a modification of Pentus' proof and a new proof of the Gaifman theorem on the basis of the (...) Lambek calculus. (shrink)
We prove the finite model property (fmp) for BCI and BCI with additive conjunction, which answers some open questions in Meyer and Ono . We also obtain similar results for some restricted versions of these systems in the style of the Lambek calculus [10, 3]. The key tool is the method of barriers which was earlier introduced by the author to prove fmp for the product-free Lambek calculus  and the commutative product-free Lambek calculus .
An important feature of some recent jurisprudential writings is the tendency to reject the precept of liberal individualism which affirms the priority of the principles of the "right conduct" over the substantive conceptions of "the good". This rejection, explicit in a recent book by Rogers M. Smith, and implicit in a recent work by Guido Calabresi, leads to strikingly illiberal consequences; hence, this provides indirect confirmation that the priority of the right over the good constitutes the most reliable defense of (...) individual liberty against majoritarian oppression. In Smith, an attempt to replace this priority with the principle of "rational liberty" leads to the disappearance of the guarantees of minority rights against orthodox majorities; in Calabresi, the doctrine of weighing and balancing competing moral principles of "the good" fails to provide an explanation for the strongly held moral intuition that some external preferences have to be disqualified at the outset, before they enter the forum of moral bargaining. (shrink)
An axiomatics of the product-free syntactic calculus L ofLambek has been presented whose only rule is the cut rule. It was alsoproved that there is no finite axiomatics of that kind. The proofs weresubsequently simplified. Analogous results for the nonassociativevariant NL of L were obtained by Kandulski. InLambek's original version of the calculus, sequent antecedents arerequired to be nonempty. By removing this restriction, we obtain theextensions L 0 and NL 0 ofL and NL, respectively. Later, the finiteaxiomatization problem for L (...) 0 andNL 0 was partially solved, viz., for formulas withoutleft (or, equivalently, right) division and an (infinite) cut-ruleaxiomatics for the whole of L 0 has been given. Thepresent paper yields an analogous axiomatics forNL 0. Like in the author's previous work, the notionof rank of an axiom is introduced which, although inessentialfor the results given below, may be useful for the expectednonfinite-axiomatizability proof. (shrink)