Gödel’s incompleteness theorems are often treated either as purely technical results with no broader philosophical significance or as evidence for far-reaching metaphysical conclusions. This paper rejects both extremes. I argue that incompleteness is best understood as revealing a structural limitation of formal representation rather than a contingent defect of particular axiomatic systems or an epistemic shortcoming of mathematical practice. After clarifying what Gödel’s theorems do and do not establish, I critically examine formalist, Platonist, and instrumentalist interpretations, showing that none (...) adequately accounts for the systematic persistence of incompleteness across expressive formal frameworks. I propose a conceptually modest notion of ontological excess to characterize the mismatch between formal systems and what they represent, without invoking speculative ontology or empirical claims. On this view, incompleteness reflects limits of formal capture, not limits of truth or knowledge. The result is a restrained account of the philosophical significance of Gödelian incompleteness, with implications for metaphysical explanation and scientific realism that remain firmly within the bounds of logical analysis. (shrink)

This paper presents Noology, a formal system that defines the highest-level protocol by which intelligence constitutes reality. Noology (Japanese: Chigaku 知学) is not a theory within science, but an operating system specifi cation for existence itself. Crucially, Noology is a meta-judgment framework: it does not generate truths internally, but adjudicates whether an externally given structure qualifi es as “real” (Res) under a given confi guration (Quaestio). By design, it avoids the premises of Gödel’s incompleteness theorems through non-interpretability (...) of arithmetic. Noology serves as the regulative layer above Operatiol- ogy, providing the axiomatic foundation from which Operatiology’s executive structure is derived. -/- Version 2 of this system rested on three independent primitive notions (Ordo, Consensus, Arbitrium), related by three absolute axioms formulated as relational constraints with non-triviality conditions, together with one governing principle. The present version revises this foundation: the triad and its three axioms are no longer independent primitives but are derived as theorems from a single primitive, Self-Closure (Ω), together with the Governing Principle, tightening the regulative foundation on which Operatiology depends. -/- The independence and minimality results of Version 2 are re-established with explicit model constructions on the re-derived axioms, and the non-applicability of Gödel’s incompleteness theorems is re-proven using the structure’s own witness model. The relation to Operatiology is restated within this single-primitive foundation, preserving the Lemma 2.1 confi gurational-sensitivity argument by which Arbitrium, Axiom 2, and Axiom 4 jointly force non-commutativity. The system remains minimal, irreducible, and self-contained: it presupposes neither arithmetic, set theory, nor physical law, and it does not, and structurally cannot, force the dimensional bound established at Tier-2; any further realization belongs to Operatiology and its algebraic layer, not to the present document. DOI: 10.5281/zenodo.20786059 Published on June 22, 2026. (shrink)

We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

Formal systems of fuzzy logic are well-established logical systems and respected members of the broad family of the so-called substructural logics closely related to the famous logic BCK. The study of fragments of logical systems is an important issue of research in any class of non-classical logics. Here we study the fragments of nine prominent fuzzy logics to all sublanguages containing implication. However, the results achieved in the paper for those nine logics are usually corollaries of theorems with much (...) wider scope of applicability. In particular, we show how many of these fragments are really distinct and we find axiomatic systems for most of them. In fact, we construct strongly separable axiomatic systems for eight of our nine logics. We also fully answer the question for which of the studied fragments the corresponding class of algebras forms a variety. Finally, we solve the problem how to axiomatize predicate versions of logics without the lattice disjunction. (shrink)

In the history of Newtonian Mechanics physicists and astronomers did not rely on so-called inertial frames, indeed they were not able to identify such frames. So the usual neo-Newtonian formalism of Newtonian Mechanics contains some superfluous components. In the present paper I will formulate a formal system for classical particle mechanics in Leibnizian space-time, where a relation, a counterpart of the second law of motion, between force on bodies and derivative of their momentum will be defined relative to (...) every, inertial or not, reference frame. And I will present a view that in the research process under Newtonian mechanics the accumulation of those models of the relation that satisfied some realistic conditions determined an additional structure of non-rotating frames to Leibnizian space-time. (shrink)

