Cesare Cozzo

In the first part of this paper I contend that Michael Dummett’s works contain a distinction between analytic and synthetic (logical) deductions. Dummett does not use Kant’s terminology. Nevertheless, based on general considerations about theories of meaning, Dummett shows how one can distinguish between deductions whose validity is recognised by merely grasping the concepts and deductions whose validity can be recognised only by “going beyond the concepts”, as Kant wrote. The latter are synthetic deductions, through which we can increase our knowledge. A special merit of Dummett’s distinction is its theoretical flexibility and generality. He does not propose a single clear-cut distinction between analytic and synthetic deductions; rather in his works we find an indication of how to draw a distinction once a theory of meaning is adopted. In the second part of the paper I consider possible developments within an inferentialist theory of meaning and draw some conclusions concerning the fallibility of deductions.

The fallibility of deduction is the thesis that a thoughtful speaker-reasoner can wrongly believe that an inference is deductively valid. The author presents an argument to the effect that the fallibility of deduction is incompatible with the widespread view that deduction is epistemically unfruitful (the conclusion is contained in the premises, and the transition from premises to conclusion never extends knowledge). If the fallibility of deduction is a fact, the argument presented is a refutation of the doctrine of the unfruitfulness of deduction. But its relevance goes further, because the argument reveals a connection between two different problems: a solution to the problem of fruitfulness (how can deductive inferences increase our knowledge?) is a starting point for a solution to the problem of fallibility (how can deductive inferences be wrong?). To solve the problem of fruitfulness, Michael Dummett proposed some general ideas concerning meaning and inference. Starting from these meaning-theoretical ideas, one can develop an explanation of the fallibility of deduction. The general explanatory strategy does not depend on the choice between a theory of meaning centered on truth, verification, inferential role, or on other key notions.

Despite the remarkable advances in behavioral and brain sciences over the last decades, the mind/body (brain) problem is still an open debate and one of the most intriguing questions for both cognitive neuroscience and philosophy of mind. Traditional approaches have conceived this problem in terms of a contrast between physicalist monism and Cartesian dualism. However, since the late sixties, the landscape of philosophical views on the problem has become more varied and complex. The Multiple Realization Thesis (MRT) claims that mental properties can be (or are) realized, and mental processes can be (or are) implemented by neural correlates of different kinds. Thus, MRT challenges the psychoneural type-identity theory and the corresponding reductionism. Many philosophers have acknowledged the a priori plausibility of MRT. However, the existence of empirical evidence in favor of intraspecific, human multiple realizations of mental processes and properties is still controversial. Here we illustrate some cases that provide empirical evidence in support of MRT. Recently, it has been proposed that foveal agnosic vision, like peripheral vision, can be restored by increasing object parts’ spacing (Strappini et al., 2017a; Crutch and Warrington, 2007). Agnosic fovea and normal periphery are both limited by crowding, that impairs object recognition, and provides the signature of visual integration. Here we define a psychological property of restored object identification and we cross-reference the data of visually-impaired patients with different etiologies. In particular, we compare the data of two stroke patients, two patients with posterior cortical atrophy (PCA), six cases of strabismic amblyopia, and one case with restored sight. We also compare these patients with unimpaired subjects tested in the periphery. We show that integration (i.e. restored recognition) seems to describe quite accurately the visual performance in all these cases. While the patients have different etiologies and different neural correlates, the unimpaired subjects have no neural damage. Thus similarity in the psychological property given the differences in the neural substrate can be interpreted in relation to MRT and provide evidence in its support. Finally, we will frame our contribution within the current debate concerning MRT providing new and compelling empirical evidence.

Professor Von Wright is a prominent analytical philosopher who has written about the very notion of analytical philosophy. Other analytical philosophers are present here and they have their ideas on this notion. As for me, I believe that it is not at all an obvious notion. Sometimes it seemed to me that analytical philosophy does not exist, or at least that there is no single common feature shared by all so-called analytical philosophers and only by them, though there are many family resemblances. Therefore I thought I might take the opportunity of this meeting in honour of Professor Von Wright and propose as one of our themes for discussion, precisely the question: “what is analytical philosophy?”. The natural start is Professor Von Wright’s description of analytical philosophy.

Alberto Coffa used the phrase "the Copernican turn in semantics" to denote a revolutionary transformation of philosophical views about the connection between the meanings of words and the acceptability of sentences and arguments containing those words. According to the new conception resulting from the Copernican turn, here called "the Copernican view", rules of use are constitutive of the meanings of words. This view has been linked with two doctrines: (A) the instances of meaning-constitutive rules are analytically and a priori true or valid; (B) to grasp a meaning is to accept its rules. The pros and cons of different versions of the Copernican view, ascribable to Wittgenstein, Carnap, Gentzen, Dummett, Prawitz, Boghossian and other authors, will be weighed. A new version will be proposed, which implies neither (A) nor (B).

