Studia humana (SH) is a multi-disciplinary peer reviewed journal publishing valuable

contributions on any aspect of human sciences such as...

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Studia humana (SH) is a multi-disciplinary peer reviewed journal publishing valuable

contributions on any aspect of human sciences such as...

read more...

The date of the publication:

2020-10-29

The number of pages:

0

The issue:

9:3/4

Commentaries:

0

The Authors

Andrew Schumann, Roman Murawski, Jean-Yves Beziau, Kazimierz Trzęsicki, Alexandre Costa-Leite, Edelcio G. de Souza, Fabien Schang, Jens Lemanski, Michał Dobrzański, Tomasz Jarmużek, Mateusz Klonowski, Rafał Palczewski, Jerzy Pogonowski, Janusz Kaczmarek, Stanisław Krajewski, Marcin Trepczyński, Wojciech Krysztofiak, Marek Zirk-Sadowski,

The Author: Andrew Schumann,

It is a Preface to Volume 9:3/4 that has brought a renewed focus to the role of truth conceptions in frameworks of semantics and logic. Jan Woleński is known due to his works on epistemological aspects of logic and his systematization of semantic truth theory. He became the successor and the worthy continuer of prominent Polish logicians: Alfred Tarski and Kazimierz Ajdukiewicz. This volume is collected on the 80th anniversary of Woleński’s birth and draws together new research papers devoted to judgments and truth. These papers take measure of the scope and impact of Woleński's views on truth conceptions, and present new contributions to the field of philosophy and logic.

The Author: Roman Murawski,

Two crucial concepts of the methodology and philosophy of mathematics

are considered: proof and truth. We distinguish between informal proofs

constructed by mathematicians in their research practice and formal

proofs as defined in the foundations of mathematics (in

metamathematics). Their role, features and interconnections are

discussed. They are confronted with the concept of truth in mathematics.

Relations between proofs and truth are analysed.

are considered: proof and truth. We distinguish between informal proofs

constructed by mathematicians in their research practice and formal

proofs as defined in the foundations of mathematics (in

metamathematics). Their role, features and interconnections are

discussed. They are confronted with the concept of truth in mathematics.

Relations between proofs and truth are analysed.

(Alice in the Wonderful Land of Logical Notions)

The Author: Jean-Yves Beziau,

We discuss a theory presented in a posthumous paper by Alfred Tarski

entitled “What are logical notions?”. Although the theory of these logical

notions is something outside of the main stream of logic, not presented in

logic textbooks, it is a very interesting theory and can easily be

understood by anybody, especially studying the simplest case of the four

basic logical notions. This is what we are doing here, as well as

introducing a challenging fifth logical notion. We first recall the context

and origin of what are here called Tarski-Lindenbaum logical notions. In

the second part, we present these notions in the simple case of a binary

relation. In the third part, we examine in which sense these are

considered as logical notions contrasting them with an example of a nonlogical

relation. In the fourth part, we discuss the formulations of the four

logical notions in natural language and in first-order logic without

equality, emphasizing the fact that two of the four logical notions cannot

be expressed in this formal language. In the fifth part, we discuss the

relations between these notions using the theory of the square of

opposition. In the sixth part, we introduce the notion of variety

corresponding to all non-logical notions and we argue that it can be

considered as a logical notion because it is invariant, always referring to

the same class of structures. In the seventh part, we present an enigma: is

variety formalizable in first-order logic without equality? There follow

recollections concerning Jan Woleński. This paper is dedicated to his 80th

birthday. We end with the bibliography, giving some precise references

for those wanting to know more about the topic.

entitled “What are logical notions?”. Although the theory of these logical

notions is something outside of the main stream of logic, not presented in

logic textbooks, it is a very interesting theory and can easily be

understood by anybody, especially studying the simplest case of the four

basic logical notions. This is what we are doing here, as well as

introducing a challenging fifth logical notion. We first recall the context

and origin of what are here called Tarski-Lindenbaum logical notions. In

the second part, we present these notions in the simple case of a binary

relation. In the third part, we examine in which sense these are

considered as logical notions contrasting them with an example of a nonlogical

relation. In the fourth part, we discuss the formulations of the four

logical notions in natural language and in first-order logic without

equality, emphasizing the fact that two of the four logical notions cannot

be expressed in this formal language. In the fifth part, we discuss the

relations between these notions using the theory of the square of

opposition. In the sixth part, we introduce the notion of variety

corresponding to all non-logical notions and we argue that it can be

considered as a logical notion because it is invariant, always referring to

the same class of structures. In the seventh part, we present an enigma: is

variety formalizable in first-order logic without equality? There follow

recollections concerning Jan Woleński. This paper is dedicated to his 80th

birthday. We end with the bibliography, giving some precise references

for those wanting to know more about the topic.

