Papers by Ahti Pietarinen
Logic in Question, Studies in Universal Logic, 2022
In the common use of logic diagrams, the positive term is conveniently located inside the circle ... more In the common use of logic diagrams, the positive term is conveniently located inside the circle while its negative counterpart is left outside. This practice, already found in Euler's original scheme, leads to trouble when one wishes to express the non-existence of the outer region or to tackle logic problems involving negative terms. In this chapter, we discuss various techniques introduced by Euler's followers to overcome this difficulty: some logicians modified the data of the problem at hand, others amended the diagrams, and another group changed the mode of representation. We also consider how modern diagrammatic systems represent negation.
Handbook of Abductive Cognition, 2022
This chapter canvasses some of the most pertinent notions that Peirce allied to his conception of... more This chapter canvasses some of the most pertinent notions that Peirce allied to his conception of abduction: divination, trustworthiness, hope, investigand, economy, uberty, seduction, instinct, insight, and imagination. While such notions may suggest Peirce sliding into psychologism about logic, Peirce's own texts show that we can give these concepts perfectly non-psychological, natural, and scientific glosses-namely those that integrate their logical, linguistic, cognitive, and semiotic meanings. Thus attempts to characterize abduction as the "heuristics" of the operation of one's psychology or cognitive architecture would leave the issue of the full nature and reach of abduction wanting.
Acta Baltica Historiae et Philosophiae Scientiarum, 2020
Controversy over Martin Heidegger's Nazi past has lasted for over fifty years. Possibly the most ... more Controversy over Martin Heidegger's Nazi past has lasted for over fifty years. Possibly the most direct light over the matter is now cast by the notes that Heidegger started to write in black-covered notebooks since autumn 1931. Closely kept from public scrutiny until 2014, three volumes of these Ponderings in densely written notebooks cover the fateful years of 1931-1941. All of the Ponderings are published in the Collected Works, which is mounting up to cover over one hundred volumes. In accordance with the philosopher's own wishes, Ponderings will be published chronologically out of sequence, as the final volumes of the series.
Signs of logic , 2006
ÖÐ × Ë ÒØ Ó Ë Ò Ö× È Ö (b. 1839), son of the mathematician Benjamin P., brought up in a circle of... more ÖÐ × Ë ÒØ Ó Ë Ò Ö× È Ö (b. 1839), son of the mathematician Benjamin P., brought up in a circle of physicists and naturalists, and specially educated as a chemist, derived his first introduction to philosophy from the K.d.R.V. [Immanuel Kant's Critique of Pure Reason, published in 1781] and other celebrated German works, and only later made acquaintance with English, Greek, and Scholastic philosophy. Accepting unreservedly Kant's opinion that the metaphysical conceptions are merely the logical conceptions differently Kant's table of functions of judgment as culpably superficial.
FCoLog Journal of Logic and its Applicationss (FLAP), 2016
Peirce's novel, post-1903 interrogative construal of abductive logic is studied in terms ... more Peirce's novel, post-1903 interrogative construal of abductive logic is studied in terms of a dynamic approach. The information flow in abduction is interpreted by a dynamic mechanism over ranges. An abductive logic is proposed that analyzes conjecture-making in scientific discovery. It explains how the updates on models representing the inquirers' information proceed when they are faced with new surprising facts. The formal semantics for this logic is given by neighborhood models. We apply our abductive logic to an analysis of some examples of scientific discovery. We thank the two anonymous reviewers of this journal for the abductive feedback that has contributed so much to the improvement of the present paper. We also thank the audience of the 15th Congress of Logic, Methodology and Philosophy of Science held in Helsinki, August 2015, in which a part of the present paper was presented in a special symposium on Pragmati(ci)st Philosophy of Science: Old and New organized by Chiara Ambrosio. * This work is supported by China National Fund of Humanities and Social Sciences (grant no. 14ZDB016).
Peirce on Perception and Reasoning, 2017
In Peirce studies and beyond, such as in the fields of the philosophy of logic and
mathematics, ... more In Peirce studies and beyond, such as in the fields of the philosophy of logic and
mathematics, mathematical practice and their histories, there have been two dominant
ideas in the mainstream and recent research on diagrammatic reasoning and
representation. The first is that diagrams, especially logical diagrams, are visual in
senses in which symbolic notations are not. The second idea is that logical diagrams are
iconic in senses in which symbolic notations are not. In this paper we submit both of
these claims under critical scrutiny. We use Peirce‘s system of Existential Graphs,
which is the mainstay of diagrammatic reasoning in both its historical and systematical
senses, as the testing ground. We show that neither of these claims is well founded.