This is an introduction to Michael Dummett’s philosophy. Unlike other books on Dummett, this work considers the historical development of his philosophical thought: 1) Dummett in Oxford in the Fifties; 2) the discovery of Frege and the context principle; 3) a critique of realism in 1959; 4) theories of meaning; 5) truth-conditional, realist theories of meaning; 6) justificationist theories of meaning; 7) philosophy of time; 8) philosophy, science and religion; 9) Chronology of life and work; 10) History of the reception of Dummett’s philosophy; 11) Bibliography.

The problem I address is: how are cogent inferences possible? In § 1 I distinguish three senses in which we say that one is “compelled” by an inference: automatic, seductive-rhetorical and epistemic compulsion. Cogency is epistemic compulsion: a cogent inference compels us to accept its conclusion, if we accept its premises and we aim at truth. In §§ 2–3 I argue that cogency is intelligible if we consider an inference as a compound linguistic act in which several component acts are related to one another by a commitment that the premises support the conclusion. Non-automatic inferences are primarily public acts in an intersubjective context. But cogency arises in special contexts described in § 4, epistemic contexts, where the participants care for truth, i.e. are intellectually virtuous. An inference is cogent in an epistemic context if it stands up to all the objections raised in the context. In § 5 I consider three different kinds of cogent inferences. In § 6 I argue that in all three cases cogency is fallible and propose a fallibilist variety of inferentialism. In § 7 I distinguish context of utterance and contexts of evaluation. Cogency is relative to epistemic contexts of evaluation. However, validity, i.e. stable cogency, is transcontextual.

PART I The first chapter contains some arguments in favour of four general requirements on a theory of meaning which Michael Dummett has formulated: connection between meaning and understanding, distinction between sense and force, compositionality, and manifestability. The second chapter contains a condensed account of the theory of meaning centered on bivalent truth-conditions, and a detailed analysis of Dummett's argument against such a theory and against classical logic. The third chapter is a description of Dummett's theory of meaning centered on the notion of direct verification, and of Prawitz's semantics which can be embedded in the latter theory of meaning so as to justify intuitionistic logic. The weakest points of Dummett's idea are two: 1) it is difficult to make verificationism compatible with the holistic character of justification; 2) logical revisionism may involve a too drastic disagreement between verificationism and linguistic practice. -/- PART II. The second part contains a presentation of a theory of meaning centered on the notion which I have called immediate argumental role. The fundamental idea of the theory is that the sense of a word is given by all the argumentation rules concerning the word. Chapters IV-VII make precise the basic idea by explaining the notion of "argumentation rule" and by defining the notion of "concerning", and other notions among which "immediate argumental role of a sentence" and "global argumental role". Chapters VIII-X deal with the main philosophical features of the theory: 1) the theory satisfies the four requirements considered in the first chapter; 2) despite its compositionality, the theory is compatible with epistemological holism; 3) the theory admits the possibility of meaningful paradoxical languages; 4) the theory distinguishes between the understandability of a language and its correctness in a given epistemic situation (understandability does not imply correctness); 5) the theory is pluralist with respect to the understandability of different logics and neutral with respect to their validity.

This study presents and develops in detail (a new version of) the argumental conception of meaning. The two basic principles of the argumental conception of meaning are: i) To know (implicitly) the sense of a word is to know (implicitly) all the argumentation rules concerning that word; ii) To know the sense of a sentence is to know the syntactic structure of that sentence and to know the senses of the words occurring in it. The sense of a sentence is called immediate argumental role of that sentence. According to the argumental conception of meaning a theory of meaning for a particular language yields a systematic specification of the understanding of every sentence of the language which consists in a specification of the immediate argumental role of the sentence. The immediate argumental role is a particular aspect of the use of a sentence in arguments. But it is not the whole use in arguments, nor is the whole use in arguments reducible to the immediate argumental role. That is why, by accepting the argumental conception of meaning, we can have epistemological holism without linguistic holism. The argumental conception distinguishes between the understanding and the correctness of a language. Such a distinction makes it possible to account for our understanding of paradoxical languages. Redundancy theory of truth, realistic conceptions of truth or epistemic conceptions of truth are all compatible with an argumental conception of sense. But here it is argued that an epistemic conception of truth is preferrable. Acceptance of the argumental conception of meaning and of an epistemic conception of truth leads to a rejection of the idea of analytic truth. The argumental conception is pluralistic with respect to the understandability of different logics, and neutral with respect to their correctness.

