We show how to construct certain " $[Unrepresented Character]_{M,T}$ -type" interpreted languages, with each such language containing meaningfulness and truth predicates which apply to itself. These languages are comparable in expressive power to the $[Unrepresented Character]_{T}$ -type, truth-theoretic languages first considered by. Kripke, yet each of our $[Unrepresented Character]_{M,T}$ -type languages possesses the additional advantage that, within it, the meaninglessness of any given meaningless expression can itself be meaningfully expressed. One therefore has, for example, the object level truth (and meaningfulness) (...) of the claim that the strengthened Liar is meaningless. (shrink)

This work is a sequel to our [16]. It is shown how Theorem 4 of [16], dealing with the translatability of HA(Heyting's arithmetic) into negationless arithmetic NA, can be extended to the case of intuitionistic arithmetic in higher types.

A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) with k inferences has an interpolant whose circuit-size is at most k. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries: (1) Feasible (...) interpolation theorems for the following proof systems: (a) resolution (b) a subsystem of LK corresponding to the bounded arithmetic theory S 2 2 (α) (c) linear equational calculus (d) cutting planes. (2) New proofs of the exponential lower bounds (for new formulas) (a) for resolution ([15]) (b) for the cutting planes proof system with coefficients written in unary ([4]). (3) An alternative proof of the independence result of [43] concerning the provability of circuit-size lower bounds in the bounded arithmetic theory S 2 2 (α). In the other direction we show that a depth 2 subsystem of LK does not admit feasible monotone interpolation theorem (the so called Lyndon theorem), and that a feasible monotone interpolation theorem for the depth 1 subsystem of LK would yield new exponential lower bounds for resolution proofs of the weak pigeonhole principle. (shrink)

A proof of the (propositional) Craig interpolation theorem for cut-free sequent calculus yields that a sequent with a cut-free proof (or with a proof with cut-formulas of restricted form; in particular, with only analytic cuts) withkinferences has an interpolant whose circuit-size is at mostk. We give a new proof of the interpolation theorem based on a communication complexity approach which allows a similar estimate for a larger class of proofs. We derive from it several corollaries:(1)Feasible interpolation theorems for the following (...) proof systems:(a)resolution(b)a subsystem ofLKcorresponding to the bounded arithmetic theory(α)(c)linear equational calculus(d)cutting planes.(2)New proofs of the exponential lower bounds (for new formulas)(a)for resolution ([15])(b)for the cutting planes proof system with coefficients written in unary ([4]).(3)An alternative proof of the independence result of [43] concerning the provability of circuit-size lower bounds in the bounded arithmetic theory(α).In the other direction we show that a depth 2 subsystem ofLKdoes not admit feasible monotone interpolation theorem (the so called Lyndon theorem), and that a feasible monotone interpolation theorem for the depth 1 subsystem ofLKwould yield new exponential lower bounds for resolution proofs of the weak pigeonhole principle. (shrink)

A comprehensive and agreed-upon account of Husserl’s relation to Gottlob Frege does not yet exist. In this situation we encounter interpretations that allow systematic dogmas to reappear that should have long been vanquished—for instance, that the author of the Logical Investigations was not only decisively influenced by Frege, but also that he had already retracted his sharpest Frege-critique by 1891. The present essay contains a largely historical response to W. Künne’s new monograph on Frege that advocates such views. We will (...) concentrate on a small remark that turns out to reference a defining moment for any understanding of Husserl’s early philosophy. We shall argue that Husserl’s supposed self-criticism does not turn on the critique that he had earlier leveled at Frege’s Grundlagen der Arithmetik; rather, it has to do exclusively with his own earlier systematic positions on the grounding of arithmetic. In this context, an important particular of Husserl’s Philosophie der Arithmetik takes center stage: this book is a mosaic composed from old and new insights, a fact that becomes most evident in the two distinct concepts of “equivalence” that are founded there, which reflects Husserl’s transition from a theory of arithmetic based on the concept of number to one based on the parallelism between proper and symbolic (improper) presentations. This change involves a long historical development that goes back to a tradition marked by the work of Bolzano, Lotze, Brentano, and Stumpf, and it is closely tied to the problem of how to distinguish between the sense and the object of an act. Systematic neglect of the historical background of the Frege–Husserl relation has led to disputes over who owns the copyright to the sense/reference distinction, but it has obscured the very core of the original line of questioning. (shrink)

