What Bar-On and Simmons call 'Conceptual Deflationism' is the thesis that truth is a 'thin' concept in the sense that it is not suited to play any explanatory role in our scientific theorizing. One obvious place it might play such a role is in semantics, so disquotationalists have been widely concerned to argued that 'compositional principles', such as -/- (C) A conjunction is true iff its conjuncts are true -/- are ultimately quite trivial and, more generally, that semantic theorists have (...) misconceived the relation between truth, meaning, and logic. This paper argues, to the contrary, that even such simple compositional principles as (C) have substantial content that cannot be captured by deflationist 'proofs' of them. The key thought is that (C) is supposed, among other things, to affirm the truth-functionality of conjunction and that disquotationalists cannot, ultimately, make sense of truth-functionality. -/- This paper is something of a companion to "The Logical Strength of Compositional Principles". (shrink)

a single life-span. Philosophers, then, do not see more or know more, and they do not see less or know less. They aim to see less detail and more of the abstract. Their details, if you like, are abstractions. Walking on God’s earth as a pedestrian, as a farmer working his fields or as a passer-by, one’s picture of one’s surroundings is every bit as intelligent as that of the pilot riding the sky. The views of the field are radically (...) different, however. One sees only a specific field and in all lively detail: the exact pattern of the land, or even the exact outline of a given leaf, grasshopper, grain of sand even. Acquaintance with minute detail is not without its price: details may stand in the way of conjuring the big picture. It may be difficult to compare whichever field one happens to be in with far off fields, with respect to their size or shape or any other quality. One may wish to inquire if far off fields were already planted, harvested, or even if they exist. A pedestrian may find it hard or even impossible to do so. The pedestrian view contains fine points that the pilot’s map never would, but it does not necessarily contain more information, for it lacks the general context. After all, there are only so many items that one can observe and account for at a single glance, a single map, a single book, a single life-span. (shrink)

