Logical form and logical analysis as the search for it have been introduced during the developmen... more Logical form and logical analysis as the search for it have been introduced during the development of logic and analytical philosophy and are still widely considered as key tools or methods for the solution of philosophical puzzles. It is instructive to have a look at a criticism of these presupositions and I present Wittgenstein as the author who provides such a criticism. I present a development of his view of logical form which went from the thesis of the ineffability of logical form to the denial of the meaningfulness of the notion of logical form as such. This refusal is linked to Wittgenstein’s abandonment of the idea of the language of pure experience. The method of philosophical therapies is presented as an alternative to logical analysis and this methodology is linked with Wittgenstein’s consideration of game and family resemblance.
This work is about bisimulation in modal logic as well as in intuicionistic logic without contrac... more This work is about bisimulation in modal logic as well as in intuicionistic logic without contraction. Bisimulation is a relation between models, which is weaker than isomorphism, yet still guarantees equivalence in the in the selected logic. It is typically used to demonstrate that some properties of models cannot be distinguished. For instance the cardinality cannot be distinguished, which is shown by disjunct union. Bisimulation also helps to clarify the relation between modal and classical logic. Apart from bisimulation, the related notion of bounded morphism is studied because it enables to elevate the unde- nability and undistinguishability to the discourse of frames. The part about modal logic is basically a compilation of well known facts, yet their interaction is made more clear and some proofs, which are usually disregarded as obvious, are presented in an explicit manner. Talking about the second part, mere reasonable de nition of the semantics is an honest work. Yet even ...
Inferentialism has brought important insights into the nature of meanings. It breaks with the rep... more Inferentialism has brought important insights into the nature of meanings. It breaks with the representationalist tradition that sees meanings as constituted primarily by representing some extra-linguistic reality. Yet the break with tradition should be pursued further. Inferentialists still regard meanings as static, and they still do not entirely abandon the idea of fully determined meaning. Following Davidon’s ideas about meanings as constituted only in the course of a specific conversation, I propose a dynamic account of what meanings are. They are described as entities belonging to the dynamic realm of Henri Bergson’s duration. The inhabitants of this realm live in constant movement and development which is more essential to them than the stages that this development goes through. My account brings about a rejection of the notion of the strict literal meaning and therewith also of the contrasting notions such as ambiguity. Meaning is understood as a dynamic entity that is chara...
Logický pluralismus v historické perspektivě Pluralita logik je pojata jako výzva k hledání hlubš... more Logický pluralismus v historické perspektivě Pluralita logik je pojata jako výzva k hledání hlubšího pochopení povahy a významu logiky. Jsou zváženy dva základní přístupy k vymezování logiky vůči jiným disciplínám, totiž přístup vycházející z teorie modelů a přístup vycházející z teorie důkazů. Zkoumání historie, která vedla k těmto dvěma přístupům, vyzvihuje postavení logiky v Kantově epistemologii jako klíčové pro další vývoj. Analogický vývoj od Kantova pojetí geometrie ke vzniku plurality geometrických teorií vede k holistickému pohledu jak na geometrii, tak na logiku. Jako klíčové se nakonec ale ukáže především správně uchopit pragmatický význam logiky. Vzhledem k problémům vážícím se ke snahám logiku vymezit se jako nejvhodnější pojetí role logiky jeví inferencialismus a logický expresivismus. Tyto přístupy jsou rozvinuty do koncepce, která zdůraňuje, v návaznosti na historickou perspektivu práce, schopnost logiky vyvíjet se. 1Logical pluralism from historical perspective - Ab...
