Cognitive psychology and cognitive science are concerned with a domain of cognition that is much broader than the realm of judgement, belief, and inference. The idea of states with semantic content is extended far beyond the space of reasons and justification. Within this broad class of states we should, however, differentiate between the states distinctive of thinking persons — centrally, beliefs, desires, and intentions — and other states. The idea of consciousness does not furnish a principle of demarcation. But the (...) distinction between states whose content is conceptualized by the person whose states they are and states for which this is not so is more promising. This principle of demarcation contains the seeds of a problem for distributed connectionism. The article ends with some more general reflections about cognitive science. (shrink)

The specific characteristics of mathematical argumentation all depend on the centrality that writing has in the practice of mathematics, but blindness to this fact is near universal. What follows concerns just one of those characteristics, justification by proof. There is a prevalent view that long proofs pose a problem for the thesis that mathematical knowledge is justified by proof. I argue that there is no such problem: in fact, virtually all the justifications of mathematical knowledge are ‘long proofs’, but because (...) these real justifications are distributed in the written archive of mathematics, proofs remain surveyable, hence good. (shrink)

The outcomes of educational assessments undoubtedly have real implications for students, teachers, schools and education in the widest sense. Assessment results are, for example, used to award qualifications that determine future educational or vocational pathways of students. The results obtained by students in assessments are also used to gauge individual teacher quality, to hold schools to account for the standards achieved by their students, and to compare international education systems. Given the current high-stakes nature of educational assessment, it is imperative (...) that the measurement practices involved have stable philosophical foundations. However, this article casts doubt on the theoretical underpinnings of contemporary educational measurement models. Aspects of Wittgenstein’s later philosophy and Bohr’s philosophy of quantum theory are used to argue that a quantum theoretical rather than a Newtonian model is appropriate for educational measurement, and the associated implications for the concept of validity are elucidated. Whilst it is acknowledged that the transition to a quantum theoretical framework would not lead to the demise of educational assessment, it is argued that, where practical, current high-stakes assessments should be reformed to become as ‘low-stakes’ as possible. This article also undermines some of the pro high-stakes testing rhetoric that has a tendency to afflict education. (shrink)

I here present and defend what I call the Triviality Theory of Truth, to be understood in analogy with Matti Eklund’s Inconsistency Theory of Truth. A specific formulation of is defended and compared with alternatives found in the literature. A number of objections against the proposed notion of meaning-constitutivity are discussed and held inconclusive. The main focus, however, is on the problem, discussed at length by Gupta and Belnap, that speakers do not accept epistemically neutral conclusions of Curry derivations. I (...) first argue that the facts about speakers’ reactions to such Curry derivations do not constitute a problem for the Triviality Theory specifically. Rather, they follow from independent, uncontroversial facts. I then propose a solution which coheres with the theory as I understand it. Finally, I consider a normative reading of their objection and offer a response. (shrink)

Karl Jaspers argued that academics must be prepared to accept, perhaps even to welcome, the fact that most students 'will learn next to nothing' from a university education. In this paper I shall argue that, while Jaspers' model is unpersuasive as an ideal and inaccurate as a description, there is an uncomfortable truth lurking behind his forthright but gloomy conclusion; viz., that university teaching pays little direct attention to the needs of the student in the wider world (i.e. to the (...) needs of the student qua employee or qua citizen or even qua rounded human being) and pays even less attention, or perhaps none at all, to the needs and expectations of third parties such as employers. In terms of the political context universities now find themselves in, this is an uncomfortable and embarrassing truth for faculty to admit, for it appears to epitomise a self-regarding and inward looking academy. Yet, despite this, perhaps it is a truth that academics should be prepared to accept, even to welcome. At least, in starting any serious discussion on the nature of a university education, it should be a truth we are prepared to admit. (shrink)

The paper provides an interpretation of Wittgenstein’s claim that a mathematical proof must be surveyable. It will be argued that this claim specifies a precondition for the applicability of the word ‘proof’. Accordingly, the latter is applicable to a proof-pattern only if we can come to agree by mere observation whether or not the pattern possesses the relevant structural features. The claim is problematic. It does not imply any questionable finitist doctrine. But it cannot be said to articulate a feature (...) of our actual usage of the word ‘proof’. The claim can be dissociated, however, from two tenable doctrines of Wittgenstein, namely that proofs can be used as paradigms for corresponding proof concepts and that a proof is not an experiment. (shrink)

Bringing the views of Grayling, Moyal-Sharrock and Stroll together, I argue that in On Certainty, Wittgenstein explores the possibility of a new kind of foundationalism. Distinguishing propositional language-games from non-propositional, actional certainty, Wittgenstein investigates a foundationalism sui generis . Although he does not forthrightly state, defend, or endorse what I am characterizing as a "new kind of foundationalism," we must bear in mind that On Certainty was a collection of first draft notes written at the end of Wittgenstein's life. The (...) work was unprogrammatic, sometimes cryptic. Yet, his exploration into areas of knowledge, certitude and doubt suggest an identifiable direction to his thoughts. (shrink)