SUMMARY1 The rational soul becomes the constant and dimensionless Euclidean point in all experience - defining the situations in which it finds itself, but itself undefined and undefinable in any situation. It is in nature but not of nature. Just as the dimensionless Euclidean point can occupy infinite positions on a line and yet remain unaltered, so the immortal, active intellect remains unaffected by the world in which it finds itself. It is not influenced by age, sense data, sickness or (...) death. It is the knower whose nature is pure knowing or reason. This is in great part the basic assumption that runs through the history of Aristotelean and modern symbolic logics24.The rational soul grasps identity, reasons consistently, and knows objectively for though it is in the world it is not of the world. Thus it is unnecessary and impossible to relate its truth to time or place or condition. As the source of understanding it need not be understood. It understands in that it knows. It is this which places the objective knower and observer outside of all systems of knowledge that it creates in philosophy, science and theology, and frees it from subjective interpretation. It is the absolute observer beyond self-observation.252 Language, values, and meanings reflect the absolute viewpoint of the dimensionless observer beyond the necessity of observation. The task of this observer is to know trie world just as the task of the animal and plant soul is motion and reproduction. The rational soul performs its task beyond nature as surely as animals and plants perform their tasks in nature. This is why it is possible to discuss the necessary evolution of living organisms in nature, but unnecessary to discuss the necessary or unnecessary nature of the evolution of this discussion. This is one of the reasons why determinism or predestination which seem so clearly applicable to nature, need not be applied to theories of determinism and predestination. These are principles grasped in reality beyond nature and totally inapplicable to the non-natural spirit that comprehends their essences. Thus self-reflexive questions about the questioner are as irrelevant as would be questions historically of “in what sense might the definition of dimensionless point itself be dimensioned or dimension-less?”26 Questions, on the other hand, that relate to the observed world are important for they can be truly answered (where questions as to the nature of the questioner cannot). In this view reality is not nature, but rather it is from reality that the objective observer, philosopher, scientist, and theologian understands and controls nature.3 Logic, the science of reason, is the science of all sciences. It reflects the pure and innate rational nature of the knowing intellect or soul. It is pure form beyond nature. Its realm is that of first principles or axioms. These too are in the world but not of it, as with Plato's eidos and Aristotle's universals. They are clear, true and self-evident. This explains the on going use of axiomatized revelations in studies in the natural and social sciences, the arts and the humanities. In symbolic logics, natural languages are in and of the world, but meta-languages are the constructs of pure intellectual activity and thus not natural. The abstract tends to become the more real, the less it can be found in nature. Rational souls, however, share a common reality that is as universal for Frege as it was for Aristotle.274 The occidental object tradition in general breaks out of the nature continuum by withdrawing into reality where the intellect knows and manipulates the world in philosophy, science, and theology from its position in and understanding of reality. Nature is a sub-set of reality and not vice versa. Axioms are the laws and determinants of nature and logic, but they are not nature.28 This means that at the basis of the occidental continuum of nature there is a qualitative and irreducible dichotomy of reality vs. nature. This has been most useful in the history of occidental science, but it produces a world view in which nature may lose the race with reality. SUMMARY IIIn the first portion of my paper, I discussed the implications of the Euclidean egg for philosophy and science as nature is understood and manipulated from reality. I shall now turn to what I see as the implications of the three-legged chicken view that the human intellect is in and of nature and that reality is a perspective in nature and is not simply the other of an irreducible qualitative dichotomy. Although there are an endless number of such implications that I could explore, the following, it seems to me are the most important:1 In the natural continuum there is no “dimensionless real” which can serve either as the locus of an external observer or a fixed position in nature. There is no perspective which is not an aspect of that upon which it is a perspective. The Chinese sage, for example, is one who sees himself/herself as one with or within natural process. This is expressed in a number of ways. Fung Yu-lan speaks of the difference between having no knowledge and having no-knowledge.34 Within such a continuum there can be no abstracting out of the absolute and unchanging. The nameless is the source of the named. First principles are the process itself and these principles are the alternation of opposites:“The Nameless is the origin of Heaven and Earth;The Named is the mother of all things.Therefore let there always be non-being so we may see their subtlety, And let there always be being so we may see their outcome. The two are the same.“352 An empty mind is not a blank mind. Where Aristotle viewed the mind as a blank tablet at birth to be filled by sense experience, Hsun Tzu speaks of its emptiness. It is the emptiness of the Tao itself:“The mind is constantly storing up things, and yet it is said to be empty. The mind is constantly marked by diversity, and yet it is said to be unified. The mind is constantly moving, and yet it is said to be still. Inevitably it will see things for itself. And although the objects it perceives may be many and diverse, if its acuity is of the highest level, it cannot become divided within itself.”36The nature in which and of which the mind is both perspective and aspect remains a totality. Being a totality, it is empty of itself just as any part of a whole, while a part of the whole, is empty of the whole. My ideas of myself are both of myself and empty of myself. This point can be illustrated with the simple example of knowing and speaking about two hands – one of which is mine, and the second of which belongs to someone else. 1 can objectify the second hand and fill my blank mind with information and observations about it, but I continue to remain outside