Lukasiewicz's Many-valued Logic and Neoplatonic Scalar Modality

This paper examines the role of ‘situations’ in John Dewey's philosophy of logic. To do this properly it is necessary to contrast Dewey's conception of experience and mentality with views characteristic of modern epistemology. The primary difference is that, rather than treat experience as peripheral and or external to mental functions (reason, etc.), we should treat experience as a field in and as a part of which thinking takes place. Experience in this broad sense subsumes theory and fact, hypothesis and evidence, reason and observation, thought and perception. Logic in this view is a formal study of the generic features of all possible kinds of experience in this broad (thick, deep, wide, multifaceted) sense. The goal of this paper is to explain what Dewey thinks a situation is in the context of this view of experience, and to argue for the fundamental importance of that idea for logic and philosophy in general.     

Kant,Boole and Peirce's Early Metaphysics

Charles Peirce is often credited for being among the first, perhaps even the first, to develop a scientific metaphysics of indeterminism. After rejecting the received view that Peirce developed his views from Darwin and Maxwell, I argue that Peirce's view results from his synthesis of Immanuel Kant's critical philosophy and George Boole's contributions to formal logic. Specifically, I claim that Kant's conception of the laws of logic as the basis for his architectonic, when combined with Boole's view of probability, yields Peirce's metaphysics of probabilistic laws. Indeterminism provides, therefore, an excellent illustration of how Peirce attempted to use logic to clarify metaphysical problems.Since everyone must have conceptions of things in general, it is most important that they should be carefully constructed. I shall enter into no criticism of the different methods of metaphysical research, but shall merely say that in the opinions of several great thinkers, the only successful mode yet lighted upon is that of adopting our logic as our metaphysics. (W1: 490, 1866)²     

Husserl and the Algebra of Logic: Husserl’s 1896 Lectures

In his 1896 lecture course on logic–reportedly a blueprint for the Prolegomena to Pure Logic–Husserl develops an explicit account of logic as an independent and purely theoretical discipline. According to Husserl, such a theory is needed for the foundations of logic (in a more general sense) to avoid psychologism in logic. The present paper shows that Husserl’s conception of logic (in a strict sense) belongs to the algebra of logic tradition. Husserl’s conception is modeled after arithmetic, and respectively logical inferences are viewed as analogical to arithmetical calculation. The paper ends with an examination of Husserl’s involvement with the key characters of the algebra of logic tradition. It is concluded that Ernst Schr?der, but presumably also Hermann and Robert Grassmann influenced Husserl most in his turn away from psychologism.     

A Semantic Interpretation of Husserl's EpochÉ

This paper presents an interpretation of Husserl's phenomenological epoché or bracketing ( Einklammerung), which makes it possible to compare his position with philosophical programs developed within the framework of modern analytical philosophy. At the same time it asks in what sense Husserl's phenomenology is a form of idealism or exceeds the traditional discussion of idealism versus realism.     

Quasi-truth,paraconsistency, and the foundations of science

In order to develop an account of scientific rationality, two problems need to be addressed: (i) how to make sense of episodes of theory change in science where the lack of a cumulative development is found, and (ii) how to accommodate cases of scientific change where lack of consistency is involved. In this paper, we sketch a model of scientific rationality that accommodates both problems. We first provide a framework within which it is possible to make sense of scientific revolutions, but which still preserves some (partial) relations between old and new theories. The existence of these relations help to explain why the break between different theories is never too radical as to make it impossible for one to interpret the process in perfectly rational terms. We then defend the view that if scientific theories are taken to be quasi-true, and if the underlying logic is paraconsistent, it’s perfectly rational for scientists and mathematicians to entertain inconsistent theories without triviality. As a result, as opposed to what is demanded by traditional approaches to rationality, it’s not irrational to entertain inconsistent theories. Finally, we conclude the paper by arguing that the view advanced here provides a new way of thinking about the foundations of science. In particular, it extends in important respects both coherentist and foundationalist approaches to knowledge, without the troubles that plague traditional views of scientific rationality.     

Quantum logic as a dynamic logic

We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear “no”. Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth’s proposal of applying Tarski’s semantical methods to the analysis of physical theories, with an empirical–experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational- realistic tradition of Jauch and Piron, i.e. as an investigation of “the logic of yes–no experiments” (or “questions”). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the “non-classicality” of quantum behavior than any perspective based on static Propositional Logic.     