This thesis is about the distributive full Lambek calculus, i.e., intuicionistic logic without th... more This thesis is about the distributive full Lambek calculus, i.e., intuicionistic logic without the structural rules of exchange, contraction and weakening and particularly about the two semantics of this logic, one of which is algebraic, the other one is a Kripke semantic. The two semantics are treated in separate chapters and some results about them are shown, for example the disjunction property is proven by amalgamation of Kripke models. The core of this thesis is nevertheless the relation of these two semantics, since it is interesting to study what do they have in common and how can they actually differ, both being a semantics of the same logic. We show how to translate frames to algebras and algebras to frames, and, moreover, we extend such translation to morphisms, thus constructing two functors between the two categories. Key words:distributive FL logic, distributive full Lambek calculus, structural rules, distributive residuated lattice, Kripke frames, frame morphisms, category, functor
Despite its popularity, model theory based on Tarski's insights is in need of deeper philosophica... more Despite its popularity, model theory based on Tarski's insights is in need of deeper philosophical reflection. A wide range of stances towards it was proposed, some seeing it as project based on fundamental misconceptions, some asserting it reveals the very essence of logic. I would like to balance these extreme views. Of particular importance will be its connection to the problem of logical constants. Identifying logical constatnts enables us to identify logical forms of statements and thus brings us close to demarcating logic. We will see that solving this issue in ways suggested by model theory has its considerable costs, while the gains are rather modest.
I would like to show that the problem of logical constants can be helped by treating the problem ... more I would like to show that the problem of logical constants can be helped by treating the problem of relationship between logic and human reasoning. Thus I will present some parallels between the respective dilemmas and show that choice of a proof-theoretic answer in one case induces an expressivist choice in the other and the other way round, as well. This does not mean that other options are closed, though the two selected ones are thus given a new plausibility. Furthermore, the prooftheoretical demarcations of logical constants can provide missing details into the expressivist story, as they say which constants and why can actually perform the expressivist job.
Henri Bergson se za svého života těšil velké popularitě. Přes jistý ústup ze slávy jeho filosofie... more Henri Bergson se za svého života těšil velké popularitě. Přes jistý ústup ze slávy jeho filosofie i v druhé polovině dvacátého století inspirovala např. Gillese Deleuze. Nicméně analytická filosofie Bergsonovi dosud mnoho pozornosti nevěnovala. Ačkoli na první pohled skutečně s analytickou filosofií nemá mnoho společného, najdeme v jeho díle některé myšlenky, které by si zasloužily, aby je analytická filosofie zhodnotila. Zaměříme se na Bergsonovo pojetí špatně položených otázek, které je v mnohém podobné pojetí logických pozitivistů. Dále navrhneme, v čem může spočívat jeho přínos pro teorii pravidel a normativistickou teorii významu. Obě témata jsou zde především programaticky nastíněna, jejich hlubší rozpracování je úkol pro další práci.
Logical pluralism as a thesis that more than one logic is correct seems very plausible for two ba... more Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical monism is called for. I review the possible forms of logical pluralism and render them more plausible. I thus arrive at logical dynamism, a synthesis of various pluralisms and monism focused on how logic develops.
The fact that there is a plurality of systems that we call logics makes it requisite to attempt a... more The fact that there is a plurality of systems that we call logics makes it requisite to attempt an explanation and thorough evaluation of the role of logic. I exploit the analogical development towards the pluralism of geometry to show that both disciplines are about some kinds of space which they explicate and that we can choose with some freedom the tools for engaging in an enterprise of these disciplines. After revisiting the development of non-classical (i.e. non-Euclidian) geometries, I present logical expressivism, as coined by Robert Brandom, and, returning again to geometry, show that an analogous doctrine of geometrical expressivism can also provide a viable account of the nature and purpose of the discipline and the reasons for plurality of both geometries and logics.
Various attempts at demarcating logic were undertaken, many of them based on specific understandi... more Various attempts at demarcating logic were undertaken, many of them based on specific understanding of how logical knowledge is formal and not material. MacFarlane has persuasively shown that general idea of formality of logic can be understood in various ways. I take two of the accounts of formality, namely the requirement of conservativity and the requirement of schematicity of logical vocabulary, into consideration as promising candidates to make the all too unclear notion of formality more precise and study to what degree they could be considered as either necessary or sufficient conditions for logicality of some piece of vocabulary. Finding both notion unsatisfactory, as they stand, I propose combining them and envisage a hierarchy of logicality of expressions of a given language. Such a hierarchy is complicated and not linear, yet still offers a valuable explication of both the range and pragmatic significance of logic, if we combine it with logical expressivism.