of it –the arbiter in my statements of its nature and reality. However, in knowing my own hand, the hand known is also the knower and what I know represents a perspective upon an aspective of a totality of which “I–my–hand” are aspects. Being an aspect of the whole is being empty of the whole. If mind is in and of nature, any perspective on nature is an aspect of the whole. A blank mind is an unnatural mind outside of nature, filling up with impressions of nature. An empty mind is nature viewing nature as aspect and perspective. The occidental would be ashamed to reach old age and still have a blank mind. The Chinese sage would be ashamed to reach old age and still not recognize that the mind is empty.3 If mind is in nature and like nature, then language too reflects natural flow and change and process. It is one thing for me to talk about myself and another for me to talk about someone else. In the case of the latter, I may insist that objectively this other subject fits into this or that category and even administer tests to determine that it does do indeed so. But when I talk about myself, the speaker and the object of speech are one and the same. The terms I select do represent a dichotomy of sorts, but it is one of aspect and perspective and not subject and object. When I say “this is my hand” for example, the words create distinctions which are aspects of awareness but do not create an / that is or is not my hand. Language does not model or even represent reality as opposed to nature. It makes reality possible as something that nature says or thinks. Reality through language is an aspect of nature and thus a perspective upon itself as aspect. This is an important distinction that translators often miss.4 Logic in this natural continuum is concerned with distinctions in a very different sense. As a consequence of the unity of nature and mind, three kinds of distinction in experience are manifested: (a) Those distinctions which come into being as aspects of the changing world.The 10,000 things are in this sense aspects and not separate “identities” as some philosophers and scientists presuppose.37 (b) Those distinctions which come into being as aspects of the human mind. These are impressions of and thoughts about the infinite distinctions of which the restless mind is capable, (c) Those distinctions which come into being by way of the mind's use of symbols. These are the distinctions which permit us to stabilize and store our experiences, preserve the answers to our questions, and name the world into compartments and relationships.Implicit in these three assumptions which connect the distinguishing mind to the unity of a nature of'10,000‘ aspects, is an inferential process of aspect to perspective to knowledge to understanding to attitude to action/response. The reasoning mind synthesizes some aspect of experience in nature with a perspective upon this aspect. This synthesis, in turn, is an aspect of mind and the reasoning process proceeds from it to a perspective upon it which is knowledge and understanding. Knowledge and understanding in turn are aspects of thinking and the reasoning process proceeds from them to a perspective upon them which is an attitude. Attitude in turn is an aspect of thinking and the reasoning process proceeds from it to a perspective upon it which is reflected in the reasoning individual's actions and responses. This inferential process is a continuum which proceeds from aspects of experience to perspectives in thought to action and response. In this sequence an aspect is always connected by a perspective which becomes an aspect, until action/non-action, response occurs. This is as applicable to the details of life as it is to mastering life as a whole. When this inference process is incomplete many problems may result, ranging from action without understanding to the confusion of aspect and perspective with one another or to “obsession with distinctions.”38In practice this is a logic of paradox. The human being is aware that he or she is a living-dying aspect of nature, but an aspect which is also a perspective upon nature's aspects of living and dying. This paradox is the process around which a profound logic of aspect/perspective is developed by the sage. This view of logic within a continuum does not mean that there is no principle of identity, contradiction or excluded middle present – as some Chinese and European philosophers assume.These principles are also implicit in the knowing of my hand versus the knowing of the hand of another. However, the content, meaning, and application of these principles may vary just as when I say propriety, I mean propriety, and when the Chinese says li he means li but the context, meaning and application of the term may differ in each case.5 Aspect logic as it relates mind to nature in a cosmological totality is a series of syntheses in a cyclic continuum organizing thinking in phases. Each phase is an aspect/perspective synthesis which becomes an aspect of a further aspect/perspective synthesis. This progression might be described thusly: The synthesis of nature/human which is Tao (non-being) translates into the aspects of being (the 10,000 things), and as such is a synthesis of aspect and perspective. This synthesis of aspect and perspective translates into an aspect of ideas and as such is a synthesis of perception and conception. This synthesis of perception and conception translates into an aspect of knowledge, and as such is a synthesis of knowledge and understanding (understanding is a perspective upon knowledge) i.e., no-knowledge. This synthesis of knowledge and understanding translates into an aspect of purpose, and as such is a synthesis of purpose and action. The perspective here on action is aesthetic and/or moral. This synthesis of purpose and actions translates again into an aspect of nature and as such is a synthesis beyond individual aspects and perspective, i.e. Tao. Thus there is a cyclic dynamic in the system which remains open to further development.Tai Chen in his Inquiry Into Goodness connects this cycle of syntheses with wisdom and benevolence:Because there are mind and intelligence, the superior man knows that the perfection of the Way of Man depends completely upon nature. When he looks at the signs of the natural (Cheng), he knows the beginning of things; when he cherishes the virtue of supreme illumination, (Shen-ming), he knows the end of things. Proceeding from mind and intelligence to the attainment of the virtue of supreme intelligence, [the superior man] in his treatment of things in the world will cause the world to return to [the principles of] benevolence; and in his treatment of the capability inherent in things, he will cause the world to follow wisdom (Chih).39. (shrink)