The Author: Kazimierz Trzęsicki,

Artificial Intelligence, both as a hope of making substantial progress, and a fear of the unknow n and unimaginable, has its roots in hum an dreams. These dreams are materialized by means of rational intellectual efforts. We see the beginnings of such a process in Lullus’s fancies. Many scholars and enthusiasts participated in the development of Lullus’s art, ars com binatoria. Amongst them, Athanasius Kircher distinguished himself. Gottfried Leibniz ended the period in whic h the idea of artificial intelligence was shap ed, and started the new period, in which artificial intelligence could be conside red part of science, by today’s standards.

Logics and Modal Operators

The Author: Alexandre Costa-Leite, Edelcio G. de Souza,

Departing from basic concepts in abstract logics, this paper introduces two

concepts: conjunctive and disjunctive limits. These notions are used to

formalize levels of modal operators.

concepts: conjunctive and disjunctive limits. These notions are used to

formalize levels of modal operators.

Professor Woleński’s Logical and Philosophical Writings

The Author: Fabien Schang,

Roman Suszko said that “Obviously, any multiplication of logical values is a mad

idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is

to qualify this ‘obvious’ statement through a number of logical and philosophical

writings by Professor Jan Woleński, all focusing on the nature of truth-values and

their multiple uses in philosophy. It results in a reconstruction of such an abstract

object, doing justice to what Suszko held a ‘mad’ project within a generalized

logic of judgments. Four main issues raised by Woleński will be considered to test

the insightfulness of such generalized truth-values, namely: the principle of

bivalence, the logic of scepticism, the coherence theory of truth, and nothingness.

idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is

to qualify this ‘obvious’ statement through a number of logical and philosophical

writings by Professor Jan Woleński, all focusing on the nature of truth-values and

their multiple uses in philosophy. It results in a reconstruction of such an abstract

object, doing justice to what Suszko held a ‘mad’ project within a generalized

logic of judgments. Four main issues raised by Woleński will be considered to test

the insightfulness of such generalized truth-values, namely: the principle of

bivalence, the logic of scepticism, the coherence theory of truth, and nothingness.

The Author: Jens Lemanski, Michał Dobrzański,

Reism or concretism are the labels for a position in ontology and semantics that

is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan

Woleński have shown, there are two dimensions with which the abstract

expression of reism can be made concrete: The ontological dimension of reism

says that only things exist; the semantic dimension of reism says that all

concepts must be reduced to concrete terms in order to be meaningful. In this

paper we argue for the following two theses: (1) Arthur Schopenhauer has

advocated a reistic philosophy of language which says that all concepts must

ultimately be based on concrete intuition in order to be meaningful. (2) In his

semantics, Schopenhauer developed a theory of logic diagrams that can be

interpreted by modern means in order to concretize the abstract position of

reism. Thus we are not only enhancing Jan Woleński’s list of well-known

reists, but we are also adding a diagrammatic dimension to concretism,

represented by Schopenhauer.

is represented by various philosophers. As Kazimierz Ajdukiewicz and Jan

Woleński have shown, there are two dimensions with which the abstract

expression of reism can be made concrete: The ontological dimension of reism

says that only things exist; the semantic dimension of reism says that all

concepts must be reduced to concrete terms in order to be meaningful. In this

paper we argue for the following two theses: (1) Arthur Schopenhauer has

advocated a reistic philosophy of language which says that all concepts must

ultimately be based on concrete intuition in order to be meaningful. (2) In his

semantics, Schopenhauer developed a theory of logic diagrams that can be

interpreted by modern means in order to concretize the abstract position of

reism. Thus we are not only enhancing Jan Woleński’s list of well-known

reists, but we are also adding a diagrammatic dimension to concretism,

represented by Schopenhauer.

