Hanoch Ben-Yami

I explain why model theory is unsatisfactory as a semantic theory and has drawbacks as a tool for proofs on logic systems. I then motivate and develop an alternative, the truth-valuational substitutional approach (TVS), and prove with it the soundness and completeness of the first order Predicate Calculus with identity and of Modal Propositional Calculus. Modal logic is developed without recourse to possible worlds. Along the way I answer a variety of difficulties that have been raised against TVS and show that, as applied to several central questions, model-theoretic semantics can be considered TVS in disguise. The conclusion is that the truth-valuational substitutional approach is an adequate tool for many of our logic inquiries, conceptually preferable over model-theoretic semantics. Another conclusion is that formal logic is independent of semantics, apart from its use of the notion of truth, but that even with respect to it its assumptions are minimal.

Descartes was the first to hold that, when we perceive, the representation need not resemble what it represents but should correspond to it. Descartes developed this ground-breaking, influential conception in his work on analytic geometry and then transferred it to his theory of perception. I trace the development of the idea in Descartes’ early mathematical works; his articulation of it in Rules for the Direction of the Mind; his first suggestions there to apply this kind of representation-by-correspondence in the scientific inquiry of colours; and, finally, the transfer of the idea to the theory of perception in The World.

The Quantified Argument Calculus (Quarc) is a formal logic system, first developed by Hanoch Ben-Yami in (Ben-Yami 2014), and since then extended and applied by several authors. The aim of this paper is to further these contributions by, first, providing a philosophical motivation for the truth-valuational, substitutional approach of (Ben-Yami 2014) and defending it against a common objection, a topic also of interest beyond its specific application to Quarc. Second, we fill the formal lacunae left in the original presentation, which did not incorporate identity systematically into Quarc, and although it proved the soundness of the system did not prove its completeness.

I try to identify elements of our mental capacities that separate us from animals. I focus on our command of logical concepts, demonstrable already in children in the second or third year of their life, which to date no animal has been shown to master. I draw various conclusions about the behavioural, intellectual, emotional, and moral capacities that depend on this mastery, and discuss recent empirical research that either supports or apparently disagrees with the claim that animals, even those we consider intelligent, are limited in these respects. My discussion is built around observations extracted from Wittgenstein.

We introduce a two-valued and a three-valued truth-valuational substitutional semantics for the Quantified Argument Calculus (Quarc). We then prove that the 2-valid arguments are identical to the 3-valid ones with strict-to-tolerant validity. Next, we introduce a Lemmon-style Natural Deduction system and prove the completeness of Quarc on both two- and three-valued versions, adapting Lindenbaum’s Lemma to truth-valuational semantics. We proceed to investigate the relations of three-valued Quarc and the Predicate Calculus (PC). Adding a logical predicate T to Quarc, true of all singular arguments, allows us to represent PC quantification in Quarc and translate PC into Quarc, preserving validity. Introducing a weak existential quantifier into PC allows us to translate Quarc into PC, also preserving validity. However, unlike the translated systems, neither extended system can have a sound and complete proof system with Cut, supporting the claim that these are basically different calculi.

Fictional characters do not really exist. Names of fictional characters refer, to fictional characters. We should divorce the idea of reference from that of existence (the picture of the name as a tag has limited applications; the Predicate Calculus, with its existential quantifier, does not adequately reflect the relevant concepts in natural language; and model theory, with its domains, might also have been misleading). Many puzzle-cases are resolved this way (among other things, there is no problem assigning negative existential statements the appropriate truth values). And fictional characters, although not existing, have real powers through their representations, which are real.

In the first chapter of his The World, Descartes compares light to words and discusses signs and ideas. This made scholars read into that passage our views of language as a representational medium and consider it Descartes’ model for representation in perception. I show, by contrast, that Descartes does not ascribe there any representational role to language; that to be a sign is for him to have a kind of causal role; and that he is concerned there only with the cause’s lack of resemblance to its effect, not with the representation’s lack of resemblance to what it represents. I support this interpretation by comparisons with other places in Descartes’ corpus and with earlier authors, Descartes’ likely sources. This interpretation may shed light both on Descartes’ understanding of the functioning of language and on the development of his theory of representation in perception.

The formalisation of Natural Language arguments in a formal language close to it in syntax has been a central aim of Moss’s Natural Logic. I examine how the Quantified Argument Calculus (Quarc) can handle the inferences Moss has considered. I show that they can be incorporated in existing versions of Quarc or in straightforward extensions of it, all within sound and complete systems. Moreover, Quarc is closer in some respects to Natural Language than are Moss’s systems – for instance, is does not use negative nouns. The process also sheds light on formal properties and presuppositions of some inferences it formalises. Directions for future work are outlined.