In this note we reproduce the book reviews that De Morgan wrote on Boole's and Jevons's first logical works. The most notable property of these documents is the mere fact of their existence and the absence of any reference to them in the specialized literature.

One of the characteristic features of contemporary logic is that it incorporates the Frege‐Russell thesis according to which verbs for being are multiply ambiguous. This thesis was not accepted before the nineteenth century. In Aristotle existence could not serve alone as a predicate term. However, it could be a part of the force of the predicate term, depending on the context. For Kant existence could not even be a part of the force of the predicate term. Hence, after Kant, existence (...) was left homeless. It found a home in the algebra of logic in which the operators corresponding to universal and particular judgments were treated as duals, and universal judgments were taken to be relative to some universe of discourse. Because of the duality, existential quantifier expressions came to express existence. The orphaned notion of existence thus found a new home in the existential quantifier. (shrink)

By way of a close reading of Boole and Frege’s solutions to the same logical problem, we highlight an underappreciated aspect of Boole’s work—and of its difference with Frege’s better-known approach—which we believe sheds light on the concepts of ‘calculus’ and ‘mechanization’ and on their history. Boole has a clear notion of a logical problem; for him, the whole point of a logical calculus is to enable systematic and goal-directed solution methods for such problems. Frege’s Begriffsschrift, on the other hand, (...) is a visual tool to scrutinize concepts and inferences, and is a calculus only in the thin sense that every possible transition between sentences is fully and unambiguously specified in advance. While Frege’s outlook has dominated much of philosophical thinking about logical symbolism, we believe there is value—particularly in light of recent interest in the role of notations in mathematics and logic—in reviving Boole’s idea of an intrinsic link between, as he put it, a ‘calculus’ and a ‘directive method’ to solve problems. (shrink)

It is well known that classical logics are able to represent only some aspects of ordinary reasoning. In particular, by accepting the law of obversion, they remove the possibility of defining any but a propositional negation; certain natural uses of negation thus elude them. Logical theories do exist, however, that are exempt from such limitations. Among these theories are those of S. Leśniewski, which differ profoundly from classical formal systems. Unlike the latter, they do not have a determined list of (...) functors of syntactical-semantical categories. Due to formalized directives for definitions, the logics of Leśniewski are constructed progressively, making new theses and consequently functors of new syntactical-semantical categories accessible. In this article we use some of these theses-definitions to define a principle of appropriateness. With this principle it is possible to represent certain logical subtleties that are used quite naturally but are neglected due to the law of obversion. (shrink)

Modelling that exploits visual elements and information visualisation are important areas that have contributed immensely to understanding and the computerisation advancements in many domains and yet remain unexplored for the benefit of the law and legal practice. This paper investigates the challenge of modelling and expressing structures and processes in legislation and the law by using visual modelling and information visualisation (InfoVis) to assist accessibility of legal knowledge, practice and knowledge formalisation as a basis for legal AI. The paper uses (...) a subset of the well-defined Unified Modelling Language (UML) to visually express the structure and process of the legislation and the law to create visual flow diagrams called lawmaps, which form the basis of further formalisation. A lawmap development methodology is presented and evaluated by creating a set of lawmaps for the practice of conveyancing and the Landlords and Tenants Act 1954 of the United Kingdom. This paper is the first of a new breed of preliminary solutions capable of application across all aspects, from legislation to practice; and capable of accelerating development of legal AI. (shrink)

En este artículo recuperamos la lógica diagramática lineal de Leibniz para la silogística y descubrimos sus propiedades lógicas y computacionales a través de una aproximación formal en términos metalógicos, lo cual es algo que, hasta donde sabemos, aún falta por hacerse. Así, en esta contribución buscamos, respectivamente, dos metas, una histórica y una lógica: i) prestar más atención a los aspectos algorítmicos del sistema diagramático lineal de Leibniz para la silogística, de los cuales creemos que han sido desdeñados por un (...) prejuicio general en contra del razonamiento diagramático; y ii) probar propiedades metalógicas del sistema para argumentar que es un sistema lógico bona fide. (shrink)

This paper deals with the influence exerted by Boole's own work on differential equations on his creation of algebraic logic. The main traits of Boole's methodology of logic, and the particular algorithms which he used in his 1847 The mathematical analysis of logic, are first pointed out. An examination of the mathematical papers which Boole wrote before the publication of the mentioned logical treatise shows that both the methodology leading to the production of his logic and the algorithms used in (...) its development were repeatedly used by him in his earlier work in analysis. (shrink)

This paper studies the possible influences on Boole's logic of the writings related to the controversy over the quantification of the predicate between the philosopher William Hamilton and the mathematician Augustus De Morgan. As Boole himself testified in the introduction to his book The mathematical analysis of logic , this controversy was the external agent that stimulated him into writing up his earlier thoughts about a new conception of logic. But in addition to the external role that was played by (...) the controversy, it seems that other kinds of influences on Boole of Hamilton's and De Morgan's ideas about logic, which were made explicit in writings related to the controversy, can also be traced. (shrink)