This article is a brief formulation of a radical thesis. We start with the formalist doctrine that mathematical objects have no meanings; we have marks and rules governing how these marks can be combined. That's all. Then I go further by arguing that the signs of a formal system of mathematics should be considered as physical objects, and the formal operations as physical processes. The rules of the formal operations are or can be expressed in terms (...) of the laws of physics governing these processes. In accordance with the physicalist understanding of mind, this is true even if the operations in question are executed in the head. A truth obtained through (mathematical) reasoning is, therefore, an observed outcome of a neuro-physiological (or other physical) experiment. Consequently, deduction is nothing but a particular case of induction. (shrink)

Section 1 contains a survey of options in constructing a formal system of dialogue rules. The distinction between material and formal systems is discussed (section 1.1). It is stressed that the material systems are, in several senses, formal as well. In section 1.2 variants as to language form (choices of logical constants and logical rules) are pointed out. Section 1.3 is concerned with options as to initial positions and the permissibility of attacks on elementary statements. The (...) problem of ending a dialogue, and of infinite dialogues, is treated in section 1.4. Other options, e.g., as to the number of attacks allowed with respect to each statement, are listed in section 1.5. Section 1.6 explains the concept of a chain of arguments.From section 2 onward four types of dialectic systems are picked out for closer study: D, E, Di and Ei. After a preliminary section on dialogue sequents and winning strategies, the equivalence of derivability in intuitionistic logic and the existence of a winning strategy (for the Proponent) on the strength of Ei is shown by simple inductive proofs. (shrink)

In the paper [8], the first author developped a topos- theoretic approach to reference and modality. (See also [5]). This approach leads naturally to modal operators on locales (or spaces without points). The aim of this paper is to develop the theory of such modal operators in the context of the theory of locales, to axiomatize the propositional modal logics arising in this context and to study completeness and decidability of the resulting systems.

Wilfried Sieg. Formal Systems, Church Turing Thesis, and Gödel's Theorems: Three Contributions to The MIT Encyclopedias of Cognitive Science.

This article connects certain writings of Raymond Smullyan on logic and formal systems with current research on constructive type theory. It also considers aspects of teaching logic to computer science students. Those students require logic in order to precisely define programming tasks and demonstrate that programs meet logical specifications of these tasks. Smullyan’s book First-Order Logic has been used for many years to teach logic to computer science students at Cornell. This article includes a brief account of an elegant (...) result from this book. It is based on an extension of a fourteen page technical report that analyzes two pages on Boolean valuations in chapter one of his classic book. The analysis and results are formulated in a formal system of type theory and proved using the Nuprl proof assistant. The article also briefly considers the role of partial types, showing how they provide a new way to prove unsolvability results, another topic on which Smullyan has written with remarkable clarity. Partial types also provide a simple and faithful semantics for Hoare’s partial correctness logic, widely used to reason about programs and taught in computer science as an important applied logic. They also make it possible to state a clean rule for defined functions in Hoare logic. (shrink)

Adopting a different method from the previous scholars, this article deduces the remaining 23 valid syllogisms just taking the syllogism AEE-4 as the basic axiom. The basic idea of this study is as follows: firstly, make full use of the trichotomy structure of categorical propositions to formalize categorical syllogisms. Then, taking advantage of the deductive rules in classical propositional logic and the basic facts in the generalized quantifier theory, we deduce the remaining 23 valid categorical syllogisms by taking just one (...) syllogism (that is, AEE-4) as the basic axiom. This article not only reveals the reducible relations between the syllogism AEE-4 and the other 23 valid syllogisms, but also establishes a concise formal axiomatic system for categorical syllogistic logic. We hope that the results and methods will provide a good mathematical paradigm for studying other kinds of syllogistic logics, and that the project will appeal to specialists in logic, linguistic semantics, computational semantics, cognitive science and artificial intelligence. (shrink)

The main purpose of this paper is to present a formal systemPin which we enjoy a smooth-running technique and which countenances a universe of classes which is symmetrical as between large and small. More exactly,Pis a system which differs from the inconsistent system of [1] only in the introduction of a rather natural new restrictive condition on the defining formulas of the elements. It will be proved that if the weaker system of [2] is consistent, thenPis (...) also consistent.After the discovery of paradoxes, it may be recalled, Russell and Zermelo in the same year proposed two different ways of safeguarding logic against contradictions. Since then various simplifications and refinements of these systems have been made. However, in the resulting systems of Zermelo set theory, generation of classes still tends to be laborious and uncertain; and in the systems of Russell's theory of types, complications in the matter of reduplication of classes and meaningfulness of formulas remain. In [2], Quine introduced a system which seems to be free from all these complications. But later it was found out that in it there appears to be an unavoidable difficulty connected with mathematical induction. Indeed, we encounter the curious situation that although we can prove in it the existence of a class V of all classes, and we can also prove particular existence theorems for each of infinitely many classes, nobody has so far contrived to prove in it that V is an infinite class or that there exists an infinite class at all. (shrink)

Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways (...) of envisaging and analyzing at least simple formal systems using fractal patterns of infinite depth. Progressively deeper dimensions of such a fractal can be used to map increasingly complex wffs or increasingly complex 'value spaces', with tautologies, contradictions, and various forms of contingency coded in terms of color. This and related approaches, it turns out, offer not only visually immediate and geometrically intriguing representations of formal systems as a whole but also promising formal links (1) between standard systems and classical patterns in fractal geometry, (2) between quite different kinds of value spaces in classical and infinite-valued logics, and (3) between cellular automata and logic. It is hoped that pattern analysis of this kind may open possibilities for a geometrical approach to further questions within logic and metalogic. (shrink)

Here, I refute the formal system proposed for proof by the founders of the Evolution 2.0 award and demonstrate its scientific inconsistency.

In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the (...) intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand. (shrink)

This paper investigates the effect of the countervailing forces within organizations of formal systems that direct employees toward ethical acts and informal systems that direct employees toward fraudulent behavior. We study the effect of these forces on deception, a key component of fraud. The results provide support for an interactive effect of these formal and informal systems. The effectiveness of formal systems is greater when there is a strong informal “push” to do wrong; conversely, in the absence (...) of a strong push to do wrong, the strength of formal systems has little impact on fraudulent behavior. These results help to explain why the implementation of formal systems within organizations has been met with mixed results and identifies when formal systems designed to promote ethical behavior will be most efficacious. (shrink)

A formal system for Ł ${}_{\infty}$, based on a "game-theoretic" analysis of the Łukasiewicz propositional connectives, is defined and proved to be complete. An "Herbrand theorem" for the Ł ${}_{\infty}$ predicate calculus (a variant of some work of Mostowski) and some corollaries relating to its axiomatizability are proved. The predicate calculus with equality is also considered.

Psychotherapy lacks agreed formal foundations. Competing theoretical schools produce measurable clinical outcomes without consensus on the formal structure of psychological change, and without such foundations the discipline cannot adjudicate between theoretical claims at any level deeper than empirical outcome comparison, distinguish genuine structural change from symptomatic management, or explain why approaches with incompatible ontological commitments sometimes yield equivalent results. Modal logic is proposed here as providing those foundations in the model-theoretic sense articulated by Suppes (1967): not as a (...) reducing theory that would dissolve the clinical level into formal axioms, but as a specification of the abstract structures that psychotherapy’s theoretical dimension instantiates, sufficient for internal coherence and systematic development without entailing completeness or uniqueness. The modal system governing practical psychological modality is derived on substantive grounds, establishing that the system is KD, with seriality holding globally and reflexivity, transitivity, symmetry, and the Euclidean property each failing globally while admissible locally. Local reflexivity is grounded in a formally defined atomic proposition s recording whether a configuration is self-sustaining through its operative mechanism, which unifies the otherwise heterogeneous cases of therapeutically consolidated and pathologically entrenched configurations under a single formal criterion. Two formal models are developed, of agoraphobic constriction under cognitive-behavioural exposure treatment and of obsessional neurosis under psychoanalytic working-through, with four propositions stated and proved, including results on formal inaccessibility of therapeutic goals from initial configurations and on minimum path lengths that formally ground the structural necessity of graduated intermediate work. A formal adequacy class for KD-frames of practical psychological modality is explicitly defined. Therapeutic transitions are characterised as link-addition operations in the graph-transformer framework of van Benthem (2011), with precondition structures enforcing the non-transitivity of the accessibility relation at the level of programme executability. The structural parallel with deontic KD is shown to be substantively informative without transferring the known paradoxes of deontic logic, which are artifacts of the normative rather than the descriptive practical interpretation. (shrink)

