On a medieval solution to the liar paradox

In this paper, I examine a solution to the Liar paradox found in the work of Ockham, Burley, and Pseudo-Sherwood. I reject the accounts of this solution offered by modern commentators. I argue that this medieval line suggests a non-hierarchical solution to the Liar, according to which ‘true’ is analysed as an indexical term, and paradox is avoided by minimal restrictions on tokens of ‘true’. In certain respects, this solution resembles the recent approaches of Charles Parsons and Tyler Burge; in other respects, it is related to a suggestion of Gödel. But, as a whole, it suggests an original solution to the Liar paradox, quite unlike any current proposals.     

Buridan's Solution to the Liar Paradox

Jean Buridan has offered a solution to the Liar Paradox, i.e. to the problem of assigning a truth-value to the sentence ‘What I am saying is false’. It has been argued that either (1) this solution is ad hoc since it would only apply to self-referencing sentences [Read, S. 2002. ‘The Liar Paradox from John Buridan back to Thomas Bradwardine’, Vivarium, 40 (2), 189–218] or else (2) it weakens his theory of truth, making his ‘a logic without truth’ [Klima, G. 2008. ‘Logic without truth: Buridan on the Liar’, in S. Rahman, T. Tulenheimo and E. Genot, Unity, Truth and the Liar: The Modern Relevance of Medieval Solutions to the Liar Paradox, Berlin: Springer, 87–112 (Chapter 5); Dutilh Novaes, C. 2011. ‘Lessons on truth from mediaeval solutions to the Liar Paradox’, The Philosophical Quarterly, 61 (242), 58–78]. Against (1), I will argue that Buridan's solution by means of truth by supposition does not involve new principles. Self-referential sentences force us to handle supposition more carefully, which does not warrant the accusation of adhoccery. I will also argue, against (2), that it is exaggerated to assert that this solution leads to a ‘weakened’ theory of truth, since it is consistent with other passages of the Sophismata, which only gives necessary conditions for the truth of affirmative propositions, but sufficient conditions for falsity.     

The Byzantine Liar

An eleventh-century Greek text, in which a fourth-century patristic text is discussed, gives an outline of a solution to the Liar Paradox. The eleventh-century text is probably the first medieval treatment of the Liar. Long passages from both texts are translated in this article. The solution to the Liar Paradox, which they entail, is analysed and compared with the results of modern scholarship on several Latin solutions to this paradox. It is found to be a solution, which bears some analogies to contemporary game semantics. Further, an overview of other Byzantine scholia on the Liar Paradox is provided. The findings and the originality of the discussed solution to the Liar Paradox suggest a change in the way in which Byzantine Logic is traditionally regarded in contemporary scholarship.     

The English contribution to logic before Ockham

Summary The change of medieval philosophy, known to have taken place in the 14th century, is accompanied by a new and extensive application of terminist logic and by a growing importance of the university of Oxford. This essay asks the question whether this development can be explained as a development of a specific English tradition within medieval logic. In the first part of the paper it is briefly shown that a certain discontinuity can be observed in the most important continental intellectual centers; the sociological conditions which make possible such distinct local traditions within the general development of medieval scholasticism are considered shortly. The second and larger part of the paper is a census of the English contribution to logic before Ockham, ordered according to the various literary genres: Summulae, Syncategoremata/sophismata, Grammar, Commentaries on the Organon. This census tends to prove that terminist logic had a continuous tradition in Oxford, a fact which may account for the preponderance of Oxford logic in the early 14th century.A first draft of this paper was read by Norman Kretzmann and Eleonore Stump. I am very grateful to them for their valuable suggestions which have made substantial parts of the text more readable and less obscure. That it still remains very speculative and fragmentary could not be avoided even with their generous aid.     

Assertoric Semantics and the Computational Power of Self-Referential Truth

There is no consensus as to whether a Liar sentence is meaningful or not. Still, a widespread conviction with respect to Liar sentences (and other ungrounded sentences) is that, whether or not they are meaningful, they are useless. The philosophical contribution of this paper is to put this conviction into question. Using the framework of assertoric semantics, which is a semantic valuation method for languages of self-referential truth that has been developed by the author, we show that certain computational problems, called query structures, can be solved more efficiently by an agent who has self-referential resources (amongst which are Liar sentences) than by an agent who has only classical resources; we establish the computational power of self-referential truth. The paper concludes with some thoughts on the implications of the established result for deflationary accounts of truth.     

Hume and the nominalist tradition

Many of the central theses of Hume's philosophy – his rejection of real relations, universals, abstract objects and necessary causal relations – had precedents in the later medieval nominalist tradition. Hume and his medieval predecessors developed complex semantic theories to show both how ontologies are apt to become inflated and how, if we understand carefully the processes by which meaning is generated, we can achieve greater ontological parsimony. Tracing a trajectory from those medieval traditions to Hume reveals Hume to be more radical, particularly in his rejection of abstraction and abstract ideas. Hume's denial of general, abstract ideas is consistent with his philosophical principles but fails to appreciate the more sophisticated nominalist approaches to abstraction, the result of which is a theoretically impoverished account of our capacity for generalization.     