FLAP, 2021
Assertive graphs (AGs) modify Peirce's Alpha part of Existential Graphs (EGs). They are u... more Assertive graphs (AGs) modify Peirce's Alpha part of Existential Graphs (EGs). They are used to reason about assertions without a need to resort to any ad hoc sign of assertion. The present paper presents an extension of propositional AGs to the Beta case by introducing two kinds of non-interdefinable lines. The absence of polarities in the theory of AGs necessitates Beta-AGs that resort to such two lines: standard lines that mean the presence of a certain method of asserting, and barbed lines that mean the presence of a general method of asserting. New rules of transformations for Beta-AGs are presented by which it is shown how to derive the theorems of quantificational intuitionistic logic. Generally, Beta-AGs offer a new non-classical system of quantification http://www.collegepublications.co.uk/downloads/ifcolog00044.pdf
Until recently, much of the literature in philosophy of notation tended to follow Leibniz in assu... more Until recently, much of the literature in philosophy of notation tended to follow Leibniz in assuming that we always or most often think in symbols. However, current debates have increasingly been driven by the recognition that any system of representation depends, to some extent, on iconicity, such that the purported line of demarcation is rather a continuum (Stjernfelt 2014). This slow but resolute turn toward iconic signs has begun to change how we see logic. With different emphases, linguists (
Diagrammatic Representation and Inference, 2021
Residuation has become an important concept in the study of algebraic structures and algebraic lo... more Residuation has become an important concept in the study of algebraic structures and algebraic logic. Relation algebras, for example, are residuated Boolean algebras and residuation is now recognized as a key feature of substructural logics. Early work on residuation can be traced back to studies in the logic of relations by De Morgan, Peirce and Schr¨oder. We know now that Peirce studied residuation enough to have listed equivalent forms that residuals may take and to have given a method for arriving at the different permutations. Here, we present for the first time a graphical treatment of residuation in Peirce’s Beta part of Existential Graphs (EGs). Residuation is captured by pairing the ordinary transformations of rules of EGs—in particular those concerning the cuts—with simple topological deformations of lines of identity. We demonstrate the effectiveness and elegance of the graphical presentation with several examples. While there might have been speculation as to whether Peirce recognized the importance of residuation in his later work, or whether residuation in fact appears in his work on EGs, we can now put the matter to rest. We cite passages where Peirce emphasizes the importance of residuation and give examples of graphs Peirce drew of residuals. We conclude that EGs are an effective means of enlightening this concept.
Logica Universalis, 2019
Published originally as "Loogisen kielentutkimuksen näköaloja", Ajatus 19, (1956), pp. 81-96, the... more Published originally as "Loogisen kielentutkimuksen näköaloja", Ajatus 19, (1956), pp. 81-96, the following piece by Jaakko Hintikka is the first essay he published in his mother tongue of Finnish. It is seen to provide both a state-of-the-art review of current topics emerging in the philosophy of language in the mid-1950, as well as outlines of Hintikka's own evaluation of major theses of that era, in particular those of Quine's and Wittgenstein's concerning language use. Hintikka evaluates contributions that the logical study of language use can make to the solving of philosophical questions. Published in 1956 in Ajatus: The Yearbook of the Philosophical Society of Finland, Hintikka's essay served to introduce these topical issues to the Finnish-speaking audience soon after the original works had appeared in print. It also puts the theses into the perspectives of Hintikka's own fledgling logical philosophy. One can see the germs of game-theoretical semantics is his comments on Wittgenstein's notion of a language-game, and his remarks on general habits of action anticipate the importance of strategic rules in Hintikka's mature, inquiry-led and 'action-first' epistemology. This is manifest in Hintikka's characteristic approach to the methodology of philosophy of science and mathematics as an attempt to understand the nature of scientific and mathematical practices and operations through the logical analysis of their central concepts. Topics indicated below thus became the hallmarks of Hintikka's next sixty years of work, which saw the development of a range of logical methods by which language and its use can be studied, and in particular in such a way that progress can be made in solving problems of genuinely philosophical nature that one encounters across various fields of science. This piece was very briefly summarized in English in 1963 by Arto Salomaa (The Journal of Symbolic Logic 28(2), 1963, p. 165), and it is translated from the original Finnish by Jukka Nikulainen and Ahti-Veikko Pietarinen.