Eine vollständige Darstellung von Edmund Husserls Verhältnis zu Gottlob Frege steht noch aus, so dass es nicht verwundert, einige Missverständnisse, dieses Verhältnis betreffend, im Umlauf zu finden. Selbst scheinbar längst überwundene systematische Dogmen tauchen wieder auf, so z.B. die Auffassung, dass Husserl nicht nur entscheidend von Gottlob Frege beeinflusst wurde, sondern darüber hinaus auch seine schärfste Frege-Kritik 1891 zurückgenommen habe. Mein Beitrag enthält eine überwiegend historisch vorgehende Entgegnung auf solche fälschlich vertretenen Ansichten wie sie sich auch in dem neu erschienenen (...) und mit vielen dokumentarischen Belegen versehenen Frege-Kommentarbuch von W. Künne finden. Die wichtigsten Argumente, die in diesem Buch gegen Husserl gerichtet werden, stützen sich auf Stellen in Husserls Frühwerk, die zwar sehr aufschlussreich für die Beurteilung des philosophischen und menschlichen Habitus Husserls in den 1890er Jahre sind, nicht aber Künnes Thesen stützen oder gar beweisen können. Die als zurückgenommene Frege-Kritik verstandene Selbstkritik Husserls betrifft jedoch nach meinen Darlegungen gerade nicht die Kritik, die er an Freges Buch Grundlagen der Arithmetik geübt hatte, sondern seine eigene systematische Stellungnahme hinsichtlich der Begründung der Arithmetik. Ausgehend von dieser Einsicht werde ich auf ein wichtiges Spezifikum von Husserls Erstlingswerk (Philosophie der Arithmetik) aufmerksam machen, das voreiligen Interpretationen einen Riegel vorschiebt: Dieses Buch ist ein Mosaik aus Einsichten verschiedener Arbeits- und Denkperioden des Verfassers, die sich vor allem auch in dem zweifachen Begriff der Äquivalenz zeigen. Dies knüpft an einen langen geschichtlichen Entwicklungsprozess an, der in eine von Bolzano, Lotze, Brentano und Carl Stumpf geprägte Tradition zurückführt und das Problem der Unterscheidung zwischen Sinn und Gegenstand eines Aktes betrifft. (shrink)

This paper deals with substructural nuclear (image-based) logics and their algebraic and Kripke-style semantics. More precisely, we first introduce a class of substructural logics with connective N satisfying nucleus property, called here substructural nuclear logics, and its subclass, called here substructural nuclear image-based logics, where N further satisfies homomorphic image property. We then consider their algebraic semantics together with algebraic characterizations of those logics. Finally, we introduce operational Kripke-style semantics for those logics and provide two sorts of completeness results for (...) them, one of which is based on algebraic completeness for all the logics and the other of which is based on set-theoretic one for the nuclear image-based logics. (shrink)

This paper proposes a formal framework for the cognitive relation understood as an ordered pair with the cognitive subject and object of cognition as its members. The cognitive subject is represented as consisting of a language, conequence relation and a stock of accepted theories, and the object as a model of those theories. This language allows a simple formulation of the realism/anti-realism controversy. In particular, Tarski’s undefinability theorem gives a philosophical argument for realism in epistemology.

The book provides a historical and systematic exposition of the semantic theory of truth formulated by Alfred Tarski in the 1930s. This theory became famous very soon and inspired logicians and philosophers. It has two different, but interconnected aspects: formal-logical and philosophical. The book deals with both, but it is intended mostly as a philosophical monograph. It explains Tarski’s motivation and presents discussions about his ideas as well as points out various applications of the semantic theory of truth to philosophical (...) problems. (shrink)

This paper briefly discusses the relations between logic and metalogic in history. Metalogic is understood as a reflection on logic in its various senses, particularly sensu stricto (formal, mathematical) and sensu largo (formal logic plus semantic plus methodology of science). It is shown that metalogic in its contemporary understanding arose after mathematical logic had become a mature discipline. Special passage is devoted to metalogic in Poland. The last part of the paper discussed so-called logocentric predicament.

König, D. [1926. ‘Sur les correspondances multivoques des ensembles’, Fundamenta Mathematica, 8, 114–34] includes a result subsequently called König's Infinity Lemma. Konig, D. [1927. ‘Über eine Schlussweise aus dem Endlichen ins Unendliche’, Acta Litterarum ac Scientiarum, Szeged, 3, 121–30] includes a graph theoretic formulation: an infinite, locally finite and connected graph includes an infinite path. Contemporary applications of the infinity lemma in logic frequently refer to a consequence of the infinity lemma: an infinite, locally finite tree with a root has (...) a infinite branch. This tree lemma can be traced to [Beth, E. W. 1955. ‘Semantic entailment and formal derivability’, Mededelingen der Kon. Ned. Akad. v. Wet., new series 18, 13, 309–42]. It is argued that Beth independently discovered the tree lemma in the early 1950s and that it was later recognized among logicians that Beth's result was a consequence of the infinity lemma. The equivalence of these lemmas is an easy consequence of a well known result in graph theory: every connected, locally finite graph has among its partial subgraphs a spanning tree. (shrink)