Human knowledge and the infinite progress of reasoning

The purpose of this paper is to explain how infinitism—the view that reasons are endless and non-repeating—solves the epistemic regress problem and to defend that solution against some objections. The first step is to explain what the epistemic regress problem is and, equally important, what it is not. Second, I will discuss the foundationalist and coherentist responses to the regress problem and offer some reasons for thinking that neither response can solve the problem, no matter how they are tweaked. Then, I want to present the infinitist solution to the problem and defend it against some of the well known objections to it.     

Critical thinking in North America: A new theory of knowledge,learning, and literacy

The pace of change in the world is accelerating, yet educational institutions have not kept pace. Indeed, schools have historically been the most static of social institutions, uncritically passing down from generation to generation outmoded didactic, lecture-and-drill-based, models of instruction. Predictable results follow. Students, on the whole, do not learn how to work by, or think for, themselves. They do not learn how to gather, analyze, synthesize and assess information. They do not learn how to analyze the diverse logic of the questions and problems they face and hence how to adjust their thinking to those problems. They do not learn how to enter sympathetically into the thinking of others, nor how to deal rationally with conflicting points of view. They do not learn to become critical readers, writers, speakers and listeners. They do not learn how to use their native languages clearly, precisely, or persuasively. They do not, therefore, become literate, in the proper sense of the word. Neither do they gain much in the way of genuine knowledge since, for the most part, they could not explain the basis for what they believe. They would be hard pressed to explain, for example, which of their beliefs were based on rational assent and which on simple conformity to what they have been told. They have little sense as to how they might critically analyze their own experience, or identify national or group bias in their own thinking. They are much more apt to learn on the basis of irrational than rational modes of thought. They lack the traits of mind of a genuinely educated person: intellectual humility, courage, integrity, perseverance, and faith in reason.Happily, there is a movement in education today striving to address these problems in a global way, with strategies and materials for the modification of instruction at all levels of education. At its foundation is an emerging new theory of knowledge, learning, and literacy, one which recognizes the centrality of independent critical thinking to all substantial learning, one which recognizes that higher-order, multilogical thinking is as important to childhood as to adult learning, and as important to foundational learning in monological as in multilogical disciplines. This educational reform movement is not proposing an educational miracle cure, for its leading proponents recognize that many social and historical forces must come together before the ideals of the critical thinking movement will become a full academic reality. Schools do not exist in a social vacuum. To the extent that the broader society is uncritical so, on the whole, will be society's schools. Nevertheless, the social conditions necessary for fundamental changes in schooling are increasingly apparent. The pressure for fundamental change is growing. Whether and to what extent these needed basic changes will be delayed or side-tracked, thus requiring new periodic resurgences of this movement, with new, more elaborate articulations of its ideals, goals, and methods — only time will tell.     

Kovesi and the Formal and Material Elements of Concepts

In his seminal work Moral Notions, Julius Kovesi presents a novel account of concept formation. At the heart of this account is a distinction between what he terms the material element and the formal element of concepts. This paper elucidates his distinction in detail and contrasts it with other distinctions such as form-matter, universal-particular, genus-difference, necessary-sufficient, and open texture-closed texture. We situate Kovesi’s distinction within his general philosophical method, outlining his views on concept formation in general and explain how his theory of concept formation is applied in moral philosophy.     

Psychological laws and non-monotonic logic

In this essay I enter into a recently published debate between Stephen Schiffer and Jerry Fodor concerning whether adequate sense can be made of the ceteris paribus conditions in special science laws, much of their focus being on the case of putative psychological laws. Schiffer argues that adequate sense cannot be made of ceteris paribus clauses, while Fodor attempts to overcome Schiffer's arguments, in defense of special science laws. More recently, Peter Mott has attempted to show that Fodor's response to Schiffer fails, and furthermore that further study shows that the logical framework in which Schiffer and Fodor address their issue is susceptible to inconsistency.In this essay I argue that adequate sense can be made of ceteris paribus conditions. Against Mott, I argue that recent work in the model theory of non-monotonic logic indicates how his problem involving logical inconsistencies can be overcome. Against Schiffer, I argue that the claims that he makes against ceteris paribus clauses would lead to a fatal skepticism concerning indefinitely many of the claims we make about the world (and indeed that his claims would be destructive of the view of the special sciences that Schiffer himself presents in his paper), and that the semantical considerations from non-monotonic logic that I present provide a suitable framework for dealing with his complaints. Thus I come out on the whole on Fodor's side of this debate, although for my own reasons, as I argue against much of Fodor's own argumentation.     

