A Theory Of Irrationality As A ‘Reasonable’ Response To An Incomplete Specification

Suppose the principles explaining how the human mind (brain) reaches logical conclusions and judgments were different from – and independent of – thoseinvolved innormatively valid reasoning. Then such principles should affect both conclusion generation and recognition that particular conclusions are or are not justified. People, however, demonstrate a discrepancy between impaired performance in generating logical conclusions as opposed to rather impressive competence in recognizing rational (versus irrational) ones. This discrepancy is hypothesized to arise from often generating an incomplete specification of a logical or judgmental problem when attempting to solve it – versus a recognition of such incompleteness when it is pointed out. The basic argument is developed, with common examples, in the context of specifying or failing to specify all possible combinations in simple logical arguments and is then extended to probabilistic reasoning, where complete versus incomplete specification corresponds to attending to all or to only some components of Bayes theorem-based reasoning.     

Framing experts' (dis)agreements about uncertain environmental events

Agreements and disagreements between expert statements influence lay people's beliefs. But few studies have examined what is perceived as a disagreement. We report six experiments where people rated agreement between pairs of probabilistic statements about environmental events, attributed to two different experts or to the same expert at two different points in time. The statements differed in frame, by focusing on complementary outcomes (45% probability that smog will have negative health effects vs. 55% probability that it will not have such effects), in probability level (45% vs. 55% probability of negative effects), or in both respects. Opposite frames strengthened disagreement when combined with different probability levels. Approximate probabilities can be “framed” in yet another way by indicating reference values they are “over” or “under”. Statements that use different directional verbal terms (over vs. under 50%) indicated greater disagreement than statements with the same directional term but different probability levels (over 50% vs. over 70%). Framing and directional terms similarly affected consistency judgments when both statements were issued by the same expert at different occasions. The effect of framing on perceived agreement was significant for medium (10 and 20 percentage points) differences between probabilities, whereas the effect of directional term was stable for numerical differences up to 40 percentage points. To emphasize agreement between different estimates, they should be framed in the same way. To accentuate disagreements or changes of opinion, opposite framings should be used.     

Probability, logic and the cognitive foundations of rational belief

Since Pascal introduced the idea of mathematical probability in the 17th century discussions of uncertainty and “rational” belief have been dogged by philosophical and technical disputes. Furthermore, the last quarter century has seen an explosion of new questions and ideas, stimulated by developments in the computer and cognitive sciences. Competing ideas about probability are often driven by different intuitions about the nature of belief that arise from the needs of different domains (e.g., economics, management theory, engineering, medicine, the life sciences etc). Taking medicine as our focus we develop three lines of argument (historical, practical and cognitive) that suggest that traditional views of probability cannot accommodate all the competing demands and diverse constraints that arise in complex real-world domains. A model of uncertain reasoning based on a form of logical argumentation appears to unify many diverse ideas. The model has precursors in informal discussions of argumentation due to Toulmin, and the notion of logical probability advocated by Keynes, but recent developments in artificial intelligence and cognitive science suggest ways of resolving epistemological and technical issues that they could not address.     

Perceived Disagreement and Heterogeneity in Social Networks: Distinct Effects on Political Participation

ABSTRACT

Although the coexistence of conflicting opinions in society is the very core of democracy, people’s tendency to avoid conflict could keep them away from political discussion and participation. On the other hand, being exposed to diverse political views could motivate citizens to participate. We conducted secondary analyses on two 2013 ITANES (Italian National Election Studies) probability samples in order to test the hypotheses that perceived network disagreement (between an individual and her/his discussion partners) and heterogeneity (among discussants holding different political opinions) exert independent and opposite effects on political participation through motivation and knowledge. Results converged in showing that disagreement dampened, while heterogeneity encouraged, political participation (voting, propensity to abstain in future, offline and online activism, and timing of vote decision) by decreasing or increasing, respectively, political interest and, in turn, knowledge.     

Explication of Inductive Probability

Inductive probability is the logical concept of probability in ordinary language. It is vague but it can be explicated by defining a clear and precise concept that can serve some of the same purposes. This paper presents a general method for doing such an explication and then a particular explication due to Carnap. Common criticisms of Carnap’s inductive logic are examined; it is shown that most of them are spurious and the others are not fundamental.     