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately (...) for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’. (shrink)

We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the (...) appearance of critical reviews by members of the Boolean school. (shrink)

The use of the symbol ∨for disjunction in formal logic is ubiquitous. Where did it come from? The paper details the evolution of the symbol ∨ in its historical and logical context. Some sources say that disjunction in its use as connecting propositions or formulas was introduced by Peano; others suggest that it originated as an abbreviation of the Latin word for “or,” vel. We show that the origin of the symbol ∨ for disjunction can be traced to Whitehead and (...) Russell’s pre-Principia work in formal logic. Because of Principia’s influence, its notation was widely adopted by philosophers working in logic (the logical empiricists in the 1920s and 1930s, especially Carnap and early Quine). Hilbert’s adoption of ∨ in his Grundzüge der theoretischen Logik guaranteed its widespread use by mathematical logicians. The origins of other logical symbols are also discussed. (shrink)

In this paper we give an example of intertranslatability between an ontology of individuals (nominalism), an ontology of properties (realism), and an ontology of facts (factualism). We demonstrate that these three ontologies are dual to each other, meaning that each ontology can be translated into, and recaptured from, each of the others. The aiin of the enterprise is to raise the possibility that, at least in some settings, there may be no need for considerations of ontological primacy. Whether the world (...) is made up of things, or properties, or facts, may be no more than a matter of how we look at it. (shrink)

Contemporary logicians continue to address problems associated with the existential import of categorical propositions. One notable problem concerns invalid instances of subalternation in the case of a universal proposition with an empty subject term. To remedy problems, logicians restrict first-order predicate logics to exclude such terms. Examining the historical origins of contemporary discussions reveals that logicians continue to make various category mistakes. We now believe that no proposition per se has existential import as commonly understood and thus it is unnecessary (...) to restrict first-order predicate logics to non-empty classes. After introducing the problem, we trace some nineteenth century treatments of the issue to locate a source of misconstruing propositional import in misconceptions of ‘implies’ and ‘affirms’ and name the process/product fallacy, along with the translation of categorical sentences using quantifiers and accommodating an empty class. Next we treat some metalogical matters to orient our discussion by which we provide a more precise nomenclature about ‘sentence’ and ‘proposition’ to correct previous misconceptions; here we uncover a common category mistake in respect of a proposition’s efficacy. The semantic distinction between agent and force is helpful in this connection. We conclude by showing that logicians have reinserted existence as a predicate, a position previously excised by Kant, and that the Frege-Russell ambiguity thesis applies only to relationships within a categorical sentence between grammatical predicate and subject. (shrink)

Quine’s philosophy comprises a bewildering set of views whose integrating principle is his "confirmed extensionalism". The paper offers a historical as well as an intellectual reconstruction of extensionalism. Traditional extensionalism (Boole) freed logic from Aristotelian essentialism that had inhibited the development of logic. Quine’s confirmed extensionalism is the acceptance, as a matter of course, of the validity of Frege’s criticism of [Boole’s] extensionalism. His confirmed extensionalism is a generalized version of the philosophy of science known as conventionalism. As such, it (...) places the advancement of science outside the province of science proper. It is, thus, at odds with Quine’s repeated expressions of alliance with the Popperian (hypothetico-deductive) model of science. (shrink)

In this paper, the foundations for setting up a knowledge industry are laid. Firstly, it is established that this industry constitutes the only way of making use of the huge amounts of knowledge produced as a result of the introduction of the Science-Technology binomial in postindustrial society. Then, the elements which will lead to such an industry are defined, that is, the resources and means. Under the ‘Means’ section, special emphasis is placed on the processes involved, in other words, inference (...) methods and commonsense reasoning. Finally, it is concluded that the establishment of this industry, calledmindfacturing because of the raw material that it processes and uses, is, more than possible, desirable, provided that the precautions outlined in the epilogue are taken. (shrink)