of Jan Woleński’s Metaethical Naturalism

The Author: Tomasz Jarmużek, Mateusz Klonowski, Rafał Palczewski,

In this paper, we indicate how Jan Woleński’s non-linguistic concept of the norm

allows us to clarify the deontic relationship between sentences and the given

normative system. A relationship of this kind constitutes a component of the

metalogic of relating deontic logic, which subjects the logical value of the deontic

sentence to the logical value of the constituent sentence and its relationship with a

given normative system in the accessible possible worlds.

allows us to clarify the deontic relationship between sentences and the given

normative system. A relationship of this kind constitutes a component of the

metalogic of relating deontic logic, which subjects the logical value of the deontic

sentence to the logical value of the constituent sentence and its relationship with a

given normative system in the accessible possible worlds.

The Author: Jerzy Pogonowski,

This note discusses some problems concerning intended, standard, and nonstandard

models of mathematical theories. We pay attention to the role of

extremal axioms in attempts at a unique characterization of the intended

models. We recall also Jan Woleński’s views on these issues.

models of mathematical theories. We pay attention to the role of

extremal axioms in attempts at a unique characterization of the intended

models. We recall also Jan Woleński’s views on these issues.

Formalization, De-formalization and Topological Hermeneutics

The Author: Janusz Kaczmarek,

In this article I want to continue the characteristics of philosophical methods

specific to analytical philosophy, which were and are important for Professor

Jan Woleński. So I refer to his work on the methods of analytical philosophy,

but I also point out a few new methods that have grown up in the climate of

studies of philosophers, especially analytical ontologists. I will therefore

describe the following methods: generalization, specialization, formalization,

de-formalization and topological hermeneutics. Instead of the term “method” I

use interchangeably the terms “operation” or “procedure”. I will show that each

of these operations makes an important contribution to ontological

investigations, and, in particular, to formal ontology.

specific to analytical philosophy, which were and are important for Professor

Jan Woleński. So I refer to his work on the methods of analytical philosophy,

but I also point out a few new methods that have grown up in the climate of

studies of philosophers, especially analytical ontologists. I will therefore

describe the following methods: generalization, specialization, formalization,

de-formalization and topological hermeneutics. Instead of the term “method” I

use interchangeably the terms “operation” or “procedure”. I will show that each

of these operations makes an important contribution to ontological

investigations, and, in particular, to formal ontology.

and Mathematical Proofs

The Author: Stanisław Krajewski,

The Euclidean ideal of mathematics as well as all the foundational schools in

the philosophy of mathematics have been contested by the new approach,

called the “maverick” trend in the philosophy of mathematics. Several points

made by its main representatives are mentioned – from the revisability of

actual proofs to the stress on real mathematical practice as opposed to its

idealized reconstruction. Main features of real proofs are then mentioned; for

example, whether they are convincing, understandable, and/or explanatory.

Therefore, the new approach questions Hilbert’s Thesis, according to which a

correct mathematical proof is in principle reducible to a formal proof, based on

explicit axioms and logic.

the philosophy of mathematics have been contested by the new approach,

called the “maverick” trend in the philosophy of mathematics. Several points

made by its main representatives are mentioned – from the revisability of

actual proofs to the stress on real mathematical practice as opposed to its

idealized reconstruction. Main features of real proofs are then mentioned; for

example, whether they are convincing, understandable, and/or explanatory.

Therefore, the new approach questions Hilbert’s Thesis, according to which a

correct mathematical proof is in principle reducible to a formal proof, based on

explicit axioms and logic.