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

We identify a class of paradoxes that is neither set-theoretical nor semantical, but that seems to depend on intensionality. In particular, these paradoxes arise out of plausible properties of propositional attitudes and their objects. We try to explain why logicians have neglected these paradoxes, and to show that, like the Russell Paradox and the direct discourse Liar Paradox, these intensional paradoxes are recalcitrant and challenge logical analysis. Indeed, when we take these paradoxes seriously, we may need to rethink the commonly (...) accepted methods for dealing with the logical paradoxes. (shrink)

In , Frank Ramsey separates paradoxes into two groups, now taken to be the logical and the semantical. But he also revises the logical system developed in Whitehead and Russellthe intensional paradoxess interest in these problems seriously, then the intensional paradoxes deserve more widespread attention than they have historically received.

This paper examines an example of learning with artifacts using the commonplace materials of string and knots. Emphases include research into learning processes as well as construction of objects to assist learning. The inquiry concerns the development of mathematical thinking, topology in particular. The research methodology combines participant observation and clinical interview within a constructionist framework. The study was set in a self-styled, self-constructed environment that consisted of knots and a social substrate encouraging lively exchanges of ideas about them. Comparisons (...) of certain knots helped to elicit conceptions of the fundamental topological relationships of neighborhood, continuity, and boundaries. The paper includes comments on the suitability of specific artifacts for specific kinds of thinking and learning, and emphasizes the importance for software design of considering different learning styles. (shrink)

Generally speaking, it appears correct to say that in a formulation of first order logic in which a large number of connectives are taken as primitive which allows us to have our cake and eat it too.

We introduce an extension of the propositional calculus to include abstracts of predicates and quantifiers, employing a single rule along with a novel comprehension schema and a principle of extensionality, which are substituted for the Bernays postulates for quantifiers and the comprehension schemata of ZF and other set theories. We prove that it is consistent in any finite Boolean subset lattice. We investigate the antinomies of Russell, Cantor, Burali-Forti, and others, and discuss the relationship of the system to other set-theoretic (...) systems ZF, NBG, and NF. We discuss two methods of axiomatizing higher order quantification and abstraction, and then very briefly discuss the application of one of these methods to areas of mathematics outside of logic. (shrink)

According to Quine, in any disagreement over basic logical laws the contesting parties must mean different things by the connectives or quantifiers implicated in those laws; when a deviant logician ‘tries to deny the doctrine he only changes the subject’. The standard semantics for intuitionism offers some confirmation for this thesis, for it represents an intuitionist as attaching quite different senses to the connectives than does a classical logician. All the same, I think Quine was wrong, even about the dispute (...) between classicists and intuitionists. I argue for this by presenting an account of consequence, and a cognate semantic theory for the language of the propositional calculus, which respects the meanings of the connectives as embodied in the familiar classical truth-tables, does not presuppose Bivalence, and with respect to which the rules of the intuitionist propositional calculus are sound and complete. Thus the disagreement between classicists and intuitionists, at least, need not stem from their attaching different senses to the connectives; one may deny the doctrine without changing the subject. The basic notion of my semantic theory is truth at a possibility, where a possibility is a way that things might be, but which differs from a possible world in that the way in question need not be fully specific or determinate. I compare my approach with a previous theory of truth at a possibility due to Lloyd Humberstone, and with a previous attempt to refute Quine’s thesis due to John McDowell. (shrink)

In Paradoxa Stoicorum, the Roman philosopher Cicero defends six important Stoic theses. Since these theses seem counterintuitive, and it is not likely that the average person would agree with them, they were generally called "paradoxes". According to the third paradox, (P3), (all) transgressions (wrong actions) are equal and (all) right actions are equal. According to one interpretation of this principle, which I will call (P3′), it means that if it is forbidden that A and it is forbidden that B, then (...) not-A is as good as not-B; and if it is permitted that A and it is permitted that B, then A is as good as B. In this paper, I show how it is possible to prove this thesis in dyadic deontic logic. I also try to defend (P3′) against some philosophical counterarguments. Furthermore, I address the claim that (P3′) is not a correct interpretation of Cicero’s third paradox and the assertion that it does not matter whether (P3′) is true or not. I argue that it does matter whether (P3′) is true or not, but acknowledge that (P3′) is perhaps a slightly different principle than Cicero’s thesis. The upshot is that (P3′) seems to be a plausible principle, and that at least one part of paradox III in Cicero’s Paradoxa Stoicorum appears to be defensible. (shrink)

