Sense and Analysis − Studies in Frege Gilead Bar-Elli 1 Sense and Analysis − Studies in Frege Gilead Bar-Elli Contents: Introduction - i-v Synopsis - vi-ix Chapter 1: The Essentials of Frege's Logic - 1 The Formal Achievement of Begriffsschrift - 5; The Logical Notation of Begriffsschrift - 13; Some Later Developments - 16; Logic and Philosophy - 18 Chapter 2: Frege's Early Conception of Logic - 21 Reference and Inference - 22; Frege on the Deficiencies of Earlier Logical Systems - 25;Lingua Characterica and Calculus Ratiocinator - 30 Chapter 3: Sense and Objectivity in Frege's Logic - 34 Two Characterizations of Sense - 36; Sense and Justification - 40; Logical Objects - 42; Frege's Principle and Equivalence-Relations - 47; Digging into the Self-Evident - 50 Chapter 4: Identity in the Begriffsschrift - 55 The Main Point of the Identity Section (8) in Begriffsschrift and Its Relation to Ueber Sinn und Bedeutung - 56; The Identity Relation, and What Identity Statements Are About - 62; The Change in Ueber Sinn und Bedeutung - 67; The "Identity Puzzle", Cognitive Value and Conceptual Content - 68 Chapter 5: Logical Structure and Intentionality - Frege and Russell on Descriptions - 71 Descriptions and Terms Lacking Reference - 73; Meaning - 79; Logical Structure in Frege - 81; Definite Descriptions In Frege's Logic - 87; Logical Structure and Intentionality in Russell's Theory of Descriptions - 90; The Status of the About- relation - 91; The Object-directedness of Descriptive Propositions - 93; "Remote Intentionality" - 96; Intentionality and Logical Structure - 97 Chapter 6: The Ontological Status of Senses - 103 Senses are Real and Objective - 109; Senses are Not Objects - 111; Senses are Not Functions - 117; The Category of Sense − Some Characteristics - 118 Chapter 7: Analyticity and Justification in Frege - 122 Proof and Justification - 123; The Notions of Analytic and A priori Should Apply to Axioms - 125; Self-Evidence, Justification and Sense - 127; Justification and Objectivity - 130; Logic and Justification - 131; Analytic in the Narrow Sense and Analytic in the Wide Sense - 136; Analyticity: The Kantian Heritage, Frege and Carnap - 138; The Significance of Frege’s Notion of Analyticity – Truth - 141; The Significance of Frege’s Notion of Analyticity − Knowledge - 147; Chapter 8: Three Kantian Strands in Frege's View of Arithmetic - 150 Sense and the Justification of Axioms - 153; The Ability to Recognize Objects - 160; Beams and Seeds − Fruitful Analytic Definitions - 166; Chapter 9: Conceptual Analysis and Analytical Definition in Frege - 173 The Principle of Implications Enrichment - 176; The Principle of About - 178; The Context Principle - 182; The Core Idea of Sense - 184; The Justificatory Significance of Sense - 185; Analytical Definitions - 188 Chapter 10: A Fregean Look at Kripke's Modal Notion of Meaning - 199 Kripke’s Modal Notion of Meaning - 203; Kripke’s Challenge from a Fregean Perspective - 208; References and Abbreviations - 218 Introduction The book is based on articles that were published in philosophical journals and books over a span of many years. Except for small editorial corrections, I have tried to minimize changes in the text of the articles. Though the articles were independently written and are devoted to various topics in Frege's philosophy, the book is still informed by some basic strands, which make it, I hope, coherent. Chief among them is an interpretation I propose for various aspects and implications of Frege's notion of sense (Sinn), which at some crucial points is different from current common ones. Frege's notion of sense and the distinction between sense and reference are often presented minimally as his special, almost ad hoc proposal to explain the cognitive value of identity statements, roughly in the following way. Frege's famous "identity puzzle" asks how an identity like "The morning star is the evening star" can be of cognitive value, since, if true, it says the same as the trivial "The morning star is the morning star". His answer is that in the first case the two sides of the identity have different senses (while their references are the same). Somewhat more charitably, and with a better and deeper understanding, his notion of sense is regarded as a general distinctive aspect of his theory of meaning. Roughly, meaning, on that view, has two "dimensions", one is reference (Bedeutung), which is what statements and thoughts are about and what determines their truth and falsity; the other is sense (Sinn), which concerns a mode of presentation of the reference, or how it is conceived, as this is expressed by terms referring to it. This evidently is a substantial, wide and deep philosophical theory that in fact started modern theories of meaning. But even this falls short of realizing the full significance of the notion of sense in logic, ontology, epistemology, philosophy of mind and other philosophical concerns. Frege's logic has been generally adopted and forms the basis of standard modern