Logical form and logical analysis as the search for it have been introduced during the developmen... more Logical form and logical analysis as the search for it have been introduced during the development of logic and analytical philosophy and are still widely considered as key tools or methods for the solution of philosophical puzzles. It is instructive to have a look at a criticism of these presupositions and I present Wittgenstein as the author who provides such a criticism. I present a development of his view of logical form which went from the thesis of the ineffability of logical form to the denial of the meaningfulness of the notion of logical form as such. This refusal is linked to Wittgenstein’s abandonment of the idea of the language of pure experience. The method of philosophical therapies is presented as an alternative to logical analysis and this methodology is linked with Wittgenstein’s consideration of game and family resemblance.
This work is about bisimulation in modal logic as well as in intuicionistic logic without contrac... more This work is about bisimulation in modal logic as well as in intuicionistic logic without contraction. Bisimulation is a relation between models, which is weaker than isomorphism, yet still guarantees equivalence in the in the selected logic. It is typically used to demonstrate that some properties of models cannot be distinguished. For instance the cardinality cannot be distinguished, which is shown by disjunct union. Bisimulation also helps to clarify the relation between modal and classical logic. Apart from bisimulation, the related notion of bounded morphism is studied because it enables to elevate the unde- nability and undistinguishability to the discourse of frames. The part about modal logic is basically a compilation of well known facts, yet their interaction is made more clear and some proofs, which are usually disregarded as obvious, are presented in an explicit manner. Talking about the second part, mere reasonable de nition of the semantics is an honest work. Yet even ...
Inferentialism has brought important insights into the nature of meanings. It breaks with the rep... more Inferentialism has brought important insights into the nature of meanings. It breaks with the representationalist tradition that sees meanings as constituted primarily by representing some extra-linguistic reality. Yet the break with tradition should be pursued further. Inferentialists still regard meanings as static, and they still do not entirely abandon the idea of fully determined meaning. Following Davidon’s ideas about meanings as constituted only in the course of a specific conversation, I propose a dynamic account of what meanings are. They are described as entities belonging to the dynamic realm of Henri Bergson’s duration. The inhabitants of this realm live in constant movement and development which is more essential to them than the stages that this development goes through. My account brings about a rejection of the notion of the strict literal meaning and therewith also of the contrasting notions such as ambiguity. Meaning is understood as a dynamic entity that is chara...
Logický pluralismus v historické perspektivě Pluralita logik je pojata jako výzva k hledání hlubš... more Logický pluralismus v historické perspektivě Pluralita logik je pojata jako výzva k hledání hlubšího pochopení povahy a významu logiky. Jsou zváženy dva základní přístupy k vymezování logiky vůči jiným disciplínám, totiž přístup vycházející z teorie modelů a přístup vycházející z teorie důkazů. Zkoumání historie, která vedla k těmto dvěma přístupům, vyzvihuje postavení logiky v Kantově epistemologii jako klíčové pro další vývoj. Analogický vývoj od Kantova pojetí geometrie ke vzniku plurality geometrických teorií vede k holistickému pohledu jak na geometrii, tak na logiku. Jako klíčové se nakonec ale ukáže především správně uchopit pragmatický význam logiky. Vzhledem k problémům vážícím se ke snahám logiku vymezit se jako nejvhodnější pojetí role logiky jeví inferencialismus a logický expresivismus. Tyto přístupy jsou rozvinuty do koncepce, která zdůraňuje, v návaznosti na historickou perspektivu práce, schopnost logiky vyvíjet se. 1Logical pluralism from historical perspective - Ab...
This thesis is about the distributive full Lambek calculus, i.e., intuicionistic logic without th... more This thesis is about the distributive full Lambek calculus, i.e., intuicionistic logic without the structural rules of exchange, contraction and weakening and particularly about the two semantics of this logic, one of which is algebraic, the other one is a Kripke semantic. The two semantics are treated in separate chapters and some results about them are shown, for example the disjunction property is proven by amalgamation of Kripke models. The core of this thesis is nevertheless the relation of these two semantics, since it is interesting to study what do they have in common and how can they actually differ, both being a semantics of the same logic. We show how to translate frames to algebras and algebras to frames, and, moreover, we extend such translation to morphisms, thus constructing two functors between the two categories. Key words:distributive FL logic, distributive full Lambek calculus, structural rules, distributive residuated lattice, Kripke frames, frame morphisms, category, functor
Despite its popularity, model theory based on Tarski's insights is in need of deeper philosophica... more Despite its popularity, model theory based on Tarski's insights is in need of deeper philosophical reflection. A wide range of stances towards it was proposed, some seeing it as project based on fundamental misconceptions, some asserting it reveals the very essence of logic. I would like to balance these extreme views. Of particular importance will be its connection to the problem of logical constants. Identifying logical constatnts enables us to identify logical forms of statements and thus brings us close to demarcating logic. We will see that solving this issue in ways suggested by model theory has its considerable costs, while the gains are rather modest.