Topoi, 2017
Clinical equipoise (CE) has been proposed as an ethical principle relating uncertainty and moral ... more Clinical equipoise (CE) has been proposed as an ethical principle relating uncertainty and moral leeway in clinical research. Although CE has traditionally been indicated as a necessary condition for a morally justified introduction of a new RCT, questions related to the interpretation of this principle remain woefully open. Recent proposals to rehabilitate CE have divided the bioethical community on its ethical merits. This paper presents a new argument that brings out the epistemological difficulties we encounter in justifying CE as a principle to connect uncertainty and moral leeway in clinical ethics. The argument proposes, first, that the methodology of hypothetical retrospection (HR) is applicable to the RCT design and that it can accommodate uncertainty. As currently understood, however, HR should give up its reliance on the assumption of uncertainty transduction, because the latter assumes the principle of indifference, which does not accommodate uncertainty in the right way. The same principle is then seen to distort also the received interpretations of CE.
Journal of Philosophical Logic, 2018
We present a dynamic approach to Peirce's original construal of abductive logic as a logic of con... more We present a dynamic approach to Peirce's original construal of abductive logic as a logic of conjecture making, and provide a new decidable, contractionfree and cut-free proof system for the dynamic logic of abductive inferences with neighborhood semantics. Our formulation of the dynamic logic of abduction follows the philosophical and scientific track that led Peirce to his late, post-1903 characterization of abductive conclusions as investigands, namely invitations to investigate propositions conjectured at the level of pre-beliefs.
Studia Logica, 2016
Charles Peirce's alpha system Sα is reformulated into a deep inference system where the rules are... more Charles Peirce's alpha system Sα is reformulated into a deep inference system where the rules are given in terms of deep graphical structures and each rule has its symmetrical rule in the system. The proof analysis of Sα is given in terms of two embedding theorems: the system Sα and Brünnler's deep inference system for classical propositional logic can be embedded into each other; and the system Sα and Gentzen sequent calculus G3c * can be embedded into each other.
Under its most fair-spoken interpretation, a form of knowledge that is known as de re knowledge m... more Under its most fair-spoken interpretation, a form of knowledge that is known as de re knowledge means that an individual is picked in epistemic alternatives so that the identity of alternatives is not known to one who is making these choices. However, if individuals can be chosen outright, so that a sentence including some propositional attitudes such as knowledge or belief becomes true, these individuals have to be taken as being the same across the alternatives, experiencing only their local manifestations or aspects in some particular alternatives. It is this interpretation that amounts to de re or specific reading of knowledge, and its logic can be implemented in game-theoretic semantics, where the relevant games are of imperfect information, and the syntax is an intensionalised version of Hintikka-Sandu independence-friendly (IF) first-order logic. The interpretation cannot operate independently of the issues concerning the identification of objects in a semantic theory. The identification semantics is here taken to include a number of cognitively meaningful modes, with repercussions to so-called puzzles of beliefs.
The emergence of the Semantic Web suggests new perspectives to knowledge acquisition and represen... more The emergence of the Semantic Web suggests new perspectives to knowledge acquisition and representation, increasing the usefulness of possible-worlds semantics of epistemic logic (knowledge, belief and information). In this poster, it is argued that possible worlds are a foundation of the Semantic Web, because one can (i) address the problem of the property of omniscience in logical approaches to knowledge, (ii) develop question-answering systems, interrogation and the semantics of questions, and (iii) see what the role model theory plays is in the Semantic Web research.
In Kuva, edited by L. Haaparanta, T. Klemola, J. Kotkavirta & S. Pihlström, 2008
Logiikassa on tavanomaista rakentaa lauseita, esittää väitteitä ja suorittaa muodollista päättely... more Logiikassa on tavanomaista rakentaa lauseita, esittää väitteitä ja suorittaa muodollista päättelyä symbolisia merkkijärjestelmiä käyttäen. Valtaosa nykyaikaisen logiikan historiasta on ollut näiden symbolisten merkkijärjestelmien tutkimusta ja niiden sovelluksia. Symboliselle logiikalle vaihtoehdon tarjoavat ns. diagrammilogiikat. Niissä keskeistä on kuvallisuus (ikonisuus), merkkijärjestelmän ilmausten tietty rakenteellinen yhteys ilmausten edustamiin asioihin.