The Modal Predicate Calculus gives rise to issues surrounding the Barcan formulas, their converses, and necessary existence. I examine these issues by means of the Quantified Argument Calculus, a recently developed, powerful formal logic system. Quarc is closer in syntax and logical properties to Natural Language than is the Predicate Calculus, a fact that lends additional interest to this examination, as Quarc might offer a better representation of our modal concepts. The validity of the Barcan formulas and their converses is shown by Quarc to be a result of the specific incorporation of quantification in the Predicate Calculus, and not as reflecting a feature of the interaction of quantification and modality more generally. Necessary existence is shown to follow from the identification, in the Predicate Calculus on its canonical interpretation, of particular quantification, ascription of existence and the ‘there is’ construction, three constructions which are distinguished in both Quarc and Natural Language. The issues surrounding the Barcan formulas, their converses and necessary existence are thus shown to be an artefact of a specific logic system, not an essential feature of our relevant modal concepts or of formal logic.

I explain in what sense the structure of space and time is probably vague or indefinite, a notion I define. This leads to the mathematical representation of location in space and time by a vague interval. From this, a principle of complementary inaccuracy between spatial location and velocity is derived, and its relation to the Uncertainty Principle discussed. In addition, even if the laws of nature are deterministic, the behaviour of systems will be random to some degree. These and other considerations draw classical physics closer to Quantum Mechanics. An arrow of entropy is also derived, given an arrow of time. Lastly, chaos is given an additional, objective meaning.

There is currently a theoretical tension between young children’s failure in False Belief Tasks (FBTs) and their success in a variety of other tasks that also seem to require the ability to ascribe false beliefs to agents. We try to explain this tension by the hypothesis that in the FBT, children think they are asked what the agent should do in the circumstances and not what the agent will do. We explain why this hypothesis is plausible. We examined the hypothesis in two experiments, each involving a new task. In the first task, the hypothesised misunderstanding of the question leads to failure without the need to ascribe a false belief, and we show that failure in this new task is correlated with failure in the FBT. In the second task, passing which requires ascribing a false belief to an agent, and for which we have partial yet encouraging results, the children are asked a question which is unlikely to be misunderstood. Children pass this task much more often than they do a standard FBT. The mentioned tension is thus resolved. We conclude that the so-called False Belief Task probably does not check the ability to ascribe false beliefs but rather linguistic development.

Ben-Yami presents Wittgenstein’s explicit criticism of the Platonic identification of an explanation with a definition and the alternative forms of explanation he employed. He then discusses a few predecessors of Wittgenstein’s criticisms and the Fregean background against which he wrote. Next, the idea of family resemblance is introduced, and objections answered. Wittgenstein’s endorsement of vagueness and the indeterminacy of sense are presented, as well as the open texture of concepts. Common misunderstandings are addressed along the way. Wittgenstein’s ideas, as is then shown, have far-reaching implications for knowledge of meaning and the nature of logic, and with them to the nature of the philosophical project and its possible achievements.

I develop a formal logic in which quantified arguments occur in argument positions of predicates. This logic also incorporates negative predication, anaphora and converse relation terms, namely, additional syntactic features of natural language. In these and additional respects, it represents the logic of natural language more adequately than does any version of Frege’s Predicate Calculus. I first introduce the system’s main ideas and familiarize it by means of translations of natural language sentences. I then develop a formal system built on these principles, the Quantified Argument Calculus or Quarc. I provide a truth-value assignment semantics and a proof system for the Quarc. I next demonstrate the system’s power by a variety of proofs; I prove its soundness; and I comment on its completeness. I then extend the system to modal logic, again providing a proof system and a truth-value assignment semantics. I proceed to show how the Quarc versions of the Barcan formulas, of their converses and of necessary existence come out straightforwardly invalid, which I argue is an advantage of the modal Quarc over modal Predicate Logic as a system intended to capture the logic of natural language.