I would like to show that the problem of logical constants can be helped by treating the problem ... more I would like to show that the problem of logical constants can be helped by treating the problem of relationship between logic and human reasoning. Thus I will present some parallels between the respective dilemmas and show that choice of a proof-theoretic answer in one case induces an expressivist choice in the other and the other way round, as well. This does not mean that other options are closed, though the two selected ones are thus given a new plausibility. Furthermore, the prooftheoretical demarcations of logical constants can provide missing details into the expressivist story, as they say which constants and why can actually perform the expressivist job.
Henri Bergson se za svého života těšil velké popularitě. Přes jistý ústup ze slávy jeho filosofie... more Henri Bergson se za svého života těšil velké popularitě. Přes jistý ústup ze slávy jeho filosofie i v druhé polovině dvacátého století inspirovala např. Gillese Deleuze. Nicméně analytická filosofie Bergsonovi dosud mnoho pozornosti nevěnovala. Ačkoli na první pohled skutečně s analytickou filosofií nemá mnoho společného, najdeme v jeho díle některé myšlenky, které by si zasloužily, aby je analytická filosofie zhodnotila. Zaměříme se na Bergsonovo pojetí špatně položených otázek, které je v mnohém podobné pojetí logických pozitivistů. Dále navrhneme, v čem může spočívat jeho přínos pro teorii pravidel a normativistickou teorii významu. Obě témata jsou zde především programaticky nastíněna, jejich hlubší rozpracování je úkol pro další práci.
Logical pluralism as a thesis that more than one logic is correct seems very plausible for two ba... more Logical pluralism as a thesis that more than one logic is correct seems very plausible for two basic reasons. First, there are so many logical systems on the market today. And it is unclear how we should decide which of them gets the logical rules right. On the other hand, logical monism as the opposite thesis still seems plausible, as well, because of normativity of logic. An approach which would manage to bring a synthesis of both logical pluralism and logical monism is called for. I review the possible forms of logical pluralism and render them more plausible. I thus arrive at logical dynamism, a synthesis of various pluralisms and monism focused on how logic develops.
The fact that there is a plurality of systems that we call logics makes it requisite to attempt a... more The fact that there is a plurality of systems that we call logics makes it requisite to attempt an explanation and thorough evaluation of the role of logic. I exploit the analogical development towards the pluralism of geometry to show that both disciplines are about some kinds of space which they explicate and that we can choose with some freedom the tools for engaging in an enterprise of these disciplines. After revisiting the development of non-classical (i.e. non-Euclidian) geometries, I present logical expressivism, as coined by Robert Brandom, and, returning again to geometry, show that an analogous doctrine of geometrical expressivism can also provide a viable account of the nature and purpose of the discipline and the reasons for plurality of both geometries and logics.
Various attempts at demarcating logic were undertaken, many of them based on specific understandi... more Various attempts at demarcating logic were undertaken, many of them based on specific understanding of how logical knowledge is formal and not material. MacFarlane has persuasively shown that general idea of formality of logic can be understood in various ways. I take two of the accounts of formality, namely the requirement of conservativity and the requirement of schematicity of logical vocabulary, into consideration as promising candidates to make the all too unclear notion of formality more precise and study to what degree they could be considered as either necessary or sufficient conditions for logicality of some piece of vocabulary. Finding both notion unsatisfactory, as they stand, I propose combining them and envisage a hierarchy of logicality of expressions of a given language. Such a hierarchy is complicated and not linear, yet still offers a valuable explication of both the range and pragmatic significance of logic, if we combine it with logical expressivism.
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