Frege's Begriffsschrift is Indeed First-Order Complete

It is widely taken that the first-order part of Frege's Begriffsschrift is complete. However, there does not seem to have been a formal verification of this received claim. The general concern is that Frege's system is one axiom short in the first-order predicate calculus comparing to, by now, standard first-order theory. Yet Frege has one extra inference rule in his system. Then the question is whether Frege's first-order calculus is still deductively sufficient as far as the first-order completeness is concerned. In this short note we confirm that the missing axiom is derivable from his stated axioms and inference rules, and hence the logic system in the Begriffsschrift is indeed first-order complete.     

The Doomsday Argument and the Simulation Argument

The Doomsday Argument and the Simulation Argument share certain structural features, and hence are often discussed together (Bostrom 2003, Are you living in a computer simulation, Philosophical Quarterly, 53:243–255; Aranyosi 2004, The Doomsday Simulation Argument. Or why isn’t the end nigh, and you’re not living in a simulation, http://philsci-archive.pitt.edu/190/; Richmond 2008, Doomsday, Bishop Ussher and simulated worlds, Ratio, 21:201–217; Bostrom and Kulczycki 2011 A patch for the Simulation Argument, Analysis, 71:54–61). Both are cases where reflecting on one’s location among a set of possibilities yields a counter-intuitive conclusion—in the first case that the end of humankind is closer than you initially thought, and in the second case that it is more likely than you initially thought that you are living in a computer simulation. Indeed, the two arguments do have some structural similarities. But there are also significant disanalogies between the two arguments, and I argue that these disanalogies mean that the Simulation Argument succeeds and the Doomsday Argument fails.     

Virtue in Argument

Virtue theories have become influential in ethics and epistemology. This paper argues for a similar approach to argumentation. Several potential obstacles to virtue theories in general, and to this new application in particular, are considered and rejected. A first attempt is made at a survey of argumentational virtues, and finally it is argued that the dialectical nature of argumentation makes it particularly suited for virtue theoretic analysis.     

Argument Structure,Argument Content,and Cognitive Change in Children's Peer Interaction

In this experimental study, the author examined whether children's conversations play a role in the processes of influence between peers. Children, aged 8 to 10 years, who were at different levels of moral development participated. The conversations of 120 children were coded and analyzed in terms of argument structure and content. Results indicated that the differences in structure between boys' and girls' arguments are stylistic and do not influence conversation outcomes. The children's use of the structural features of conversations suggested that when a more advanced position is adopted, the arguments themselves appear to inspire cognitive change. However, when a less advanced position is adopted, the children who influence their peers invoke a particular and insistent conversational style. Results are discussed in terms of transmission and constructivist accounts of the role of social interaction in cognitive development.     

Explanation and Evidence in Informal Argument

A substantial body of evidence shows that people tend to rely too heavily on explanations when trying to justify an opinion. Some research suggests these errors may arise from an inability to distinguish between explanations and the evidence that bears upon them. We examine an alternative account, that many people do distinguish between explanations and evidence, but rely more heavily on unsubstantiated explanations when evidence is scarce or absent. We examine the philosophical and psychological distinctions between explanation and evidence, and show that participants use explanations as a substitute for missing evidence. Experiment 1 replicates the results of other researchers, but further shows that participants generate more evidence when they are not constrained by their lack of data. Merely mentioning a source of data can alter both their evaluation (Experiment 2) and their production (Experiment 3) of explanations and evidence. In Experiment 4, we show that participants can explicitly consider the availability of evidence and other pragmatic factors when evaluating arguments. Finally, we consider the implications of using explanations to replace missing evidence as a strategy in argument.     

Argument Status and PP-Attachment

Prepositional phrase attachment was investigated in temporarily ambiguous sentences. Both attachment site (noun phrase or verb phrase) and argument status (argument or adjunct) were manipulated to test the hypothesis that arguments are processed differently than adjuncts. Contrary to this hypothesis, some previous research suggested that arguments and adjuncts are initially processed in the same manner, following a general bias to attach prepositional phrases to the verb phrase whenever possible [Clifton, Speer, & Abney (1991) Journal of Memory and Language, 30, 251–271]. The current study supports the hypothesis for differential processing, even during the initial stages of syntactic analysis. In an eye movement experiment, readers spent less first-pass time on argument prepositional phrases (PPs) than adjunct PPs. The results support a view in which a noun’s or verb’s argument structure can facilitate the analysis of its arguments.This research was supported by NSF grants SBR-9729056 and SBR-9720473 to the first author. We gratefully thank Gerry Altmann, Rick Lewis, Brian McElree, Don Mitchell, Neal Pearlmutter, Shari Speer, and Suzanne Stevenson for useful discussions and helpful comments. We would also like to acknowledge the Rutgers University Center for Cognitive Science, where the eye movement data were collected and an initial draft of the paper was written.     

Argument practices

The move to Postmodernism in argumentation is often predicated on the rejection of the formal basis of argument in logic. While this rejection may be justified, and is widely discussed in the literature, the loss of logic creates problems that a Postmodern theory of argument must address without recourse to logic and its attendant modernist assumptions. This essay argues that conceiving of argument in terms ofpractices will address the key problematics of Postmodernism without abandoning those features of argumentation that make it an important social, cultural and political practice. Implications for both theory and pedagogy are discussed.The author would like to acknowledge the invaluable commentary of, and discussions with, John Lyne, Charles Willard, Steven Fuller, and Ed Schiappa.     

