The goal of creating Artificial General Intelligence (AGI) – or in other words of creating Turing machines (modern computers) that can behave in a way that mimics human intelligence – has occupied AI researchers ever since the idea of AI was first proposed. One common theme in these discussions is the thesis that the ability of a machine to conduct convincing dialogues with human beings can serve as at least a sufficient criterion of AGI. We argue that this very ability (...) should be accepted also as a necessary condition of AGI, and we provide a description of the nature of human dialogue in particular and of human language in general against this background. We then argue that it is for mathematical reasons impossible to program a machine in such a way that it could master human dialogue behaviour in its full generality. This is (1) because there are no traditional explicitly designed mathematical models that could be used as a starting point for creating such programs; and (2) because even the sorts of automated models generated by using machine learning, which have been used successfully in areas such as machine translation, cannot be extended to cope with human dialogue. If this is so, then we can conclude that a Turing machine also cannot possess AGI, because it fails to fulfil a necessary condition thereof. At the same time, however, we acknowledge the potential of Turing machines to master dialogue behaviour in highly restricted contexts, where what is called “narrow” AI can still be of considerable utility. (shrink)

The five English words—sentence, proposition, judgment, statement, and fact—are central to coherent discussion in logic. However, each is ambiguous in that logicians use each with multiple normal meanings. Several of their meanings are vague in the sense of admitting borderline cases. In the course of displaying and describing the phenomena discussed using these words, this paper juxtaposes, distinguishes, and analyzes several senses of these and related words, focusing on a constellation of recommended senses. One of the purposes of this paper (...) is to demonstrate that ordinary English properly used has the resources for intricate and philosophically sound investigation of rather deep issues in logic and philosophy of language. No mathematical, logical, or linguistic symbols are used. Meanings need to be identified and clarified before being expressed in symbols. We hope to establish that clarity is served by deferring the extensive use of formalized or logically perfect languages until a solid “informal” foundation has been established. Questions of “ontological status”—e.g., whether propositions or sentences, or for that matter characters, numbers, truth-values, or instants, are “real entities”, are “idealizations”, or are “theoretical constructs”—plays no role in this paper. As is suggested by the title, this paper is written to be read aloud. -/- I hope that reading this aloud in groups will unite people in the enjoyment of the humanistic spirit of analytic philosophy. (shrink)

Biochemists often adopt what may be called the “Strategy of Decomposition” for the causal discovery of biochemical pathway dynamic behaviours. This involves decomposing a pathway into a set of isolated parts, which are then analysed separately. It is assumed that knowledge gained of the isolated parts can then be used to explain the dynamic behaviours of the whole pathway. My thesis addresses the extent to which use of the Strategy of Decomposition is warranted. I evaluate two challenges contained in Bechtel (...) and Richardson’s Discovering Complexity. The first challenge is that pathways lack the ‘modular’ structure assumed in the Strategy of Decomposition. Bechtel and Richardson take biochemists to use a concept of modularity called ‘near decomposability’. The second challenge is that pathways have ‘Pathway Emergent’ behaviours. I reject both challenges. I show that near decomposability is the wrong type of modularity to apply to pathways, and that the occurrence of Pathway Emergence has not been established. I argue that an underlying problem with Bechtel and Richardson’s analyses is that they overstate the consequences of feedback and nonlinearity for the Strategy of Decomposition. Instead, the analysis of pathway modularity and emergence needs to be centered on the context-sensitivity of pathways’ ‘local causal laws’. I identify that the type of modularity assumed in the Strategy of Decomposition is ‘causal law modularity’, which requires the invariance of local causal laws. I also identify a necessary condition for Pathway Emergence: a pathway must manifest at least one local causal law that is not manifested by its isolated parts. I argue that the use of the Strategy of Decomposition may often be unwarranted. This is because the local causal laws of pathways are highly context-sensitive, and pathways might often not be causal law modular. This context-sensitivity also leaves open the possibility of Pathway Emergence. (shrink)

One of Tarski’s stated aims was to give an explication of the classical conception of truth—truth as ‘saying it how it is’. Many subsequent commentators have felt that he achieved this aim. Tarski’s core idea of defining truth via satisfaction has now found its way into standard logic textbooks. This paper looks at such textbook definitions of truth in a model for standard first-order languages and argues that they fail from the point of view of explication of the classical notion (...) of truth. The paper furthermore argues that a subtly different definition—also to be found in classic textbooks but much less prevalent than the kind of definition that proceeds via satisfaction—succeeds from this point of view. (shrink)

This article is about the ontological dispute between finitists, who claim that only finitely many numbers exist, and infinitists, who claim that infinitely many numbers exist. Van Bendegem set out to solve the 'general problem' for finitism: how can one recast finite fragments of classical mathematics in finitist terms? To solve this problem Van Bendegem comes up with a new brand of finitism, namely so-called 'apophatic finitism'. In this article it will be argued that apophatic finitism is unable to represent (...) the negative ontological commitments of infinitism or, in other words, that which does not exist according to infinitism. However, there is a brand of infinitism, so-called 'apophatic infinitism', that is able to represent both the positive and the negative ontological commitments of apophatic finitism. Unfortunately, apophatic finitism cannot adopt that way without losing the ability to represent the positive ontological commitments of infinitism. (shrink)

The subject of the first section is Carnapian modal logic. One of the things I will do there is to prove that certain description principles, viz. the ''self-predication principles'', i.e. the principles according to which a descriptive term satisfies its own descriptive condition, are theorems and that others are not. The second section will be devoted to Carnapian modal arithmetic. I will prove that, if the arithmetical theory contains the standard weak principle of induction, modal truth collapses to truth. Then (...) I will propose a different formulation of Carnapian modal arithmetic and establish that it is free of collapse. Noteworthy is that one can retain the standard strong principle of induction. I will occupy myself in the third section with Carnapian epistemic logic and arithmetic. Here too it is claimed that the standard weak principle of induction is invalid and that the alternative principle is valid. In the fourth and last section I will get back to the self-predication principles and I will point to some of the consequences if one adds them to Carnapian Epistemic arithmetic. The interaction of self-predication principles and the strong principle of induction results in a collapse of de re knowability. (shrink)