My starting point for this paper is a problem in critical thinking pedagogy—the difficult of bringing students to a point where they are able, and motivated, critically to evaluate their own deeply held beliefs. I first interrogate the very idea of a deeply held belief, drawing upon Wittgenstein’s idea of a framework belief—a belief that forms part of a ‘scaffolding’ for our thoughts—or of a belief that functions as a hinge around which other beliefs pivot. I then examine the role (...) of deeply held beliefs, thus conceived, in our ways of being in the world, exploring the extent to which engagement with others whose deeply held beliefs differ from ours may be possible through imaginative ‘travel’. Finally, I reflect upon the extent to which these imaginative moments also offer up opportunities for critical reflection upon our own deeply held beliefs and, thus, the possibility of changing or adapting those beliefs. (shrink)

Although the expression “form of life” and its plural “forms of life” occur only five times in Philosophical Investigations, and generally few times in his works, it is commonly agreed that this is one of the most relevant issues in Wittgenstein’s later philosophy. Starting from the analysis of the contexts in which Wittgenstein makes use of this concept, the paper focuses on the different interpretations that have been given in secondary literature, and proposes a classification based on two axes of (...) debate: the monistic versus pluralistic interpretation, and the empirical versus transcendental interpretation. After placing some well-known readings in the resulting scheme, an attempt will be made to offer an evolutionary reading of Wittgenstein’s own ideas about forms of life. It will be argued that the empirical and plural view that seems characteristic of his writings in the Thirties, slowly appears to turn towards a monistic view, sometimes with transcendental tones, although within a pragmatic perspective. This turn remains nevertheless rooted in Wittgenstein’s general attitude towards philosophy intended as a conceptual inquiry with clarifying and therapeutic aims. (shrink)

Plusieurs auteurs se sont inspirés des thèses du deuxième Wittgenstein pour proposer une nouvelle approche en sciences sociales qui viserait la justification plutôt que l'explication de l'action. Sur la base d'une étude de trois types d'énoncés formulés grâce au langage de l'action (factuels, normatifs et attributifs d'états mentaux), cet article évalue les difficultés et possibilités d'une telle suggestion.

My main aim is to sketch a certain reading (‘genealogical’) of later Wittgenstein’s views on logical necessity. Along the way, I engage with the inferentialism currently debated in the literature on the epistemology of deductive logic.

The question of whether desert depends on institutions or institutions on desert continues to divide politicians and political theorists, particularly in disputes over the justification of the welfare state. Even though it is a significant question with direct relevance for issues of economic justice, little has been done so far to evaluate the various positions in dispute and to make explicit the concepts involved. In this paper, I first present the main senses in which the concepts of desert, dependence and (...) institution are used by different desert theorists and I argue that conflicting claims concerning desert's pre/institutional nature may turn out to be compatible and similar claims, inconsistent, when the senses of these concepts are made explicit. Secondly, I identify the senses of 'desert', 'dependence' and 'institution' which are most appropriate for the debate. Thirdly, I argue that, from the perspective of this conceptual framework, it is not possible to decide whether or not desert depends on institutions, unless the framework is supplemented by a more precise specification of the concept of institution. (shrink)

Christine Atkinson; Beginning to Learn, Journal of Philosophy of Education, Volume 16, Issue 1, 30 May 2006, Pages 69–76, https://doi.org/10.1111/j.1467-9752.19.

An attempt is made to show that Wittgenstein's later philosophy of logic is not the kind of conventionalism which is often ascribed to him. On the contrary, Wittgenstein gives expression to a “mixed” theory which is not only interesting but tends to resolve the perplexities usually associated with the question of the a priori character of logical truth. I try to show that Wittgenstein is better understood not as denying that there are such things as “logical rules” nor as denying (...) that the results of applying such rules are “logically necessary,” but as trying to understand what it is to appeal to a logical rule and what it means to say that the results of applying such a rule are “necessary.” He is not so much overthrowing standard accounts of logical necessity as discovering the limits of the concept. (shrink)

The goal of this paper is to connect Rota's discussion of the Husserlian notion of Fundierung with Rota's project of giving combinatorics a foundation in his 1964 paper ‘On the foundations of combinatorial theory I’. Section 2 gives the basic tenets of this seminal paper. Sections 3 and 4 spell out the connections made there between Rota's philosophical writings and his mathematical achievements. Section 5 shows how these two developments fit into Rota's analysis of the place of combinatorics in mathematics.