The author presents a theory of meaning centred upon the notion of "immediate argumental role", which distinguishes between understandability and correctness of a language. First, the theoretical and quasi-empirical criteria of adequacy and the relevant data for such a theory are described. Then the sense of a word is defined as given by a set of argumentation rules. The immediate argumental role of a sentence is determined by its syntactic structure and by the senses of the component words. The immediate argumental role of a sentence is distinguished from its global argumental role. Different conceptions of truth are compatible with the resulting theory of sense, but the author gives some reasons for preferring an epistemic conception of truth. The possibility of understandable and meaningful paradoxical languages and of many different understandable logics is a consequence of such a view.

Gilbert Harman has written: “Williamson‟s Knowledge and its Limits is the most important philosophical discussion of knowledge in many years. It sets the agenda for epistemology for the next decade and beyond” (Harman 2002, p. 417). Timothy Williamson‟s ground-breaking proposal is that knowing is “merely a state of mind”. In other words, for every proposition p “there is a state of mind being in which is necessary and sufficient for knowing p” (Williamson 2000, p. 21). When first advanced, Williamson‟s view ran contrary to the general trend. The “standard view” (ibidem) was that “believing is merely a state of mind, but..

The compulsion of proofs is an ancient idea, which plays an important role in Plato’s dialogues. The reader perhaps recalls Socrates’ question to the slave boy in the Meno: “If the side of a square A is 2 feet, and the corresponding area is 4, how long is the side of a square whose area is double, i.e. 8?”. The slave answers: “Obviously, Socrates, it will be twice the length” (cf. Me 82-85). A straightforward analogy: if the area is double, the side is double. Nevertheless, the answer is wrong. Socrates wants to lead the slave to the right conclusion. The boy should reach the truth through steps that are all “his own”, performed with full conviction. To this aim, Socrates addresses a series of short pressing questions to the slave boy. Simple questions provoke equally simple replies, though the boy is sometimes puzzled and surprised by the answers he feels compelled to give. In the first part of the exchange the boy is gradually forced to admit that a square B with double side (i.e. side of length 4) has an area which is not double, but four times as big, i. e. 16. In the second part the boy hazards the guess that the square with double area has a side of length 3, since 3 is between 2 and 4. But Socrates easily drives him to acknowledging that if the side is 3, the area of the resulting square C is 9, not 8. The boy can only exclaim: “By Zeus, Socrates, I do not know!”. In the third part, at Socrates’ prompting, the diagonal of the original square A is drawn within the second fourfold square B. Responding to Socrates’ questions, the boy is led to conclude that the square D whose side is the diagonal of A is precisely the required square: its area is 8.

The intuitionistic conception of truth defended by Dummett, Martin Löf and Prawitz, according to which the notion of proof is conceptually prior1 to the notion of truth, is a particular version of the epistemic conception of truth. The paradox of knowability (first published by Frederic Fitch in 1963) has been described by many authors2 as an argument which threatens the epistemic, and the intuitionistic, conception of truth. In order to establish whether this is really so, one has to understand what the epistemic conception of truth really is. So I shall start inpart I with a description of the matter at issue between theepistemic conception of truth and the opposite position, therealistic conception of truth. Inpart II I shall very briefly describe the paradox. Inpart III I shall try to answer the question which appears in the title of this paper: What can we learn from the paradox of knowability?. My conclusion will be that the paradox of knowability is not a refutation of the epistemic conception of truth, but helps us to better formulate (and understand) such a view.

The traditional opposition between mathematical proof and rhetorical argument is based on a non-contextual picture of proof, against which historical and theoretical objections have been raised. The author advocates a different opposition, between epistemic rhetoric and instrumental rhetoric. Instrumental rhetoric aims at persuasion without caring for truth. Epistemic rhetoric is a practice aimed at both persuasion and truth. Aiming at truth is a way of acting, which can be characterized in terms of epistemically virtuous behavioural traits. In this sense epistemic rhetoric aims at truth, even though it is contextual and addressed to a particular audience. Real life mathematical proofs are instances of epistemic rhetoric and contextual rigour. But it is right to contrast proofs with instrumentally rhetoric arguments.

How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy - the heuristic conception. This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word 'heuristic' points to Cellucci's favorite theme and the main difference between him and Quine: the emphasis on discovery and building a 'logic' for generating new knowledge. This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci's work, dealing with some of the most challenging questions in logic, science and philosophy.

Ideas on meaning, rules and mathematical proofs abound in Wittgenstein’s writings. The undeniable fact that they are present together, sometimes intertwined in the same passage of Philosophical Investigations or Remarks on the Foundations of Mathematics, does not show, however, that the connection between these ideas is necessary or inextricable. The possibility remains, and ought to be checked, that they can be plausibly and consistently separated. I am going to examine two views detectable in Wittgenstein’s works: one about proofs, the other about meaning and rules. The first is the denial of the objectivity of proof. The second is a conception of meaning stemming from the rule-following considerations. I shall argue that, though Wittgenstein seems to conjoin the two views, they can be, and should be, separated1.

