This is a slightly edited transcript of a lecture given by Per Martin‐Löf on 26 October 2022 at the Rolf Schock Symposium in Stockholm. In 2020, the Rolf Schock Prize in Logic and Philosophy was awarded to Dag Prawitz and Per Martin‐Löf, and the symposium was organised in their honour. The transcript was prepared by Ansten Klev and edited by the author.

This paper explores the sense in which correctness applies to belief-like imaginings. It begins by establishing that when we imagine, we ‘direct’ our imaginings at a certain imaginary world, taking the propositions we imagine to be assessed for truth in that world. It then examines the relation between belief-like imagining and positing truths in an imaginary world. Rejecting the claim that correctness, in the literal sense, is applicable to imaginings, it shows that the imaginer takes on, vis-à-vis the (...) imaginary world, the first-person perspective of a believer. Imaginings, it concludes, ‘mimic’ beliefs with respect to the property of being correct or incorrect by virtue of having true or false content. (shrink)

In what ways is comedy subversive? This vital new book critically considers the importance of comedy in challenging and redefining our relations to race and racism through the lens of political correctness. By viewing comedy as both a constitutive feature of social interaction and as a necessary requirement in the appraisal of what is often deemed to be ‘politically correct’, this book provides an innovative and multidisciplinary approach to the study of comedy and popular culture. In doing so, it (...) engages with the social and cultural tensions inherent to our understandings of political correctness, arguing that comedy can subversively redefine our approach to ‘PC Debates’, contestations surrounding free speech and the popular portrayal of political correctness in the media and society. Aided by the work of both Slavoj Žižek and Alenka Zupančič, this unique analysis adopts a psychoanalytic/philosophical framework to explore issues of race, racism and political correctness in the widely acclaimed BBC ‘mockumentary’, The Office (UK), as well as a variety of television comedies. Drawing from psychoanalysis, social psychology and philosophy, this book will be highly relevant for postgraduate students and academic researchers studying comedy, race/racism, multiculturalism, political correctness and television/film. (shrink)

According to the normativists, dispositionalist theories of meaning fail because meaning is normative, not descriptive. One way to understand this notion of normativity is in terms of semantic correctness conditions. Anti-normativists typically accept that meaning implies semantic correctness but deny that this in turn implies that meaning is normative. Jeffrey Kaplan has recently argued that while semantic correctness may not imply full-blown normativity, semantic correctness is not descriptive either. I contend that Kaplan's argument has two main (...) problems. First, his focus on dispositionalism leaves it open for other descriptive facts to provide the basis of semantic correctness conditions. Second, he fails to show that the problems of dispositionalism are connected to semantic correctness in a way that demonstrates problems with descriptive theories of meaning. (shrink)

This paper develops Richard Wollheim’s claim that the proper appreciation of a picture involves not only enjoying a seeing-in experience but also abiding by a standard of correctness. While scholars have so far focused on what fixes the standard, thereby discussing the alternative between intentions and causal mechanisms, the paper focuses on what the standard does, that is, establishing which kinds, individuals, features and standpoints are relevant to the understanding of pictures. It is argued that, while standards concerning kinds, (...) individuals and features can be relevant also to ordinary perception, standards concerning standpoints are specific to pictorial experience. Drawing on all this, the paper proposes an ontology of depiction according to which a picture is constituted by both its visual appearance and its standard of correctness. (shrink)

Saul Kripke’s paradoxical argument in Wittgenstein on Rules and Private Language (1982) has generated an extravagant number of responses. A major debate prompted by this book has focused on the plausibility and role of the supposed normative character of meaning; the argument itself is often taken to rely on the assumption that meaning is irreducibly normative. Following Boghossian (1989), the normativity of meaning has been understood as closely tied to the existence of semantic correctness conditions. After a brief introduction (...) to the background of the debate, this work will focus on whether the normativity of meaning may be better understood as stemming from a different type of correctness, namely linguistic correctness. Linguistic correctness differs from semantic correctness insofar as it is related to conventional, and not truth-functional, meaning. I will begin by clarifying some of the features of linguistic correctness. First, I will outline some reasons why the distinction between linguistic and semantic correctness should be maintained. Then, I will anticipate a possible criticism and argue that linguistic correctness does not belong to the domain of pragmatics, as it is relevant to our understanding of conventional meaning. Finally, I will try to show that linguistic “oughts” are constitutive of meaning. Having established these basic features of linguistic correctness, I will investigate whether the fact that it is constitutive of meaning can vindicate the idea that meaning is robustly, irreducibly normative. By applying arguments from the realm of moral philosophy – within which, too, there have been attempts to show that constitutive facts can give rise to categorical moral norms – I will argue that linguistic correctness cannot give rise to categorical semantic norms. Linguistic correctness may be, nevertheless, a useful tool for explaining some of our intuitions about meaning. (shrink)