logic, and the essentials of his theory of reference form the basis of elementary formal semantics. His notion of sense, however, is seldom taken seriously in modern logic, and some proposals to explicate it in formal terms − mainly in terms of possible worlds in modal logics − sin to essential elements of his notion. There are, of course, many allusions and remarks in the literature concerning the notion of sense in other areas of philosophy, but they are often casual, sometimes negative, and almost always made from a limited perspective of a specific issue (like e.g. propositional and de se attitudes). However, Frege's notion of sense is, I believe, one of the profoundest and most general i ideas in philosophy, whose significance touches almost any area or topic. Sure, Frege's notion of sense cannot be detached from his theory of reference; In fact I shall go further and argue that sense is supervenient on reference, and this is vital for understanding its role in a theory of intentionality (and makes Frege also the founder of "externalism"). But it has wider significance that concerns many other fundamental philosophical notions, on which Frege was much sparser in his explicit pronouncements. Evidently, on all these other philosophers have other views and other approaches, which may have their own merits, but his way, I believe, has often not been given its due weight. The prime significance of the notion of sense is in the philosophy of mind and a theory of intentionality. Thoughts, in Frege's theory, are senses (of complete sentences) whose constituents are senses (of sub-sentential terms). Whenever we think or entertain a thought about things in the world we do it by grasping senses. Hence, belief, knowledge and other so called propositional attitudes, which comprise many of our mental concepts, are concerned with senses. These would make the notion important enough. But other basic notions like truth, objectivity, justification, intentionality, proof, analysis, complexity, causality, explanation, etc. turn out to involve or even depend on the notion of sense. Some will be dealt with in subsequent chapters. Like with many other ideas of Frege's, his notion of sense, as a way in which something is conceived as this is expressed by the linguistic terms referring to it, has been absorbed in the philosophical world and influenced it to such an extent that it is often hardly noticed. Some examples will be discussed in the following chapters. To give one more example, which I don't discuss in this book, I would mention the prevalent use of "under description" idioms (like "event under description"), made popular in wide circles since the 60s of the last century by Morgenbesser, Davidson, Kim and others. Putting aside some unclarities and problems in the use of these expressions, it seems that this is a special case of the general Fregan doctrine of conceiving a reference "under a sense". I put special emphasis on Frege's characterizing sense as a mode of presentation or of being given or of conceiving a reference, expressed by linguistic phrases referring to it (I call it the "core idea" of sense). Genuine senses are thus supervenient on their references. Regarding the use of indexicals and demonstratives (like "I", "here", "now", "this", etc) Frege remarks that elements of the contexts are also parts of the senses concerned, which enhances the above supervenience on reference and the externalistic ii predilections. I present this as distinct from other characterizations, like e.g. Dummett's influential "route to the reference" idea. This, I believe, has a slim basis in Frege, and a common explication of it as a condition whose sole satisfier is the reference seems flatly wrong in suggesting a predicative construal of the relationship of sense to reference, to which Frege explicitly opposed. Consequently I play down the alleged role of sense in the use of terms lacking reference and in sentences that are neither true nor false. These, evidently, need explanation, but focusing on these (as unfortunately is quite current in many interpretations) is not only unfair to Frege's main lines of thought, and conflicts with many of his pronouncements, but also distracts from its main significance, and misleads as to its ontological character, its epistemic nature, its explanatory and justificatory role and its crucial significance in a theory of intentionality and the capacity of thoughts to be about things in the world. Some alternatives (including perhaps Dummett's) are also philosophically problematic and make the relationship between sense and "its" reference (when it has one) quite mysterious. Many of these problems don't arise, or are satisfactorily met, when the core idea of sense, as mentioned above and elaborated in the book, is properly understood. On my interpretation of the notion of sense it is the basis of Frege's positions on, and contributions to many perennial philosophical problems in ontology, epistemology, logic and the philosophy of language.