Descartes and More on the infinity of the world

ABSTRACT

In this paper, I address the controversy between Henry More and René Descartes on the indefinite extension of the world. I provide a new reading of Descartes’ famous final answer of 15 April 1649. I read the entire debate in the terms of a disagreement concerning the epistemological status of the necessity of our judgement about the extension of the universe. Accordingly, the disagreement on the infinity of the world constitutes a case of a more general disagreement on the nature of the necessity of the theorems of Cartesian Physics. In particular, as concerns Descartes’ last reply, I argue that his assertion that a finite world is contradictory should be interpreted as a reply to More’s claim that the thesis of the infinity of the world, in so far as it cannot be grounded on the identity between matter and extension, does not express a logical necessity. Descartes’ assertion of the logical impossibility of a finite world, far from being, as it has always been read, a concession he made under the pressure of More’s objections, expresses the more radical element of the entire debate about the extension of the universe.     

Disagreement about Taste: Commonality Presuppositions and Coordination

This paper confronts the disagreement argument for relativism about matters of taste, defending a specific form of contextualism. It is first considered whether the disagreement data might manifest an invariantist attitude that speakers have pre-reflectively. Semantic and ontological enlightenment should then make the impressions of disagreement vanish, or at least leave them as lingering ineffectual Müller-Lyer-like illusions; but it is granted to relativists that this does not fully happen. López de Sa's appeal to presuppositions of commonality and Sundell's appeal to metalinguistic disagreement are discussed, and it is argued that, although they help to clarify the issues, they do not fully explain why such impressions remain under enlightenment. To explain it, the paper develops a suggestion that other writers have made, that the lingering impression of disagreement is a consequence of a practical conflict, appealing to dispositions to practical coordination that come together with presuppositions of commonality in axiological matters.     

The Logical Structure of Linguistic Commitment III Brandomian Scorekeeping and Incompatibility

Curiously, though he provides in Making It Explicit (MIE) elaborate accounts of various representational idioms, of anaphora and deixis, and of quantification, Robert Brandom nowhere attempts to lay out how his understanding of content and his view of the role of logical idioms combine in even the simplest cases of what he calls paradigmatic logical vocabulary. That is, Brandom has a philosophical account of content as updating potential – as inferential potential understood in the sense of commitment or entitlement preservation – and says that the point of logical vocabulary is to make available the expressive resources to make explicit such semantic structures as arise from discursive scorekeeping practice. Thus, one would expect an account of the updating or inferential potential of sentences involving logical vocabulary, an account which is such as to assign to those sentences the inferential significance necessary for this expressive job. In short, one would expect a semantics of logical vocabulary – &, , – in terms of the difference an assertion of a sentence involving it makes to the atomic score of a linguistic agent, and a completeness proof for the logic generated by this semantics. Despite this, no such semantics is given in MIE. It is in the current paper.     

The logic of epistemic justification

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases—predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic.     

Standard Decision Theory Corrected

Where there are infinitely many possible basic states of the world, a standard probability function must assign zero probability to each state – since any finite probability would sum to over one. This generates problems for any decision theory that appeals to expected utility or related notions. For it leads to the view that a situation in which one wins a million dollars if any of a thousand of the equally probable states is realized has an expected value of zero (since each such state has probability zero). But such a situation dominates the situation in which one wins nothing no matter what (which also has an expected value of zero), and so surely is more desirable. I formulate and defend some principles for evaluating options where standard probability functions cannot strictly represent probability – and in particular for where there is an infinitely spread, uniform distribution of probability. The principles appeal to standard probability functions, but overcome at least some of their limitations in such cases.     