Hypotheticals, conditionals, and their connecting relation, implication, dramatically changed their meanings during the nineteenth and early part of the twentieth century. Modern logicians ordinarily do not distinguish between the terms hypothetical and conditional. Yet in the late nineteenth century their meanings were quite different, their ties to the implication relation either were unclear, or the implication relation was used exclusively as a logical operator. I will trace the development of implication as an inference operator from these earlier notions into the (...) first third of the twentieth century using as the starting point the ideas primarily of R. Whately and W. Hamilton before discussing the work of the transitional logicians, A. De Morgan and G. Boole on these topics. Then we discuss the relevant views of four prominent but relatively unknown nineteenth century British logicians, W.E. Johnson, J.N. Keynes, E.E.C. Jones, and H. MacColl, as well as those of the more influential logicians, W.S. Jevons and J. Venn, closing with a section on ‘implication as inference’ where we explore some key ideas of B. Russell and sketch the work of D. Hilbert, P. Hertz, and G. Gentzen who together are responsible for the development of the modern ideas related to the subjects of this paper. (shrink)

“Formal logic”, an expression created by Kant to characterize Aristotelian logic, has also been used as a name for modern logic, originated by Boole and Frege, which in many aspects differs radically from traditional logic. We shed light on this paradox by distinguishing in this paper five different meanings of the expression “formal logic”: (1) Formal reasoning according to the Aristotelian dichotomy of form and content, (2) Formal logic as a formal science by opposition to an empirical science, (3) Formal (...) systems in the sense of Hilbert, Curry and the formalist school, (4) Symbolic logic, a science using symbols, such as Venn diagrams, (5) Mathematical logic, a mathematical approach to reasoning. We argue that these five meanings are independent and that the meaning (5) is the one which better characterized modern logic, which should therefore not be called “formal logic”. (shrink)

Computational complexity is a discipline of computer science and mathematics which classifies computational problems depending on their inherent difficulty, i.e. categorizes algorithms according to their performance, and relates these classes to each other. P problems are a class of computational problems that can be solved in polynomial time using a deterministic Turing machine while solutions to NP problems can be verified in polynomial time, but we still do not know whether they can be solved in polynomial time as well. A (...) solution for the so-called NP-complete problems will also be a solution for any other such problems. Its artificial-intelligence analogue is the class of AI-complete problems, for which a complete mathematical formalization still does not exist. In this chapter we will focus on analysing computational classes to better understand possible formalizations of AI-complete problems, and to see whether a universal algorithm, such as a Turing test, could exist for all AI-complete problems. In order to better observe how modern computer science tries to deal with computational complexity issues, we present several different deep-learning strategies involving optimization methods to see that the inability to exactly solve a problem from a higher order computational class does not mean there is not a satisfactory solution using state-of-the-art machine-learning techniques. Such methods are compared to philosophical issues and psychological research regarding human abilities of solving analogous NP-complete problems, to fortify the claim that we do not need to have an exact and correct way of solving AI-complete problems to nevertheless possibly achieve the notion of strong AI. (shrink)

A discussion of the connections and differences between completeness and representation theorems in logic, with examples drawn from classical and modal logic, the logic of friendliness, and nonmonotonic reasoning.

In the article we consider the relationship of traditional provisions of basic logical concepts and confront them with new and modern approaches to the same concepts. Logic is characterized in different ways when it is associated with syllogistics (referential – semantical model of logic) or with symbolic logic (inferential – syntactical model of logic). This is not only a difference in the logical calculation of (1) concepts, (2) statements, and (3) predicates, but this difference also appears in the treatment of (...) the calculative abilities of logical forms, the ontological-referential status of conceptual content and the inferential-categorical status of logical forms. The basic markers or basic ideas that separate ontologically oriented logic from categorically oriented logic are the (1) concept of truth, the (2) concept of meaning, the (3) concept of identity, and the (4) concept of predication. Here, this differences are explicitly demonstrated by the introduction of differential terminology. From this differential methodology follows a new set of characterizations of logic. (shrink)

§§3-4 of the Begriffsschrift present Frege’s objections to a dominant if murky nineteenth-century semantic picture. I sketch a minimalist variant of the pre-Fregean picture which escapes Frege’s criticisms by positing a thin notion of semantic content which then interacts with a multiplicity of kinds of truth to account for phenomena such as modality. After exploring several ways in which we can understand the existence of multiple truth properties, I discuss the roles of pointwise and setwise truth properties in modal logic. (...) I argue that thinking of supertruth and determinate truth as setwise truth properties allows an understanding of supervaluationist approaches to vagueness which escapes both Williamson’s objections to and a needless metalinguistic orientation of traditional supervaluationism. (shrink)