RésuméPaul Boghossian soutient contre Wittgenstein que le normativisme au sujet de la logique et des mathématiques est incompatible avec le fait de tenir les énoncés logiques et mathématiques pour vrais et que le normativisme entraîne une régression indue. Je soutiens, pour ma part, que le normativisme n'entraîne pas une telle régression, parce que les normes peuvent être implicites et que le normativisme peut bien être «factualiste» si l'on rejette ce que Rockney Jacobsen appelle le «cognitivisme sémantique». Je tiens en outre (...) que la position de Boghossian repose sur la façon trompeuse dont il découpe le terrain conceptuel. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models.Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)

Latest Sermon from the Church of Fundamentalist Naturalism by Pastor Hofstadter. Like his much more famous (or infamous for its relentless philosophical errors) work Godel, Escher, Bach, it has a superficial plausibility but if one understands that this is rampant scientism which mixes real scientific issues with philosophical ones (i.e., the only real issues are what language games we ought to play) then almost all its interest disappears. I provide a framework for analysis based in evolutionary psychology and the work (...) of Wittgenstein (since updated in my more recent writings). -/- Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019). (shrink)

In §8 of Remarks on the Foundations of Mathematics (RFM), Appendix 3 Wittgenstein imagines what conclusions would have to be drawn if the Gödel formula P or ¬P would be derivable in PM. In this case, he says, one has to conclude that the interpretation of P as “P is unprovable” must be given up. This “notorious paragraph” has heated up a debate on whether the point Wittgenstein has to make is one of “great philosophical interest” revealing “remarkable insight” in (...) Gödel’s proof, as Floyd and Putnam suggest (Floyd (2000), Floyd (2001)), or whether this remark reveals Wittgenstein’s misunderstanding of Gödel’s proof as Rodych and Steiner argued for recently (Rodych (1999, 2002, 2003), Steiner (2001)). In the following the arguments of both interpretations will be sketched and some deficiencies will be identified. Afterwards a detailed reconstruction of Wittgenstein’s argument will be offered. It will be seen that Wittgenstein’s argumentation is meant to be a rejection of Gödel’s proof but that it cannot satisfy this pretension. (shrink)

Some readers, even though well versed in philosophy, may be bewildered by Wittgenstein's posthumous book on the philosophy of mathematics and unable to find a dominant theme running through even a part of it; to list the main contents–headings would make them none the wiser. Although two main themes may in the end be discerned in it, they do not pervade the book after the usual manner of themes; one has rather the sense of wandering about the corridors of a (...) maze; and, to add to the reader's perplexity, the maze has no definite centre. This mode of presentation, leading one through a maze, whose “centre” is the discovery that there is no centre, in itself conveys some philosophical message. Can we possibly say what Wittgenstein was trying to do? To answer this, seeing that this work is largely in line with the rest of his philosophizing, I propose to bid the present book a long farewell, to take an excursion into the field of Wittgensteinian and related philosophy, and against this background to try to give some picture and assessment of the contents of the work. (shrink)

My aim in this paper is twofold: to establish that Kierkegaard's so‐called theory of the leap strongly anticipates a line of argument that is central to Wittgenstein's so‐called rule‐following considerations; and to begin to show how Kierkegaard's work has fruitful contributions of its own to make to on‐going discussions about rules and rule‐following. The paper focuses throughout on the question of how, if at all, human rule‐following can be distinguished from behaviour that is merely mechanical or instinctual. I identify a (...) central line of argument in Wittgenstein that problematizes this question by establishing the basis our ability to follow rules in our spontaneous responses. I argue that Kierkegaard not only strongly anticipates this line of argument but also offers a distinctive story about what, at bottom, makes the difference between human rule‐following and behaviour that is merely mechanical or instinctual. In a word, on Kierkegaard's story, what makes the difference is: anxiety. (shrink)

Here I defend dispositionalism about meaning and rule-following from Kripkenstein's infamous anti-dispositionalist arguments. The problems of finitude, error, and normativity are all addressed. The general lesson I draw is that Kripkenstein's arguments trade on an overly simplistic version of dispositionalism.

According to Barry Stroud, Wittgenstein thought that language is social only in this minimal way: we cannot make sense of the idea of someone having a language unless we can describe her as using signs in conformity with the linguistic practices of some community. Since a solitary person could meet this condition, Stroud concludes that, for Wittgenstein, solitary languages are possible. I argue that Wittgenstein in fact thought that language is social in a much more robust way. Solitary languages are (...) not possible because we cannot make sense of the idea of someone having a language unless we can think of her as actively participating in the linguistic practices that fix the standards governing the applications of her words. (shrink)

A set of hypotheses is formulated for a connectionist approach to cognitive modeling. These hypotheses are shown to be incompatible with the hypotheses underlying traditional cognitive models. The connectionist models considered are massively parallel numerical computational systems that are a kind of continuous dynamical system. The numerical variables in the system correspond semantically to fine-grained features below the level of the concepts consciously used to describe the task domain. The level of analysis is intermediate between those of symbolic cognitive models (...) and neural models. The explanations of behavior provided are like those traditional in the physical sciences, unlike the explanations provided by symbolic models. Higher-level analyses of these connectionist models reveal subtle relations to symbolic models. Parallel connectionist memory and linguistic processes are hypothesized to give rise to processes that are describable at a higher level as sequential rule application. At the lower level, computation has the character of massively parallel satisfaction of soft numerical constraints; at the higher level, this can lead to competence characterizable by hard rules. Performance will typically deviate from this competence since behavior is achieved not by interpreting hard rules but by satisfying soft constraints. The result is a picture in which traditional and connectionist theoretical constructs collaborate intimately to provide an understanding of cognition. (shrink)