This is a collection of papers read at an international logic colloquium held at Oxford in 1963. The first half contains articles on intuitionistic and modal logics, the propositional calculus, and languages with infinitely long expressions by such logicians as Kripke, Bull, Harrop, and Tait. The second part is primarily concerned with recursive functions and features a monograph by Crossley on constructive order types, as well as contributions by Goodstein, Schütte, and Wang, among others. Especially noteworthy is Kripke's paper which (...) applies Cohen's methods to the semantics of intuitionistic logic.—P. J. M. (shrink)

A formal system ℒ for descriptive and normative statements is given based on first-order predicate calculus augmented by deontic operators. Hume's separation thesis is then given the following formulation and proved in ℒ: there is no theorem in ℒ of the form P ⊃ M where P is a consistent descriptive statement and M is a normative statement. We attempt to show that the formal system ℒ is actually true for the intended model by giving an (...) interpretation of the formal system. It turns out that there are three mutually exclusive classes of statements; namely, descriptive statements, statements equivalent to purely normative statements, and hybrid statements. It is shown that theories that have not offered a proper treatment of hybrid statements have led to a great deal of confusion in the past. A brief discussion of the philosophical importance of the results is given. (shrink)

Solving numeric, logic and language puzzles and paradoxes is common within a wide community of high school and university students, fact witnessed by the increasing number of books published by mathematicians such as Martin Gardner, Douglas Hofstadter [in one of the best popular science books on paradoxes ], inspired by Gödel’s incompleteness theorems), Patrick Hughes and George Brecht and Raymond M. Smullyan, inter alia. Books by Smullyan are, however, much more involved, since they introduce learning trajectories and strategies across several (...) subjects of mathematical logic, as difficult as combinatorial logic, computability theory, and proof theory. These books provide solutions to their suggested exercises. Both statements and their solutions are written in the natural language, introducing some informal algorithms. As an exercise in Mathematics we wonder if an easy proof system could be devised to solve the amusing equations proposed by Smullyan in his books. Moreover, university students of logic could well train themselves in constructing deductive systems to solve puzzles instead of a non-uniform treatment one by one. In this paper, addressing students, we introduce one such formal systems, a tableaux approach able to provide the solutions to the puzzles involving either propositional logic, first order logic, or aspect logic. Let the reader amuse herself or himself! (shrink)

A formal logical system for sortal quantifiers, sortal identity and (second order) quantification over sortal concepts is formulated. The absolute consistency of the system is proved. A completeness proof for the system is also constructed. This proof is relative to a concept of logical validity provided by a semantics, which assumes as its philosophical background an approach to sortals from a modern form of conceptualism.

This paper addresses a structural question at the intersection of philosophy and science: why has the constitutional layer of theoretical systems remained institutionally vacant since the late 19th century, and what are the formal consequences of this vacancy? -/- We introduce a functional distinction between two layers present in any theoretical construction. The operational layer executes inference, computation, and expansion. The constitutional layer specifies what a theory is, within what scope it is valid, and what identity criteria it adopts. (...) Historical analysis from 1870 to 2000 demonstrates that the divergence of mathematical physics from philosophical methodology produced an institutional separation in which the constitutional layer was systematically left without an explicit custodian. -/- The central formal result, the Internal Closure Impossibility Theorem, proves that no operational layer can generate its own constitutive conditions as internal operations. The proof proceeds by reductio ad absurdum: assuming such internal generation exists produces an infinite regress that cannot terminate within finite computational resources. An external fixation point, termed Arbitrium, is therefore structurally necessary. -/- This result is not a reformulation of Gödel incompleteness or Tarski's truth hierarchy. Gödel operates at the syntactic level of formal systems; Tarski at the level of linguistic hierarchies. The present theorem operates at the constitutive level of theoretical construction itself. -/- The framework employed is Noology, a formal system developed within Cognitional Mechanics, which provides axiomatic foundations for the functional separation of constitutional and operational layers. Re-implementing the audit function in a form compatible with contemporary mathematical physics constitutes the logical responsibility identified by this paper. (shrink)