Holism, Strawberries and Hairdryers

The paper "Does Epistemological Holism lead to Meaning – Holism" (Cozzo, 2002) touches one of the main problems of a molecularist theory of meaning: how to restrict the class of inferences connected with a word, in order to define the sense of the word. I will discuss the starting point of this approach, mainly the pre-theoretical criterion against meaning holism: meaning holism, following a well-known argument by Dummett, reduces communication to a mystery. However there is a strong background assumption of this argument: communication is sharing the same meanings. Accepting this assumption without acknowledging it makes the entire proposal more problematic than it appears at first sight. In what follows I will try to clarify the possibility of a different reaction to meaning holism, putting forward some distinctions which come to light when the above stated assumption is made explicit. Then, some other comments will follow on the difficulty of avoiding extreme meaning holism, even within Cozzo's elegant attempt to implement a molecularist vision; in the end, his notion of the sense of a word will appear to be difficult to define, if these holistic aspects of language take the space they deserve even in his theory. I conclude with two remarks regarding two relevant requirements for a theory of meaning (conservativeness and harmony). This revised version was published online in June 2006 with corrections to the Cover Date.     

Two Challenges to the Requirement of Substantive General Covariance

It is generally acknowledged that the requirement that the laws of a spacetime theory be covariant under a general coordinate transformation is a restriction on the form but not the content of the theory. The prevalent view in the physics community holds that the substantive version of general covariance – exhibited, for example, by Einstein’s general theory of relativity – consists in the requirement that diffeomorphism invariance is a gauge symmetry of the theory. This conception of general covariance is explained and confronted by two challenges. One challenge claims, in effect, that substantive general covariance is not deserving of the name since, just as it is possible to rewrite any spacetime so that it satisfies formal general covariance, so it is also possible to rewrite the theory so that it satisfies the proffered version of substantive general covariance. The other challenge claims that the proffered version of substantive general covariance is not strong enough to guarantee the intended meaning of general covariance. Both challenges are discussed in terms of concrete examples. It is argued that both challenges fail but, at the same time, that they help to clarify what is at stake on the seemingly never ending dispute over the nature and status of general covariance.     

人类非逻辑思维辨析

按照皮亚杰的观点,成人的思维发展已达到“形式运算”的阶段,能够依据形式逻辑规则进行抽象的合乎逻辑的判断和推理。从此以后,根据逻辑的标准判断人类的推理是否是理性的就自然而然被接受了。然而最近的一些研究发现,人类在现实生活中并不完全遵照形式逻辑的规则来思维,在许多时候都表现出非逻辑的一面,似乎有另一种大家公认的“心理逻辑”。但是,非逻辑并不意味着非理性,从生态学的角度说,很多时候心理逻辑具有理性的一面。     

Frege on the generality of logical laws

Frege claims that the laws of logic are characterized by their “generality,” but it is hard to see how this could identify a special feature of those laws. I argue that we must understand this talk of generality in normative terms, but that what Frege says provides a normative demarcation of the logical laws only once we connect it with his thinking about truth and science. He means to be identifying the laws of logic as those that appear in every one of the scientific systems whose construction is the ultimate aim of science, and in which all truths have a place. Though an account of logic in terms of scientific systems might seem hopelessly antiquated, I argue that it is not: A basically Fregean account of the nature of logic still looks quite promising.     