In this paper, we contrast the different ways in which the representationalist and the attitudinalist in the theory of emotions account for the fact that emotions have evaluative correctness conditions. We argue that the attitudinalist has the resources to defend her view against recent attacks from the representationalist. To this end, we elaborate on the idea that emotional attitudes have a rich profile and explain how it supports the claim that these attitudes generate the wished-for evaluative correctness conditions. (...) Our argument rests on the idea that emotional attitudes manifest a sensitivity to evaluative evidence and that this sensitivity secures the kind of normativity we expect of the emotions. We bring our discussion to a close by assessing whether the psychological underpinnings of this sensitivity to evaluative evidence are such as to threaten the foundation of attitudinalism: the idea that emotions do not represent values. Given the available models of how we might access values prior to emotional experience, we conclude that the attitudinalist is still in the game. (shrink)

This paper outlines three broad ways one might think about logical correctness: the Realist approach, the One-Language approach and my own Neo-Carnapian view. Although the realist and one-language views have dominated the philosophy of logic in recent years, I argue against them, favouring of the Neo-Carnapian approach.

In this paper I discuss Pascal Engel’s recent work on doxastic correctness. I raise worries about two elements of his view—the role played in it by the distinction between i -correctness and e -correctness, and the construal of doxastic correctness as an ideal of reason. I propose an alternative approach.

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian (...) mathematical procedure texts – mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive. (shrink)

It is widely maintained that doxastic norms that govern how people should believe can be explained by the truism that belief is governed by the correctness norm: believing p is correct if and only if p. This approach fails because it confuses two kinds of correctness norm: (1) It is correct for S to believe p if and only p; and (2) believing p is correct qua belief if and only if p. Only can (2) be said to (...) be a truism about belief, but it cannot ground doxastic norms. (shrink)

This paper offers arguments against Francesco Ademollo’s redundancy thesis about the notion of the correctness of names in the Cratylus. The paper distinguishes between two versions of the redundancy thesis and provides arguments against each of them. In addition to supporting the rejection of both versions of the redundancy thesis, the arguments provide new interpretations of important issues inside and outside of the Cratylus. These issues include the philological evidence from the Classical period, the view of correctness expressed (...) by Plato’s Socrates in other dialogues, and Socrates’ initial discussion with Cratylus. (shrink)

Semantic information is usually supposed to satisfy the veridicality thesis: p qualifies as semantic information only if p is true. However, what it means for semantic information to be true is often left implicit, with correspondentist interpretations representing the most popular, default option. The article develops an alternative approach, namely a correctness theory of truth (CTT) for semantic information. This is meant as a contribution not only to the philosophy of information but also to the philosophical debate on the (...) nature of truth. After the introduction, in Sect. 2, semantic information is shown to be translatable into propositional semantic information (i). In Sect. 3, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in Sect. 4, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + A]. This completes the reduction of the truth of i to the correctness of A. In Sects. 5 and 6, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates Q by verifying and validating it (in the computer science’s sense of verification and validation ); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of proxy ) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of commutation ); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. Sect. 7 provides some further clarifications about CTT, in the light of semantic paradoxes. Section 8 draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. In the course of the article all technical expressions from computer science are explained. (shrink)

In the 1980s and early 1990s, the normativity of meaning was thought to be more-or-less 'incontestable.' But in the last 25 years, many philosophers of mind and language have contested it in several seemingly different ways. This, however, is somewhat illusory. There is an unappreciated commonality among most anti-normativist arguments, and this commonality, I argue, poses a problem for anti-normativism. The result, however, is not a wholesale rejection of anti-normativism. Rather, an insight from the anti-normativist position can be harnessed to (...) reveal an unappreciated position in the normativity of meaning debate. (shrink)

Credal reductivism is the view that outright belief is reducible to degrees of confidence or ‘credence’. The most popular versions of credal reductivism all have the consequence that if you are near-maximally confident that p in a low-stakes situation, then you outright believe p. This paper addresses a recent objection to this consequence—the Correctness Objection— introduced by Jeremy Fantl and Matthew McGrath and further developed by Jacob Ross and Mark Schroeder. The objection is that near-maximal confidence cannot entail outright (...) belief because when you believe a false proposition, you are wrong or incorrect, whereas you can be highly confident of a false proposition in a low-stakes situation without being incorrect. Both Fantl and McGrath’s and Ross and Schoeder’s versions of the Correctness Objection admit of multiple interpretations. But it is argued that even on the most charitable interpretations the objection fails. (shrink)

Argues that Daoism and dandyism, linked by likeminded philosophies of "carefree wandering," deconstruct the puritanism and political correctness sought by Confucianism, Victorianism, and contemporary neoliberal culture.