Lorenzen, in his book Einführung in die operative Logik und Mathematik has given a relatively precise form of syntactical system which he calls a calculus. The present paper deals with the relationship of Lorenzen's notion of calculus with the notion of formal system. It is shown that the obs of a formal system can be represented as the theses of a calculus of a certain type just when the calculus has a property called the tectonic (...) property, and conditions are given under which one form of system can be transformed into the other.ZusammenfassungLorenzen hat in seinem Buch, Einführung in die operative Logik und Mathematik, eine ziemlich genaue Auffassung eines syntaktischen Systems angegeben, die er Kalkül nennt. Die vorliegende Abhandlung betrifft die Verwandtschaft dieses Lorenzenschen Begriffs mit dem eines formalen Systems. Es wird bewiesen, dass die « Obs » eines formalen Systems sich als die Thesen eines passenden Kalküls genau dann repräsentieren lassen, wenn dieser Kalkül eine gewisse Eigenschaft, die « tectonic property » heisst, besitzt; die Bedingungen für die Überführung einer Art von System in die andere werden aufgezeigt.RésuméLorenzen, dans son livre Einführung in die operative Logik und Mathematik, a exposé une forme assez précise de systéme syntaxique qu'il a appelée un calcul. L'article actuel traite les relations entre cette idée et celle d'un système formel. L'auteur dèmontre que les « obs » d'un système formel peuvent se représenter comme les thèses d'un calcul d'une certaine espèce justement quand le calcul a une propriété que l'on appelle « the tectonic property »; et it énonce des conditions pour qu'un type de système soit transformable en l'autre. (shrink)

ZusammenfassungIn einem typenfreien formalen System, das widerspruchsfrei ist und alle Begriffe der klassischen Mathematik darzustellen vermag, können nicht alle Gesetze der klassischen Aussagenlogik gelten. Es entsteht daher das Problem, die aussagenlogischen Eigenschaften formaler Systeme allgemein zu untersuchen. Unter gewissen Voraussetzungen in aussagenlogischer Hinsicht wird die « aussagenlogische Vollständigkeit » und die « aussagenlogische Widerspruchsfreiheit » eines formalen Systems durch das Tertium non datur beziehungsweise durch die Schlussregel des Ex falso quodlibet charakterisiert. Es werden Entscheidungsverfahren für diejenigen syntaktischen Schlussregeln entwickelt, (...) die unter den vorliegenden aussagenlogischen Voraus‐setzungen in jedem formalen System beziehungsweise in jedem aussagen‐logisch vollständigen formalen System beziehungsweise in jedem aussagen‐logisch widerspruchsfreien formalen System gelten.RésuméDans un système formel sans types sans contradictions et qui pent représenter toutes les notions des mathkmatiques classiques, toutes les lois de la logiqrie propositionelle classique ne peuvent pas êvalables. C'est de là que s'ensuit le problème de discuter généralement les propriétés des systèmes formels en ce qu'elles concernent la logique des propositions. Sous certaines suppositions à I'Cgard des expressions propositionelles le « complet propositionel » et la « non‐contradiction propositionelle » se caractérisent par le tertium non datur ou plutôt par la rkgle d'inférence du ex falso quodlibet. On développe des méthodes de décision pour ces règles d'inférence syntactiques qui sont valables dans chaque système formel sous les suppositions données et pour ces régles d'inférence qui sont valables dans chaque système complet ou consistarit au point de vue de la logiqire des propositions.In a formal system without types which contains no contradictions and is able to represent all notions of classical mathematics, all the laws of classical propositional calculus cannot be valid. From this fact ensues the problem generally to explore the properties of formal systems from the point of view of the propositional calculus. Under certain assumptions conrerninq the propositional expressions the « propositional completeness » and the « propositional consistency » of a formal system is characterized through the tertium Ron datur, respectively through the inference rule of the ex falso quodlibet. There are decision procedures for the syntactical inference rules which in every formal system are valid under the given assumptions and for the syntactical inference rules of every formal system which is complete or consistent with respect to the propositional calculus. (shrink)

A system of logic is a formal theory equipped with laws and elementary syntactic and semantic definitions specifying ways of applying those laws in reasoning and revising assumptions out of which certain conclusions could be drawn from certain premises. Here, I shall discuss the universe of discourse to a variant of three-valued logic called Ezumezu and show that the traditional laws of thought are inadequate hence, I will discuss the three new supplementary laws of thought which were introduced (...) in chapter six. Having already formulated some of its syntactic and semantic rules in the previous chapters, I will show that in logic, Ezumezu system is comparable to systems developed by the likes of Lukasiewicz, Graham Priest, Stephen Read and other alternative logics. I will discuss two important theses namely, ontological and logical theses that will enable us to further understand the three pillars of Ezumezu logic namely, nwa-nsa, nwa-nju and nwa-izugbe already discussed in the preceding chapter. Finally, I will demonstrate the formal structure of Ezumezu logic using its two argument types called arumaristic and ohakaristic to show how conclusions could be drawn from premises. (shrink)