Logic,Logic, and Logic

In his recent paper in History and Philosophy of Logic, John Kearns argues for a solution of the Liar paradox using an illocutionary logic (Kearns 2007 Kearns, J. 2007. ‘An illocutionary logical explanation of the Liar Paradox’. History and Philosophy of Logic, 28: 31–66. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]). Paraconsistent approaches, especially dialetheism, which accepts the Liar as being both true and false, are rejected by Kearns as making no ‘clear sense’ (p. 51). In this critical note, I want to highlight some shortcomings of Kearns' approach that concern a general difficulty for supposed solutions to (semantic) antinomies like the Liar. It is not controversial that there are languages which avoid the Liar. For example, the language which consists of the single sentence ‘Benedict XVI was born in Germany’ lacks the resources to talk about semantics at all and thus avoids the Liar. Similarly, more interesting languages such as the propositional calculus avoid the Liar by lacking the power to express semantic concepts or to quantify over propositions. Kearns also agrees with the dialetheist claim that natural languages are semantically closed (i.e. are able to talk about their sentences and the semantic concepts and distinctions they employ). Without semantic closure, the Liar would be no real problem for us (speakers of natural languages). But given the claim, the expressive power of natural languages may lead to the semantic antinomies. The dialetheist argues for his position by proposing a general hypothesis (cf. Bremer 2005 Bremer, M. 2005. An Introduction to Paraconsistent Logics, Bern: Lang.  [Google Scholar], pp. 27–28): ‘(Dilemma) A linguistic framework that solves some antinomies and is able to express its linguistic resources is confronted with strengthened versions of the antinomies’. Thus, the dialetheist claims that either some semantic concepts used in a supposed solution to a semantic antinomy are inexpressible in the framework used (and so, in view of the claim, violate the aim of being a model of natural language), or else old antinomies are exchanged for new ones. One horn of the dilemma is having inexpressible semantic properties. The other is having strengthened versions of the antinomies, once all semantic properties used are expressible. This dilemma applies, I claim, to Kearns' approach as well.     

On the logic of theocracy

I identify the objectionable element in theocracy, not with reliance on God as such, nor with the idea that God might have something to do with morality, but with the anti-human propensity to issue orders without communicating good reasons for them. In medieval discussion prohibitions not based on good reasons attracted the labelmalum quia prohibitum, bad because forbidden and I take this to be the criterion of theocracy in its objectionable form. I examine, in part of the Vatican’s doctrine against contraception, a persistent tendency towards this approach, a tendency incompatible with the tradition of the Church and ultimately incompatible even with the thirteenth century discussion of such issues in the work of Thomas Aquinas.     

Three Problems for the Singularity Theory of Truth

In this paper I present three problems for Simmons singularity theory of truth as he presents it in Universality and the Liar. I begin with a brief overview of the theory and then present the three problems I see for it.The first problem shows that the singularity theory is in conflict with our ordinary notion of truth. I present a set of sentences that the singularity theory evaluates differently than does our pretheoretic concept of truth.The second problem shows that Simmons theory is incomplete, in the sense that there are sentences of its object language of which it does not have the resources to evaluate.The third problem suggests that Simmons theory does not, contrary to the claim of the book, allow for semantic universality. I consider Simmons extension of the singularity theory to accommodate truth-in-a-context and show that it is inconsistent with his basic theory. Specifically I present a sentence which diagonalizes out of the basic theory.     

From metasemantics to analyticity

In this paper, I argue from a metasemantic principle to the existence of analytic sentences. According to the metasemantic principle, an external feature is relevant to determining which concept one expresses with an expression only if one is disposed to treat this feature as relevant. This entails that if one isn’t disposed to treat external features as relevant to determining which concept one expresses, and one still expresses a given concept, then something other than external features must determine that one does. I argue that, in such cases, what determines that one expresses the concept also puts one in a position to know that certain sentences are true—these sentences are thus analytic relative to this determination basis. Finally, I argue that there are such cases: some sentences are analytic relative to what determines that we express certain key concepts, and these sentences include ones that have always been thought to be the best candidates for being analytic, namely, stipulative truths, and first principles of mathematics.     

A FailedCassatio: Goldstein on the Liar

The purpose of this note is to express some doubts about Goldstein's cassationist solution to the Liar Paradox. After sketching his theory (§I), we argue that the notions he introduces in order to solve the Strengthened Liar give rise to paradoxes the theory cannot deal with (§II).     