“Identità” qui si intende nel senso già precisato da Aristotele di “identità numerica”, che si ha “quando i nomi sono parecchi, ma la cosa è una sola” e, non nel senso di “identità specifica”, che si ha invece “quando gli oggetti, pur essendo parecchi, non rivelano differenze quanto alla specie”.1 In questo articolo intendo fornire al lettore indicazioni introduttive (non certo esaustive) sul posto che la nozione di identità numerica occupa nella logica contemporanea e nell’area di riflessione filosofica del Novecento più strettamente legata alla logica, la filosofia analitica. Nella terza parte proporrò qualche spunto per un’indagine originale.

Is a rational dispute over the validity of a fundamental logical law possible? In his lecture ‘Logics and Metalogics’, Timothy Williamson criticizes Dummett’s approach to this problem and maintains that a semantic theory does not provide a way of settling disputes over the validity of fundamental logical laws. I argue that Dummett’s view is different from the view criticized by Williamson. Dummett does not think that a semantic theory alone can settle a dispute over the validity of a fundamental logical law. Such disputes, according to Dummett, should be settled by the theory of meaning. A semantic theory in the sense that is usual among logicians is a theory of logical consequence . A meaning theory is a theory of understanding .

In spite of some objections voiced by Cora Diamond, the author agrees with Michael Dummett, who detects in Wittgenstein’s Remarks on the Foundations of Mathematics a denial of the objectivity of proof: Wittgenstein identifies being-a-proof with being-treated-as-a-proof. The denial of the objectivity of proof is implausible. But it seems to be a consequence of the rule-following considerations. After examining interpretations of the rule-following considerations advanced by Saul Kripke, Crispin Wright and John McDowell, an argument is exhibited, which starts from Wright’s interpretation and leads to the denial of the objectivity of proof. It is shown, however, that the argument contains at least two problematic steps and should be rejected. The result is that one can consistently adopt the view that meaning is «plastic» or «open» which stems from the rule-following considerations) without renouncing the objectivity of proof.

The concept of “necessity of thought” plays a central role in Dag Prawitz’s essay “Logical Consequence from a Constructivist Point of View” (Prawitz 2005). The theme is later developed in various articles devoted to the notion of valid inference (Prawitz, 2009, forthcoming a, forthcoming b). In section 1 I explain how the notion of necessity of thought emerges from Prawitz’s analysis of logical consequence. I try to expound Prawitz’s views concerning the necessity of thought in sections 2, 3 and 4. In sections 5 and 6 I discuss some problems arising with regard to Prawitz’s views.

What is the role of a notion of truth in our form of life? What is it to possess a notion of truth? How different would we be, if we did not possess a notion of truth? Gulliver’s description of three peoples encountered during his fifth travel will help me to answer. One might say that the basic anti-realist tenet is that we should explain the notion of truth by connecting it with our practice of assertion. In this sense the outcome of my commentary of the fifth part of Gulliver’s Travels will amount to a non-reductive anti-realist conception of truth. It can be called a dialectical conception of truth because it focuses on a particular way of resolving disagreements: an epistemically virtuous practice of verbal exchange that cares for truth. The main thesis is that an implicit awareness of the epistemically virtuous practice is a necessary condition for being in full possession of the notion of truth. The commentary will also involve an argument against deflationism and a critique of some claims made by Huw Price

Chi ha l'abitudine di sfogliare le riviste filosofiche sa che "metafisica" non è più una parola che scotta. I maestri dell'inizio del secolo (gli empiristi logici sono l'esempio più tipico) identificarono la metafisica con il non-senso e usarono la parola come un marchio di infamia. Non mancavano precedenti nella storia della filosofia. Ma oggi gli allievi di quei maestri preferiscono rifarsi ad un uso diverso, meno fazioso, del termine per indicare con esso un'indagine filosofica, che non solo non deve essere trascurata, ma concerne i fondamenti di molte altre ricerche, ed è quindi per molti versi centrale.

In his book Perché ancora la filosofia Carlo Cellucci argues that truth does not play any role in (modern) science: truth is only a chimera that prevents us «from adequately understanding the character of knowledge» and therefore «must be disposed of». I summarize Cellucci’s evidence for his contention that truth is a chimera. I then raise four objections to Cellucci’s views on truth. My conclusion is that, Cellucci’s arguments notwithstanding, a notion of truth is necessary for the human activity of problem solving and therefore for an adequate understanding of the phenomenon of knowledge.