The Author: Marcin Trepczyński,

In this paper, the theory of necessity proposed by Robert Grosseteste is

presented. After showing the wide range of various kinds of

determination discussed by him (connected with: (1) one’s knowledge

about the future, (2) predestination, (3) fate, (4) grace, (5) sin and

temptation), a different context of Grosseteste’s use of the notion of

necessity is analyzed (within logical and metaphysical approaches). At

the heart of his theory lie: the definition of necessity, which is that

something lacks the capacity (posse) for its opposite, and the distinction

between two perspectives within which we can consider necessity: (1)

the one according to which the truthfulness of a dictum determines that it

cannot be the opposite, (2) a pre- or atemporal one, as if something had

not yet begun. On these grounds, Robert explains that God’s omniscience

is compatible with contingency, including human free decisions. Robert’s

theory is still relevant and useful in contemporary debates, as it can

provide strong arguments and enrich discussions, thanks to the twoperspectives

approach, which generates nine kinds of positions on the

spectrum of determinism and indeterminism.

presented. After showing the wide range of various kinds of

determination discussed by him (connected with: (1) one’s knowledge

about the future, (2) predestination, (3) fate, (4) grace, (5) sin and

temptation), a different context of Grosseteste’s use of the notion of

necessity is analyzed (within logical and metaphysical approaches). At

the heart of his theory lie: the definition of necessity, which is that

something lacks the capacity (posse) for its opposite, and the distinction

between two perspectives within which we can consider necessity: (1)

the one according to which the truthfulness of a dictum determines that it

cannot be the opposite, (2) a pre- or atemporal one, as if something had

not yet begun. On these grounds, Robert explains that God’s omniscience

is compatible with contingency, including human free decisions. Robert’s

theory is still relevant and useful in contemporary debates, as it can

provide strong arguments and enrich discussions, thanks to the twoperspectives

approach, which generates nine kinds of positions on the

spectrum of determinism and indeterminism.

The Author: Wojciech Krysztofiak,

In the paper, there is presented the theory of logical consequence operators

indexed with taboo functions. It describes the mechanisms of logical inference

in the environment of forbidden sentences. This kind of processes take place in

ideological discourses within which their participants create various narrative

worlds (mental worlds). A peculiar feature of ideological discourses is their

association with taboo structures of deduction which penalize speech acts. The

development of discourse involves, among others, transforming its deduction

structure towards the proliferation of consequence operators and modifying

penalty functions. The presented theory enables to define various processes of

these transformations in the precise way. It may be used in analyses of conflicts

between competing elm experts acting within a discourse.

indexed with taboo functions. It describes the mechanisms of logical inference

in the environment of forbidden sentences. This kind of processes take place in

ideological discourses within which their participants create various narrative

worlds (mental worlds). A peculiar feature of ideological discourses is their

association with taboo structures of deduction which penalize speech acts. The

development of discourse involves, among others, transforming its deduction

structure towards the proliferation of consequence operators and modifying

penalty functions. The presented theory enables to define various processes of

these transformations in the precise way. It may be used in analyses of conflicts

between competing elm experts acting within a discourse.

The Author: Marek Zirk-Sadowski,

The author proves that rejecting the existence of permissive norms and limitation

of norms to prohibitions and commands alone is possible only with reducing the

idea of a function. The essence of the function is then the ability of the expression

to generate independently the universal norm formation. Such manipulation is easy

on the level of logical analysis, but proves risky from other points of view. If we

want the deontic logic, which we construct, to consider the fact that permission is

pragmatically necessary for the law-maker to convey his normative preferences,

we must solve the consequences of the adopted structure of the function of norms,

which originate on the socio-linguistic level. It appears, however, that due to a lack

of a pragmatic theory useful for lawyers, there is no proof that the pragmatically

strong permission can be expressed by means of a lot of prohibitions and

commands (dos and don’ts). Besides, reducing permissions only to the language of

legal rules is an obligation to accept the structure of an act of communication,

which can find its full motivation in the Husserl’s structure of the direct cognition.

of norms to prohibitions and commands alone is possible only with reducing the

idea of a function. The essence of the function is then the ability of the expression

to generate independently the universal norm formation. Such manipulation is easy

on the level of logical analysis, but proves risky from other points of view. If we

want the deontic logic, which we construct, to consider the fact that permission is

pragmatically necessary for the law-maker to convey his normative preferences,

we must solve the consequences of the adopted structure of the function of norms,

which originate on the socio-linguistic level. It appears, however, that due to a lack

of a pragmatic theory useful for lawyers, there is no proof that the pragmatically

strong permission can be expressed by means of a lot of prohibitions and

commands (dos and don’ts). Besides, reducing permissions only to the language of

legal rules is an obligation to accept the structure of an act of communication,

which can find its full motivation in the Husserl’s structure of the direct cognition.