The dynamic lexicon in a truth-conditional framework; or how to have Your cake and eat it

A fundamental principle of all truth-conditional approaches to semantics is that the meanings of sentences of natural language can be compositionally specified in terms of truth conditions, where the meanings of the sentences’ parts (words/lexical items) are specified in terms of the contribution they make to such conditions their host sentences possess. Thus, meanings of words fit the meanings of sentences at least to the extent that the stability of what a sentence might mean as specified in a theory is in accord with the stability of what a word might mean as similarly specified. In this paper, I shall be concerned with Ludlow’s (2014) idea that, in fact, there need be no such sympathy between words and sentences. He proposes that we can square what he calls a dynamic lexicon, where word meaning is not stable at all, with a traditional truth-conditional approach of the kind indicated, where sentence meaning is delivered via ‘absolute truth conditions’. I share Ludlow’s aspiration to accommodate dynamic features of word meaning with a truth conditional approach, but not his belief that the marriage is an easy deal. Thus, I shall present a problem for Ludlow’s position and show how resolving this problem leads to an alternative picture of how the meaning of a sentence may be truth-conditionally specified with all relevant dynamic features of the lexicon retained.     

Acting Out of Affections: Embodiment,morality and (post) modernity

This article discusses how the epistemological emphasis given to instrumental reason and cognitive classification (mathesis) during modernity resulted in the disparagement of the role of embodiment in constructions of the moral and spiritual self. I show how the disenchantment and desacralisation of nature which accompanied this shift led to an internalisation of the sources of moral action. I suggest that what is now required is a similar attention to embodiment that the medieval Christian tradition of affective imitation and ritual expression encouraged. Drawing primarily from the work of Durkheim, Bauman, and Mestrovic, I discuss how recent sociological work examines and endorses this need to rediscover the sources of moral and spiritual development in authentic somatic experience.     

Tradition and Experimentation: the Development of the Samatha Trust

ABSTRACT

Theravāda Buddhism has travelled. This article gives some history of the practice of samatha breathing mindfulness, in the Theravāda tradition, in the UK. It first gives some background in Britain to the arrival of the meditation in the 1960s, then summarises the life of Nai Boonman Poonyathiro, who introduced this method into the UK, a story that is not generally known. The paper describes some aspects of the development of the Samatha Trust in the UK, attempting to show ways a system that was popular in Thailand when it arrived in a new region has prospered, even while becoming markedly less prominent in its own regions. As I am a practitioner in this tradition, before the conclusion I make some personal comment. To conclude, I speculate about features which appear to characterise Buddhist groups in general in the UK, before considering ways that this specialised tradition has adapted in a new setting.     

GRATIAN AND MENGZI

In this essay, I compare two pioneer thinkers of the “just war” tradition across cultures: Gratian in the Christian tradition, and Mengzi (Mencius) in the Confucian tradition. I examine their historical-cultural contexts and the need for both to discuss just war, introduce the nature of their treatises and the rudimentary theories of just war therein, and trace the influence both thinkers’ theories have had on subsequent just war ethics. Both deemed just cause, proper authority, and right intention to be necessary conditions for initiating a just war. However, Gratian’s theory has a presumption against injustice whereas Mengzi’s theory has a presumption against war. As a jurist of the Church, Gratian sought to discriminate just from unjust wars, while Mengzi, a moral-political advisor to rulers, was more concerned with avoiding bloodshed and building lasting peace. In addition to examining these thinkers’ respective historical influences, I submit that Gratian’s Decretum and the Mengzi are pioneering in two more senses. First, they offer important clues to understanding how just war ideas were developed very differently in medieval Europe and in premodern China. Second, both embodied features that helped shape their subsequent intellectual tradition, which in turn molded the different legacies of these two works.     

Two modes of unsaying in the early thirteenth century Islamic lands: theorizing apophasis through Maimonides and Ibn ‘Arabī

This comparative study juxtaposes two celebrated medieval examples of negative speech, apophasis, and theorizes the languages of unsaying in the great medieval thinkers, Maimonides (d.1204) and Ibn ‘Arabī (d.1240). The paper coins a distinction between ‘asymmetrical’ versus ‘symmetrical’ approaches to language as a heuristic to analyze the two philosophical apophatic accounts comparatively. While apophatic thinkers in Neoplatonic traditions generally oscillate between these two poles in their various apophatic moments, the paper argues that Maimonides and Ibn ‘Arabī represented the climax of these two non-linear poles in a visible tension and conversant with each other. I frame philosophical apophasis in the medieval Islamic lands in terms of the problem of God’s transcendence versus imminence. Maimonides celebrates apophasis and claims that negative speech, asymptotically approaching silence, is the only genuine praise to God. As an uncompromising exponent of absolute transcendence, and a severe critic of those who ascribe attributes to God, he privileges apophasis to kataphasis; he presents negative speech as a medium of purification and spiritual progress. Ibn ‘Arabī, on the other hand, is critical of this widespread asymmetry, and defends the gathering together of transcendence and imminence for human perfection. His intricate theory of transcendence and imminence appeals to a dialectical logic, explaining why kataphasis and apophasis are symmetrical in front of the Absolute. The productive tension between two apophatic minds challenges Hegelian habits of reading the history of thought, as well as various scholarly prejudices about medieval intellectual landscapes.