A theory of objective mathematical correctness is developed. The theory is consistent with both mathematical realism and mathematical anti-realism, and versions of realism and anti-realism are developed that dovetail with the theory of correctness. It is argued that these are the best versions of realism and anti-realism and that the theory of correctness behind them is true. Along the way, it is shown that, contrary to the traditional wisdom, the question of whether undecidable sentences like the continuum (...) hypothesis have objectively determinate truth values is independent of the question of whether mathematical realism is true. (shrink)

What is the relation between legal certainty and correctness? This question poses one of the perpetual problems of the theory and practice of law—and for this reason: The answer turns on the main question in legal philosophy, the question of the concept and the nature of law. Thus, in an initial step, I will briefly look at the concept and the nature of law. In a second step, I will attempt to explain what the concept and the nature of (...) law, thus understood, imply for the relation between legal certainty and correctness. Here three issues will be considered: first, the Radbruch formula as an answer to the problem of extreme injustice; second, the special case thesis, which claims that legal argumentation is a special case of general practical argumentation; and, third, the problem of the judicial development of the law. (shrink)

Debates about political correctness often proceed as if proponents see nothing to fear in erecting norms that inhibit expression on the one side, and opponents see nothing but misguided efforts to silence political enemies on the other.1 Both views are mistaken. Political correctness, as I argue, is an important attempt to advance the legitimate interests of certain groups in the public sphere. However, this type of norm comes with costs that mustn’t be neglected–sometimes in the form of conflict (...) with other values we hold dear, but often by creating an internal schism that threatens us with collective irrationality. Political correctness thus sets up dilemmas I wish to set out (but not, alas, resolve). The cliché is that political correctness tramples on rights to free-speech, as if the potential loss were merely expressive; the real issue is that in filtering public discourse, political correctness may defeat our own substantive aims. (shrink)

Logical anti-exceptionalism has been frequently defined on negative terms: it is a view according to which logic is not an exceptional discipline. More positively, anti-exceptionalism sees logic as similar to other empirical sciences. That leaves a lot of space to characterize what the view actually (positively) amounts to. We propose that one fruitful way to do that is through the so-called ‘logic as models’ view. One of the benefits of doing so concerns the crucial notion of a true or right (...) logic. By framing anti-exceptionalism in terms of models, we are in a better position to borrow from the philosophical literature on models to articulate views of how a model/theory relates to its target, accounting for what sense can be made of the very idea of a correct theory. We discuss two such accounts, and how anti-exceptionalism may be impacted by them. (shrink)

Ali Enayat had asked whether two halves of Disjunctive Correctness ([Formula: see text]) for the compositional truth predicate are conservative over Peano Arithmetic (PA). In this paper, we show that the principle “every true disjunction has a true disjunct” is equivalent to bounded induction for the compositional truth predicate and thus it is not conservative. On the other hand, the converse implication “any disjunction with a true disjunct is true” can be conservatively added to [Formula: see text]. The methods (...) introduced here allow us to give a direct nonconservativeness proof for [Formula: see text]. (shrink)

While in practice full correctness proofs are rarely forthcoming, computer scientists still employ tools that guarantee some form of correctness. One of these tools is a type checker for the language. Types fine-tune the grammatical structure of the language, and bring semantic intuitions to the grammatical party. The following is a quote from Pierce’s text on types in programming languages.

The article develops a correctness theory of truth (CTT) for semantic information. After the introduction, in section two, semantic information is shown to be translatable into propositional semantic information (i). In section three, i is polarised into a query (Q) and a result (R), qualified by a specific context, a level of abstraction and a purpose. This polarization is normalised in section four, where [Q + R] is transformed into a Boolean question and its relative yes/no answer [Q + (...) A]. This completes the reduction of the truth of i to the correctness of A. In sections five and six, it is argued that (1) A is the correct answer to Q if and only if (2) A correctly saturates (in a Fregean sense) Q by verifying and validating it (in the computer science’s sense of “verification” and “validation”); that (2) is the case if and only if (3) [Q + A] generates an adequate model (m) of the relevant system (s) identified by Q; that (3) is the case if and only if (4) m is a proxy of s (in the computer science’s sense of “proxy”) and (5) proximal access to m commutes with the distal access to s (in the category theory’s sense of “commutation”); and that (5) is the case if and only if (6) reading/writing (accessing, in the computer science’s technical sense of the term) m enables one to read/write (access) s. The last section draws a general conclusion about the nature of CTT as a theory for systems designers not just systems users. (shrink)