In book: Murtuvat merkitPublisher: GaudeamusEditors: E. Hannula and U. Oksanen, 2009
matisismiin liittyvää aineistoa hän tuotti 1890-luvulta alkaen. 2 (Apel 1995; Pietarinen & Snellm... more matisismiin liittyvää aineistoa hän tuotti 1890-luvulta alkaen. 2 (Apel 1995; Pietarinen & Snellman 2006). Yleisen tulkinnan ja merkityksen teorian, pragmatisismin, muotoilu fi losofi sta, loogista ja merkkiteoreettista käsitevälineistöä käyttäen oli hänen merkit-tävin saavutuksensa. Pragmatismilla ja pragmatisismilla tarkoitetaan molemmilla kantaa, jonka mukaan kielen ulkoiseen maailmaan liittyvät käytännöt vaikuttavat ilmauksen merkitykseen. Peirce oli erittäin systemaattinen ajattelija ja pyrki luomaan arkkitehtonisen fi losofi an, joka on osa tieteitten kokonaisjärjestelmää, mutta hän ei koskaan luonut yleisesitystä pragmatisismista ja sen erityispiirteistä. Tutkijat ovat pyrkineet rakentamaan kuvaa tästä myöhemmän kauden ajat-telusta Peircen jälkeensä jättämien käsikirjoitusten perusteella. 3 Peirce on kuvannut oman fi losofi sen menetelmänsä vastaavan laboratoriotutkijan menetelmiä. Sen mukaan ilmausten ja merk-kien merkitys perustuu niiden tuottamiin koetuloksiin, jos vain se...
Ajatus tieteestä ja tieteellisestä tutkimuksesta ihmiskunnan hyvinvoinnin ja teknologian takeena ... more Ajatus tieteestä ja tieteellisestä tutkimuksesta ihmiskunnan hyvinvoinnin ja teknologian takeena ei ole kovin iäkäs, eikä se myöskään ole universaali. Länsimaisen elämänpiirin ulkopuolella teknologiset innovaatiot eivät pitkään nojanneet tieteellisiin toiminta-ja ajatustapoihin, eivätkä ne sitä aina ole tehneet länsimaissakaan. Vielä tuoreempi on käsityksemme tieteen metodologiasta ja tieteellisen tutkimuksen perusluonteesta, tuskin paljoa yli satavuotias. Kuinka tieteelliset käsitykset viime kädessä muotoutuvat? Miten tieteellinen keksiminen ja innovointi on mahdollista? Tiede perustuu arvauksille. Tämä on perustavaa laatua oleva tosiseikka, joka herättää myös paljon kysymyksiä. Arvausten luonne ymmärretään helposti väärin. Tieteellinen arvaaminen ei tee tieteenteosta satunnaista spekulaatiota. Arvaaminen ei ole epärationaalista, impulsiivista tai tee tieteen tarkoituksesta samaa kuin kirjallisuus fiktiosta. Siitä ei seuraa skeptisismiä, ajatusta, että tiedolla tulee olla absoluutt...
What Is So Special about Logical Diagrams?
DESCRIPTION Working Paper, Diagrammatic Mind Research Group
We show that Neil Tennant's critical study of Jaakko Hintikka's book The Principles of Mathematic... more We show that Neil Tennant's critical study of Jaakko Hintikka's book The Principles of Mathematics Revisited is based on systematic misunderstandings and misrepresentations of the content of the book.
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Papers by Ahti Pietarinen
mathematics, mathematical practice and their histories, there have been two dominant
ideas in the mainstream and recent research on diagrammatic reasoning and
representation. The first is that diagrams, especially logical diagrams, are visual in
senses in which symbolic notations are not. The second idea is that logical diagrams are
iconic in senses in which symbolic notations are not. In this paper we submit both of
these claims under critical scrutiny. We use Peirce‘s system of Existential Graphs,
which is the mainstay of diagrammatic reasoning in both its historical and systematical
senses, as the testing ground. We show that neither of these claims is well founded.