I develop a solution to the Sorites Paradox, according to which a concatenation of valid arguments need not itself be valid. I specify which chains of valid arguments are those that do not preserve validity: those that pass the vague boundary between cases where the relevant concept applies and cases where that concept does not apply. I also develop various criticisms of this solution and show why they fail; basically, they all involve a petitio at some stage. I criticise the conviction that if every short argument in a long concatenated argument is valid, so is the long argument: it is, I argue, the result of an unjustified generalisation from the case of arguments that do not employ vague concepts (as in mathematics) to arguments that do employ them. My approach is Wittgensteinian in its “leaving everything as it is,” in its claiming that the “beginning” has been searched too far back (see paper's epigraph) and in its claim that the paradox was generated by a misapplication of a partial picture of the behaviour of arguments. I conclude my paper by comparing and contrasting my approach to the few precedents found in the vagueness literature and by answering a few additional objections that were raised there

Functionalists define a given mental state as a state that is apt to be the cause of specific effects and the effect of specific causes. Two tokens of the same belief, however, often cause and are caused by very different events: what makes them beliefs of the same type? Several answers, including the one relying on the identity of actual plus counterfactual causal relations, are considered and rejected. Functionalists did not notice that they have to specify how a state which is to be identified as mental is to be individuated, but, given their theory, this cannot be done

In this book, Ben-Yami reassesses the way Descartes developed and justified some of his revolutionary philosophical ideas. The first part of the book shows that one of Descartes' most innovative and influential ideas was that of representation without resemblance. Ben-Yami shows how Descartes transfers insights originating in his work on analytic geometry to his theory of perception. The second part shows how Descartes was influenced by the technology of the period, notably clockwork automata, in holding life to be a mechanical phenomenon, reducing the soul to the mind and considering it immaterial. Ben-Yami explores the later role of the digital computer in Turing's criticism of Descartes' ideas. The last part discusses the Meditations: far from starting everything afresh without presupposing anything that can be doubted, Descartes' innovations in the dream argument, the cogito and elsewhere are modifications of old ideas based upon considerations issuing from his separately developed theories, formed under the influence of the technology, mathematics and science of his age.

David Malament tried to show that the causal theory of time leads to a unique determination of simultaneity relative to an inertial observer, namely standard simultaneity. I show that the causal relation Malament uses in his proofs, causal connectibility, should be replaced by a different causal relation, the one used by Reichenbach in his formulation of the theory. I also explain why Malament's reliance on the assumption that the observer has an eternal inertial history modifies our conception of simultaneity, and I therefore eliminate it. Having made these changes, Malament's uniqueness result no longer follows, although the conventionality of simultaneity is not reinstated. I contrast my approach with previous criticisms of Malament. Introduction Causality and Temporal Order Malament's Argument Causality versus Causal Connectibility Simultaneity and History Conclusion.

Curtain. On the stage there's a row of about forty heads, of natural size, on a long and narrow white board roughly chest height, arranged facing the audience with equal spaces between them from near the left end of the stage to near its right end. The heads are all identical apart from two features. First, the leftmost head is completely bald, the rightmost head has lots of hair on its scalp, and the amount of hair on the heads increases gradually and uniformly from left to right, so that it is hard to discern a difference between any two consecutive heads. Secondly, the colour of the heads changes from bright red on the left to bright orange on the right, again so gradually that it is hard to discern a difference between any two consecutive heads. Apart from the row of heads the stage is empty, with dark background

This paper criticizes Kripke’s and Putnam’s theory of the semantics of natural kind terms (KPT) and develops an alternative theory. It first examines description theories of natural kind terms, to see what their flaws are and what can be preserved of them. It then presents the KPT and makes three main criticisms. These rely on the meaning of elementary particles’ names, on reactions to the absence of a common essential nature, and on applications of old terms to new cases. Lastly, it develops a theory that takes noun phrases to be plural referring expressions, and shows how that theory meets the objections to the KPT.

Ned Block. Psychologism and behaviorism. Philosophical Review, 90, 5-43.) argued that a behaviorist conception of intelligence is mistaken, and that the nature of an agent's internal processes is relevant for determining whether the agent has intelligence. He did that by describing a machine which lacks intelligence, yet can answer questions put to it as an intelligent person would. The nature of his machine's internal processes, he concluded, is relevant for determining that it lacks intelligence. I argue against Block that it is not the nature of its processes but of its linguistic behavior which is responsible for his machine's lack of intelligence. As I show, not only has Block failed to establish that the nature of internal processes is conceptually relevant for psychology, in fact his machine example actually supports some version of behaviorism. As Wittgenstein has maintained, as far as psychology is concerned, there may be chaos inside

I have attempted to show that many attributive adjectives can be dealt with within the framework of first-order predicate calculus by the method suggested in this paper. I've also supplied independent reasons for the claim that attributive adjectives that are not responsive to this method require a formal treatment different from the one that the adjectives successfully dealt with by that method require. Thus, if the method I've argued for is sound, then the scope of first-order predicate calculus was shown to be wider than assumed by several logicians. This I take to be of interest from a logical point of view

I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an relation. Next, I sketch a different approach that is more adequate than PQL for capturing plural aspects of natural language semantics and logic. I conclude with a criticism of the claim that PQL should replace natural language for specific philosophical or scientific purposes