In recent years, a significant amount of research has investigated the Vienna Circle’s ramifications. Otto Neurath has received much attention as one of the most prominent and energetic adherents, but less conspicuous philosophers now find themselves at the center of historical research. This article’s aim is to investigate Arne Naess’s connection to Logical Empiricism. Two crucial influences on Naess’s work are identified: Otto Neurath and the psychologist Egon Brunswik. This article’s most significant contributions are that, from the perspective of a (...) historian of philosophy of science, (a) Brunswik’s notion of “depth of intention” and his scientific methodological standards are reflected in Naess’s philosophy, (b) both Naess and Brunswik are adherents of Neurath’s physicalism, (c) Naess explicates Neurath’s notoriously vague concept of “congestions” in his “empirical semantics,” and (d) the latter is applied in Naess’s deep-ecology approach. (shrink)

We use a new version of the Definability Theorem of Beth in order to unify classical theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory.

I thank the editors for inviting me to contribute to this issue on critical views of logic. Kant invented the critical philosophy. He fashioned its doctrines (Understanding versus Reason, synthetic...

ABSTRACT This paper aims to show that intuitionistic Kripke models are a powerful tool for interpreting Kant’s ‘Critical Philosophy’. Part I reviews some old work of mine that applies these models to provide a reading of Kant’s second antinomy about the divisibility of matter and to answer several attacks on Kant’s antinomies. But it also points out three shortcomings of that original application. First, the reading fails to account for Kant’s second antinomy claim that matter is divisible ‘ad infinitum’ and (...) his first antinomy claim that empirical space extends only ‘ad indefinitum’. Secondly, in conformity with the ‘assertability’ heuristics for Kripke models, it attributes an assertability semantics to Kant. In fact, it attributes a pair of assertability semantics to Kant, but neither of these accords with modern assertabilism. And finally, one must wonder the propriety of using contemporary assertability and contemporary formal logic to save an eighteenth-century text. Part II goes historical to solve the problems about assertability. It outlines the Descartes–Leibniz dialectic about the infinite/indefinite distinction and demonstrates how each position reflects larger philosophical positions. It then demonstrates that Kant’s two versions of assertability and his version of the infinite/indefinite dichotomy emerge naturally from his attempts to resolve a tension in Leibniz’s philosophy. In light of this demonstration, Part III adapts the Kripke model interpretation so that it does reflect that dichotomy. It then refines the Kripke semantics in order to model some of Kant’s signature critical doctrines, and it shows how Kant’s critical version of the infinite/indefinite distinction differs from all those of his predecessors and from his own pre-critical version. It also addresses the question of using contemporary logical machinery to interpret Kant. Part IV turns the tables and uses what we have learned about Kant and modern semantics in order to address a pair of issues in the contemporary critical foundations of logic. (shrink)

We inquire into the question whether the Aristotelean or classical \emph{ideal} of science has been realised by the Model Revolution, initiated at Stanford University during the 1950ies and spread all around the world of philosophy of science --- \emph{salute} P.\ Suppes. The guiding principle of the Model Revolution is: \emph{a scientific theory is a set of structures in the domain of discourse of axiomatic set-theory}, characterised by a set-theoretical predicate. We expound some critical reflections on the Model Revolution; the conclusions (...) will be that the philosophical problem of what a \emph{scientific theory} is has \emph{not} been solved yet --- \emph{pace} P.\ Suppes. While reflecting critically on the Model Revolution, we also explore a proposal of how to complete the Revolution and briefly address the intertwined subject of \emph{scientific representation}, which has come to occupy center stage in philosophy of science over the past decade. (shrink)

A discussion is given of the research in the foundations of mathematics of Mario Pieri and how it compares with the works of Christian von Staudt, Giuseppe Peano...

The paper first formalizes the ramified type theory as (informally) described in the Principia Mathematica [32]. This formalization is close to the ideas of the Principia, but also meets contemporary requirements on formality and accuracy, and therefore is a new supply to the known literature on the Principia (like [25], [19], [6] and [7]).As an alternative, notions from the ramified type theory are expressed in a lambda calculus style. This situates the type system of Russell and Whitehead in a modern (...) setting. Both formalizations are inspired by current developments in research on type theory and typed lambda calculus; see [3]. (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)

A similarity relation is a reflexive and symmetric binary relation between objects. Similarity is relative: it depends on the set of properties of objects used in determining their similarity or dissimilarity. A multi-modal logical language for reasoning about relative similarities is presented. The modalities correspond semantically to the upper and lower approximations of a set of objects by similarity relations corresponding to all subsets of a given set of properties of objects. A complete deduction system for the language is presented.