Aristotle's Prior Analytics and Boole's Laws of Thought

Prior Analytics by the Greek philosopher Aristotle (384?–?322 BCE) and Laws of Thought by the English mathematician George Boole (1815?–?1864) are the two most important surviving original logical works from before the advent of modern logic. This article has a single goal: to compare Aristotle's system with the system that Boole constructed over twenty-two centuries later intending to extend and perfect what Aristotle had started. This comparison merits an article itself. Accordingly, this article does not discuss many other historically and philosophically important aspects of Boole's book, e.g. his confused attempt to apply differential calculus to logic, his misguided effort to make his system of ‘class logic’ serve as a kind of ‘truth-functional logic’, his now almost forgotten foray into probability theory, or his blindness to the fact that a truth-functional combination of equations that follows from a given truth-functional combination of equations need not follow truth-functionally. One of the main conclusions is that Boole's contribution widened logic and changed its nature to such an extent that he fully deserves to share with Aristotle the status of being a founding figure in logic. By setting forth in clear and systematic fashion the basic methods for establishing validity and for establishing invalidity, Aristotle became the founder of logic as formal epistemology. By making the first unmistakable steps toward opening logic to the study of ‘laws of thought’—tautologies and laws such as excluded middle and non-contradiction—Boole became the founder of logic as formal ontology.

… using mathematical methods … has led to more knowledge about logic in one century than had been obtained from the death of Aristotle up to … when Boole's masterpiece was published.     

The Economic Sphere

Herman Dooyeweerd (1985) argued that among the modalities making up the fabric of reality a specifically economic one is to be found. The aim of the present paper is to discuss the texture of such a modality and how it both differentiates and intertwines with others. For an updated brief, albeit cogent and analytically lucid presentation of the Law Framework ontology, see Clouser (2009). Dooyeweerd’s view entails that the proper object of economics is irreducible to that of other disciplines, but a non-reductionist view of the object of economics presupposes that the nuclear meaning of that discipline has been clearly delimited: this is required in order to determine its nature and separate identity as a scientific discipline. By ‘the nuclear meaning of a discipline’ I understand a pre-theoretical delimitation of its field of research, such as that of the field of physics, characterized by the laws governing force and energy. Within one and the same field there may be many theories, theories competing to explain the same phenomena, or dealing with phenomena so different that it is nearly impossible to trace conceptual connections among them. This last situation calls for a unified-field theory. In the second section of this paper I will attempt to defend a rather commonly accepted definition of the field of economics that sees this discipline as a science of choice. In the third I will show how the analytical conception it involves can be naturally complemented with a classificatory one. According to a classificatory conception, the aggregated social-level phenomena, patterns and regularities economic theories usually deal with, are economic in that sense, even though they are not prima facie cases of individual behavior, or are unintended consequences of aggregated individual choices. In the fourth I will discuss the meaning of the most general, supra-arbitrary economic laws—the modal laws of economics. In the final section I will offer a non-reductionist view of economics that nevertheless takes into account its intertwining with other spheres.     

Fictions within fictions

This paper examines the logic of fictions within fictions. I argue that consistently nested consistent fictions must have certain formal characteristics. The most important is that they form a tree structure. Depending on one’s theory of fictional objects, additional constraints may apply regarding the appearance of a fictional object in two or more fictional universes. The background motivation for the paper is to use iterated fiction operators as a tool for making sense of iterated modal operators; I conclude by noting briefly where the results about nested fictions can, and where they cannot, be extended to nested possible worlds.     

Shoemaker on Phenomenal Content

Sydney Shoemaker has given a sophisticated theory of phenomenal content, motivated by the transparency of experience and by the possibility of spectrum inversion without illusion (1994, 2000, 2001, 2002). It centers on the idea that color experiences represent what he calls “appearance properties”. I consider the different sorts of appearance properties that Shoemaker has suggested might enter into phenomenal content – occurrent appearance properties, dispositional appearance properties, and higher-order dispositional appearance properties – and argue that none of them are plausibly represented by color experiences. I argue that Shoemaker's theory faces a dilemma – either it makes misperception too difficult, or it does not truly accommodate veridical spectrum inversion. I then examine some alternative Russellian theories of phenomenal content that might be consistent with Shoemaker's motivations, including a different sort of proposal recently suggested by Shoemaker (forthcoming). I argue that these views are also lacking, for similar reasons as the appearance property view. Finally, I conclude that in order for a representationalist theory to properly accommodate spectrum inversion without illusion, phenomenal content must include an indexical element. Such a view requires the adoption of a broadly Fregean theory of phenomenal content, according to which sameness of phenomenal character does not entail sameness in extension. What phenomenally identical experiences have in common is not what they represent, but how they represent.     

Applied Logic without Psychologism

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.