On the continuing utility of argument in a postmodern world

In this essay we contend that traditional theories of argument are consonant with and enrich the project of postmodernity. Reading postmodernity as a rhetoric underscores how the process of discursively resolving conflicts is occasionally threatened by politically motivated efforts to misuse the methods of argument; it alerts us to the egregious acts that are and can be performed in the name of, but not because of, rationality. Postmodernity is thus an attempt by a new generation of theorists to recast and draw attention to perennial philosophical problems in the context of contemporary political difficulties.     

The Archaelogy of Spirit and the Unique Self: A Husserlian Reading of Conrad-Martius

Although the connections of Hedwig Conrad-Martius’ ontological phenomenology, what she called, “realontology,” to Husserl’s transcendental phenomenology were constant concerns that usually remained in the background of her work, on occasion they became foreground. Similarly the problems surrounding the individuation of the person and spirit were persistent but rather marginal in her writings. In this paper I want first to review some of the issues as they are connected to ontological and transcendental phenomenology. Then I want to relate them to the cosmological and theological issues that were no less important for Conrad-Martius.

How is the question ‘Is Existence a Predicate?’ relevant to the ontological argument?

It is often said that the ontological argument fails because it wrongly treats existence as a first-level property or predicate. This has proved a controversial claim, and efforts to evaluate it are complicated by the fact that the words ‘existence is not a property/predicate’ have been used by philosophers to make at least three different negative claims: (a) one about a first-level phenomenon possessed by objects like horses, stones, you and me; (b) another about the logical form of assertions of existence; and (c) still another about a second-level phenomenon possessed by concepts when they are instantiated. I argue that only the last of these claims, originally voiced by Kant, is both plausible and relevant to the ontological argument. And I try to show that the relevance of the Kantian version comes from its providing the underlying justification for a different, and far less controversial, criticism of the ontological argument.     

Heterogeneous Fibring of Deductive Systems Via Abstract Proof Systems

Fibring is a meta-logical constructor that applied to two logicsproduces a new logic whose formulas allow the mixing of symbols.Homogeneous fibring assumes that the original logics are presentedin the same way (e.g via Hilbert calculi). Heterogeneous fibring,allowing the original logics to have different presentations(e.g. one presented by a Hilbert calculus and the other by asequent calculus), has been an open problem. Herein, consequencesystems are shown to be a good solution for heterogeneous fibringwhen one of the logics is presented in a semantic way and theother by a calculus and also a solution for the heterogeneousfibring of calculi. The new notion of abstract proof systemis shown to provide a better solution to heterogeneous fibringof calculi namely because derivations in the fibring keep theconstructive nature of derivations in the original logics. Preservationof compactness and semi-decidability is investigated.     

Socratic Proofs

Journal of Philosophical Logic - Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: “Is A derivable from...     

The Uses of Argument in Mathematics

Stephen Toulmin once observed that ‘it has never been customary for philosophers to pay much attention to the rhetoric of mathematical debate’ [Toulmin et al., 1979, An Introduction to Reasoning, Macmillan, London, p. 89]. Might the application of Toulmin’s layout of arguments to mathematics remedy this oversight? Toulmin’s critics fault the layout as requiring so much abstraction as to permit incompatible reconstructions. Mathematical proofs may indeed be represented by fundamentally distinct layouts. However, cases of genuine conflict characteristically reflect an underlying disagreement about the nature of the proof in question.     

犯罪心理学研究中运用量化方法引起的理论思考

量化与统计分析,是一项重要的研究方法。这一方法在犯罪心理学研究中得到了广泛运用,同时也存在着使用的局限性。犯罪人有很强的心理掩饰性,对包括犯罪人在内的人的心理的测量实际上是一种间接测量,测得的数据是心理学家标定的数据,兼有客观性与主观性。量化研究如果不与科学思维相结合,有可能得出浅薄平庸甚至错误的结论。心理学研究应当以"人性"为基点,多种方法综合运用,实现量化方法与非量化方法的有机结合。     

Five Observations Concerning the Intended Meaning of the Intuitionistic Logical Constants

This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of `proof"; (2) Kreisel"s explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of can be easily and safely ameliorated; (4) the definition of in terms of `proofs from premises" results in a loss of the inductive character of the definitions of and and (5) the same occurs with the definition of in terms of `proofs with free variables".     

Inferential Intensionality

The paper is a study of properties of quasi-consequence operation which is a key notion of the so-called inferential approach in the theory of sentential calculi established in [5]. The principal motivation behind the quasi-consequence, q-consequence for short, stems from the mathematical practice which treats some auxiliary assumptions as mere hypotheses rather than axioms and their further occurrence in place of conclusions may be justified or not. The main semantic feature of the q-consequence reflecting the idea is that its rules lead from the non-rejected assumptions to the accepted conclusions.First, we focus on the syntactic features of the framework and present the q-consequence as related to the notion of proof. Such a presentation uncovers the reasons for which the adjective inferential is used to characterize the approach and, possibly, the term inference operation replaces q-consequence. It also shows that the inferential approach is a generalisation of the Tarski setting and, therefore, it may potentially absorb several concepts from the theory of sentential calculi, cf. [10]. However, as some concrete applications show, see e.g.[4], the new approach opens perspectives for further exploration.The main part of the paper is devoted to some notions absent, in Tarski approach. We show that for a given q-consequence operation W instead of one W-equivalence established by the properties of W we may consider two congruence relations. For one of them the current name is kept preserved and for the other the term W-equality is adopted. While the two relations coincide for any W which is a consequence operation, for an arbitrary W the inferential equality and the inferential equivalence may differ. Further to this we introduce the concepts of inferential extensionality and intensionality for q-consequence operations and connectives. Some general results obtained in Section 2 sufficiently confirm the importance of these notions. To complete a view, in Section 4 we apply the new intensionality-extensionality distinction to inferential extensions of a version of the ukasiewicz four valued modal logic.