In this article, we study the prehistory of type theory up to 1910 and its development between Russell and Whitehead's Principia Mathematica ([71], 1910-1912) and Church's simply typed λ-calculus of 1940. We first argue that the concept of types has always been present in mathematics, though nobody was incorporating them explicitly as such, before the end of the 19th century. Then we proceed by describing how the logical paradoxes entered the formal systems of Frege, Cantor and Peano concentrating on Frege's (...) Grundgesetze der Arithmetik for which Russell applied his famous paradox and this led him to introduce the first theory of types, the Ramified Type Theory (RTT). We present RTT formally using the modern notation for type theory and we discuss how Ramsey, Hilbert and Ackermann removed the orders from RTT leading to the simple theory of types STT. We present STT and Church's own simply typed λ-calculus (λ → C) and we finish by comparing RTT, STT and λ → C. (shrink)

An unconventional formalization of the canonical square of opposition in the notation of classical symbolic logic secures all but one of the canonical square’s grid of logical interrelations between four A-E-I-O categorical sentence types. The canonical square is first formalized in the functional calculus in Frege’s Begriffsschrift, from which it can be directly transcribed into the syntax of contemporary symbolic logic. Difficulties in received formalizations of the canonical square motivate translating I categoricals, ‘Some S is P’, into symbolic logical notation, (...) not conjunctively as \, but unconventionally instead in an ontically neutral conditional logical symbolization, as \. The virtues and drawbacks of the proposal are compared at length on twelve grounds with the explicit existence expansion of A and E categoricals as the default strategy for symbolizing the canonical square preserving all original logical interrelations. (shrink)

According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by freely proceeding choice sequences, i.e., sequences created by repeated free choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of choice sequences, this paper argues against Brouwer’s claim.

According to L.E.J. Brouwer, there is room for non-definable real numbers within the intuitionistic ontology of mental constructions. That room is allegedly provided by freely proceeding choice sequences, i.e., sequences created by repeated free choices of elements by a creating subject in a potentially infinite process. Through an analysis of the constitution of choice sequences, this paper argues against Brouwer’s claim.

Pour le philosophe intéressé aux structures et aux fondements du savoir théorétique, à la constitution d'une « méta-théorétique «, θεωρíα., qui, mieux que les « Wissenschaftslehre » fichtéenne ou husserlienne et par-delà les débris de la métaphysique, veut dans une intention nouvelle faire la synthèse du « théorétique », la logique mathématique se révèle un objet privilégié.

Charles L. Dodgson's reputation as a significant figure in nineteenth-century logic was firmly established when the philosopher and historian of philosophy William Warren Bartley, III published Dodgson's ?lost? book of logic, Part II of Symbolic Logic, in 1977. Bartley's commentary and annotations confirm that Dodgson was a superb technical innovator. In this paper, I closely examine Dodgson's methods and their evolution in the two parts of Symbolic Logic to clarify and justify Bartley's claims. Then, using more recent publications and unpublished (...) letters, I argue that Dodgson approached the elimination problem in class logic differently than his contemporaries, and in doing so, anticipated several important concepts and techniques in automated deductive reasoning. These materials also provide additional insight into his reasons for writing this book. (shrink)

(1995). In the shadow of giants: The work of mario pieri in the foundations of mathematics. History and Philosophy of Logic: Vol. 16, No. 1, pp. 107-119.

Throughout more than two millennia philosophers adhered massively to ideal standards of scientific rationality going back ultimately to Aristotle’s Analytica posteriora . These standards got progressively shaped by and adapted to new scientific needs and tendencies. Nevertheless, a core of conditions capturing the fundamentals of what a proper science should look like remained remarkably constant all along. Call this cluster of conditions the Classical Model of Science . In this paper we will do two things. First of all, we will (...) propose a general and systematized account of the Classical Model of Science. Secondly, we will offer an analysis of the philosophical significance of this model at different historical junctures by giving an overview of the connections it has had with a number of important topics. The latter include the analytic-synthetic distinction, the axiomatic method, the hierarchical order of sciences and the status of logic as a science. Our claim is that particularly fruitful insights are gained by seeing themes such as these against the background of the Classical Model of Science. In an appendix we deal with the historiographical background of this model by considering the systematizations of Aristotle’s theory of science offered by Heinrich Scholz, and in his footsteps by Evert W. Beth. (shrink)

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)