Dispensability in the Indispensability Argument

One of the most influential arguments for realism about mathematical objects is the indispensability argument. Simply put, this is the argument that insofar as we are committed to the existence of the physical objects existentially quantified over in our best scientific theories, we are also committed to the mathematical objects existentially quantified over in these theories. Following the Quine–Putnam formulation of the indispensability argument, some proponents of the indispensability argument have made the mistake of taking confirmational holism to be an essential premise of the argument. In this paper, I consider the reasons philosophers have taken confirmational holism to be essential to the argument and argue that, contrary to the traditional view, confirmational holism is dispensable.     

The Knowledge Argument and Objectivity

In this paper I argue that Frank Jackson’s Knowledge Argument is better considered not as an argument against physicalism, but as an argument that objective theories must be incomplete. I argue that despite the apparent diversity of responses to the knowledge argument, they all boil down to a response according to which genuine epistemic gains are made when an individual has an experience. I call this the acquaintance response. I then argue that this response violates an intuitive stricture on the objectivity of theories. Therefore, the knowledge argument does show that objective theories cannot provide a complete understanding of the world. The result, however, is that both objective dualism and objective physicalism are refuted by the argument. In the end it is suggested that the notion of “subjective physicalism” is one that should be pursued.     

Idealism and the Ontological Argument

The ontological proof became something of a signature argument for the British Idealist movement and this paper examines how and why that was so. Beginning with an account of Hegel's understanding of the argument, it looks at how the thesis was picked up, developed and criticized by the Cairds, Bradley, Pringle-Pattison and others. The importance of Bradley's reading in particular is stressed. Lastly, consideration is given to Collingwood's lifelong interest in the proof and it is argued that his attention is best understood as a direct continuation of theirs. In view of the fact that recent commentators have tried to draw a sharp line between Collingwood's approach to metaphysics and ontology and that of his predecessors, the establishment of this connection calls for a measure of reassessment on both sides.     

Negotiation, Persuasion and Argument

Argument is often taken to deal with conflicting opinion or belief, while negotiation deals with conflicting goals or interests. It is widely accepted that argument ought to comply with some principles or norms. On the other hand, negotiation and bargaining involve concession exchange and tactical use of power, which may be contrasted with attempts to convince others through argument. However, there are cases where it is difficult to draw a clear distinction between bargaining and argument: notably cases where negotiators persuade others through `framing' and cases where the aims of negotiation have to do with public assertion and acceptance. Those cases suggest that the distinction between negotiation and argument is not absolute, and this raises the question whether rules about what is acceptable in argument and rules about what is acceptable in negotiation can all be viewed as instances of more general common norms about human interaction.     

Argument Quality and Cultural Difference

Central to argumentation theory is a concern with normativity. Argumentation theorists are concerned, among other things, with explaining why some arguments are good (or at least better than others) in the sense that a given argument provides reasons for embracing its conclusion which are such that a fair- minded appraisal of the argument yields the judgment that the conclusion ought to be accepted -- is worthy of acceptance -- by all who so appraise it.This conception of argument quality presupposes that the goodness of arguments is characterizable in terms of features of the argument itself. It makes no reference either to the attributes of the persons appraising the argument and judging its normative force, or to the context in which that appraisal is carried out. But recent work by a wide range of philosophers, argumentation theorists, and social theorists rejects such an abstract, impersonal notion of argument goodness. Instead, these theorists insist upon taking seriously, in the evaluation of arguments, the features of the evaluators themselves. In particular, such theorists emphasize the importance of cultural difference in argument appraisal. Often locating themselves under the banner of multiculturalism, they argue that the quality of an argument depends upon culturally-specific beliefs, values, and presuppositions; that an argument may be of high quality in one cultural context but of low quality in another. Consequently, they contend, no abstract, impersonal characterization of argument quality can succeed.In this paper I consider this multiculturalist approach to argument quality. I argue that while there is much merit in the general multiculturalist perspective, the multiculturalist argument against impersonal conceptions of argument quality fails. It fails for several reasons detailed below; most fundamentally, it fails because it itself presupposes just the kind of impersonal account of argument quality it seeks to reject. I call this presupposition that of transcultural normative reach. I identify this presupposition in the multiculturalist argument, and show how it undercuts the multiculturalist challenge to abstract, impersonal, transcultural conceptions of argument quality. I conclude with an evaluation of the strengths, and weaknesses, of the multiculturalist challenge to such conceptions of argument quality.     

The Pareto Argument and Inequality

The Pareto argument for inequality holds that any change from a position of equality to one of inequality is justified so long as everyone benefits from the change. G.A. Cohen criticizes this argument (which he attributes to Rawls) on the ground that changes can normally be found which preserve both equality and Pareto-efficiency. However, this does not resolve the basic conflict between the two desiderata . Strong egalitarians hold that Pareto changes are not for the better if they increase inequality too greatly. Thus if the Pareto argument holds, then strong egalitarianism is unsustainable. I argue that egalitarians need not be troubled by the Pareto argument for inequality. The Pareto criterion would not be widely accepted unless it takes account of moral harms; but if it does take account of moral harms then there is no reason to doubt that egalitarian concerns can be incorporated into the Pareto argument.
email : p.shaw@philosophy.arts.gla.ac.uk     

Logical Argument Structures in Decision-making

Perelman and Olbrechts-Tyteca's practical reasoning theory has attracted a great deal of interest since its publication in 1969. Their most important assertion, however, that argument is the logical basis for practical decision-making, has been under-utilized, primarily because it was not sufficiently operationalized for research purposes. This essay presents an operationalization of practical reasoning for use in analyzing argument logics that emerge through group interaction. Particular elements of discourse and argument are identified as responding to principles put forward by Perelman and Olbrechts-Tyteca, and are viewed as fitting together in a kind of logical argument structure that is well suited to the study of practical arguments in decision-making. Both the content elements and the logical argument structure are illustrated using examples from two studies examining decision logics in public participation and jury decision-making. Advantages of this approach and proposed recognition of a new `filtered' type of argument structure are discussed.