This paper presents the concept of paradeduction in order to justify that we can overlook contradictory information taking into account only what is consistent. Besides that, it uses paradeduction to show that there is a way to transform any logic, introduced as an axiomatic formal system, into a paraconsistent one. © 2019 Elsevier B.V., All rights reserved.

I offer a formal ontological theory where the basic building blocks of the world are timeless events. The composition of events results in processes. Spacetime emerges as the system of all events. Things are construed as bundles of processes. I maintain that such a view is in accord with General Relativity and offers interesting prospects for the foundations of classical and quantum gravity.

Integrated Information Theory (IIT) stands out as one of the most promising theories for dealing with the hard problem of consciousness. Founded on five axioms derived from phenomenology, IIT seeks for the physical substrate of consciousness that complies with such axioms according to the criterion of maximally integrated information (Φ). Eventually, IIT identifies phenomenal consciousness with maximal Φ or, what is the same thing, with the strongest cause-effect power in the system. Among the scholars critical of this theory, some (...) point to the so-called Intrinsicality Problem (IP), namely that consciousness cannot be an intrinsic property of the system because maximal Φ crucially depends on the possible existence of bigger values of Φ if the initial system is appropriately linked to or embedded in larger systems. Although proposals in the recent literature aim to solve the IP by going beyond reductionism and physicalism, none of them tackle the real issue, i.e., the insufficiency of IIT’s causal-metaphysical structure. This papers endeavors to provide a solution to the IP in IIT within a hylomorphist ontology that includes formal causation. Complementing IIT with formal causation provides the theory with a criterion of individuation that solves the IP and, by relaxing identification between maximal Φ and consciousness, it lends a more robust metaphysical structure. To wit, maximal Φ is a necessary but not sufficient condition for the existence of consciousness. (shrink)

Formal dialectic has its roots in ancient dialectic. We can trace this influence in Charles Hamblin’s book on fallacies, in which he introduced his first formal dialectical systems. Earlier, Paul Lorenzen proposed systems of dialogical logic, which were in fact formal dialectical systems avant la lettre, with roles similar to those of the Greek Questioner and Answerer. In order to make a comparison between ancient dialectic and contemporary formal dialectic, I shall formalize part of the Aristotelian (...) procedure for Academic debates. The resulting system will be compared (1) with Van Eemeren and Grootendorst’s system of rules of Critical Discussion (the pragma-dialectical discussion procedure), which must, however, first itself be reconstructed as a formal dialectical system, and (2) with a Hamblin-type system, and (3) a Lorenzen-type system. When drawing comparisons, it will become clear that there is a line to be drawn from Aristotle to formal dialectic and pragma-dialectics, extending to contemporary computational models of argument. (shrink)

One of the most interesting and entertaining philosophical discussions of the last few decades is the discussion between Daniel Dennett and John Searle on the existence of intrinsic intentionality. Dennett denies the existence of phenomena with intrinsic intentionality. Searle, however, is convinced that some mental phenomena exhibit intrinsic intentionality. According to me, this discussion has been obscured by some serious misunderstandings with regard to the concept ‘intrinsic intentionality’. For instance, most philosophers fail to realize that it is possible that the (...) intentionality of a phenomenon is partly intrinsic and partly observer relative. Moreover, many philosophers are mixing up the concepts ‘original intentionality’ and ‘intrinsic intentionality’. In fact, there is, in the philosophical literature, no strict and unambiguous definition of the concept ‘intrinsic intentionality’. In this article, I will try to remedy this. I will also try to give strict and unambiguous definitions of the concepts ‘observer relative intentionality’, ‘original intentionality’, and ‘derived intentionality’. These definitions will be used for an examination of the intentionality of formal mathematical systems. In conclusion, I will make a comparison between the (intrinsic) intentionality of formal mathematical systems on the one hand, and the (intrinsic) intentionality of human beings on the other hand. (shrink)