In Being and Time Heidegger seems to reject the correspondence theory of truth and replace it with an account of truth as assertions ‘uncovering’ entities. But ‘uncovering’ is not his definition of propositional truth, since he insists that false assertions also uncover. Instead, according to Heidegger, the being-uncovering of assertions is what makes the very idea of truth as correspondence intelligible. Moreover, the theoretically useless metaphor of correspondence is derivative of a more basic concept of propositional truth as correctness. (...) Heidegger’s argument, then, is that the being-uncovering of assertions is a necessary (but insufficient) condition for our regarding them as correct. Put otherwise, deeming assertions correct is possible only on the basis of the practice of making assertions, just as—à la Moore’s Paradox—judging a belief true is possible only on the basis of having it. The being-uncovering of beliefs and assertions is our commitment to them. (shrink)

In this paper I will present and evaluate Anandi Hattiangadi’s arguments for the conclusion that meaning is not intrinsically normative or prescriptive. I will argue that she misconstrues the way the thesis that meaning is normative is presented in the literature and that there is an important class of semantic rules that she fails to consider and rule out. According to Hattiangadi, defenders of meaning prescriptivity argue that speaking truthfully is a necessary condition for speaking meaningfully. I will maintain that (...) this is not how prescriptivity is construed by ‘normativists’ such as Kripke, Hacker and Baker, Brandom and Millar. I think that Hattiangadi misconstrues the prescriptivity thesis because she does not distinguish between the general notion of correctness of use and the specific notion of correctness of application. In other words, she does not distinguish between using a term correctly and applying it truthfully. In addition, I submit that there is an important class of semantic rules determining correct use that Hattiangadi does not consider. Following the later Wittgenstein, Hacker and Baker argue that accepted explanations of the meanings of words have the function of semantic rules. These rules are categorically prescriptive because following them is constitutive of being a speaker of a language. (shrink)

This article addresses the longstanding puzzle of what Cratylus’ silence means. It argues that Plato’s Cratylus goes silent to convey his position regarding the correctness of names, and it does this by demonstrating how Cratylus is silent in imitation of a literary trope for portraying the significance of a character’s silence. The philosophical payoff of this imitation is that, for Cratylus, correctness consists not in saying, but in showing.

We introduce a new correctness criterion for multiplicative non commutative proof nets which can be considered as the non- commutative counterpart to the Danos-Regnier criterion for proof nets of linear logic. The main intuition relies on the fact that any switching for a proof net can be naturally viewed as a series-parallel order variety on the conclusions of the proof net.

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These are the answers I gave to Brian Bix, Peter Koller, Ralf Posher, Torben Spaak, Timothy Endicott, and Jan Sieckmann at the end of a splendid conference day in 2018. The critique given to me concerned important aspects of three main themes in my work: the claim to correctness, human and constitutional rights, and the ideal dimension of law. In the last decades I have attempted to connect these themes systematically. The result is the idea of democratic constitutionalism as (...) an institutionalization of practical reason. (shrink)

Programming involves the construction of programs that meet their specifications. This draws in all the associated activities of programming such as testing, verification, and establishing correctness. And these are rule following activities.

Free speech and academic freedom are vitally important values. According to growing media reports, however, they are under attack and they are under attack in the exact place where they ought to be most protected: in our institutions of higher learning. This chapter explores two phenomena alleged to silence people on academic campuses: politically correct culture and microaggressions. These sorts of silencing involve a person deciding against speaking and deciding this because of the speaker’s beliefs about how the audience would (...) respond to her speaking. As this chapter will show, not all cases of choosing to remain silent are on a par; the issues are complex but each sort of these two sorts of academic silencing is a real possibility. (shrink)

This paper addresses the issue of political correctness from a Freirean point of view. An identification of the range of areas to which the label ‘political correctness’ has been applied reveals a confusingly multifaceted term. The author concentrates on the key characteristics of intolerance, conformity, the impeding of questioning and criticism, the stifling of debate, and the denial of alternatives. Thus defined, ‘political correctness’ has no place in Freirean education.

The simple mapping account of correctness reduces correctness to extensional agreement. While we have indicated various means of cutting down the number of solutions, restricting them in some way, there is something more substantial missing from our account. An assumption underlying the simple mapping account is that computation and programming are notions that can be fully characterized independently of any intentions.