NECESSITY, APRIORITY, AND LOGICAL STRUCTURE

Logical structure may explain the necessity and a priori knowability of such truths as that if A is red then A is either red or green. But this explanation cannot be extended to sentences that, while necessary and knowable a priori, do not wear the appropriate logical structure on their sleeves – sentences like 'if A is a point and A is red, then A is not green,' or 'if A is a sphere, then A is not a cube.' The real origin of these sentences' necessity and a priori knowability is a relationship between the meanings of their component atomic sentences – a relationship which cannot be systematically reduced to logical structure by translating those atomic sentences into any kind of 'ideal' language. Moreover, this kind of relationship is one to which any atomic sentences are susceptible if they have a classifying, or comparison-implying, content. Arguably, then, all atomic sentences are capable of being related to others in ways that are necessary and knowable a priori.     

Are investors really willing to agree to disagree? An experimental investigation of how disagreement and attention to disagreement affect trading behavior

Using a series of laboratory markets, this paper provides evidence that a willingness to engage in speculative trade is largely driven by a failure of traders to account for information about value implicit in other traders’ actions and that this behavior arises because traders construct myopic mental models that ignore the perspective of other traders. In a baseline set of markets, where traders are prompted to estimate fundamental value but are not overtly prompted to consider disagreement, I find that traders are generally insensitive to adverse selection and readily engage in suboptimal, speculative trade. Moreover, this effect does not decline across trials suggesting that market feedback alone is unlikely to correct traders’ behavior. In contrast, when traders are prompted to assess disagreement over asset values or when they trade in more transparent markets, they appear less willing to “agree to disagree.” These results provide insight into why investors depart from rational trading strategies and how investor psychology will influence trading behavior.     

The Existential Quantifier, Composition and Contingency

There is a good deal of disagreement about composition. There is first-order disagreement: there are radically different answers to the special composition question—the question of under what circumstances the xs compose a y. There is second-order disagreement: there are different answers to the question of whether first-order disagreement is real or merely semantic. Virtually all disputants with respect to both the first- and second-order issues agree that the answer or answers to the special composition question will take the form of a necessary truth or truths even though, as I will argue, such answers do not appear to be good candidates to be necessary truths. This paper provides an analysis of the concept of <exists> as it pertains to concrete objects, that fulfils two functions. First, it explicates the sense in which claims about composition are contingent and the sense in which they are necessary, and second, it provides a way of understanding when first-order disputes are substantial and when they are merely semantic.     

What differentiates meta-analysis from other forms of review1

An issue of friendly disagreement between Cooper and Arkin (1981) and Cook and Leviton (1980) involves the definition of meta-analysis. Cooper and Arkin favor a definition stressing the degree of quantification in review studies, while we claim that studies labeled as “meta-analysis” are differentiated from other reviews in terms of the aggregation of effect sizes or probability values across studies for the purpose of reaching numerical estimates of the average magnitude of a relationship (as preferred by Glass) or the probability of reaching the average probability by chance (as originally preferred by Rosenthal). This definitional issue is important because the major objection to past meta-analytic studies raised by Cook and Leviton involved the possibility that meta-analysis might be used uncritically by some persons to derive “bottom line” estimates that are biased because confounds biasing the estimate in one direction are more prevalent than confounds biasing it in the opposite direction. Defining meta-analysis as more quantification takes much of the steam out of our critique, but it also reduces the saliency of what has been unique about past efforts labeled as meta-analysis–the generation of a single numerical estimate of a relationship derived from a set of many related studies.     

The Semantic or Model-Theoretic View of Theories and Scientific Realism

The semantic view of theoriesis one according to which theoriesare construed as models of their linguisticformulations. The implications of thisview for scientific realism have been little discussed. Contraryto the suggestion of various champions of the semantic view,it is argued that this approach does not makesupport for a plausible scientific realism anyless problematic than it might otherwise be.Though a degree of independence of theory fromlanguage may ensure safety frompitfalls associated with logical empiricism, realism cannot be entertained unless models or (abstractedand/or idealized) aspects thereof are spelled out in terms of linguistic formulations (such as mathematical equations),which can be interpreted in terms of correspondencewith the world. The putative advantage of thesemantic approach – its linguistic independence – isthus of no help to the realist. I consider recent treatmentsof the model-theoretic view (Suppe, Giere, Smith), and find that although some of these accounts harbour the promiseof realism, this promise is deceptive.     

Software Description Form

Abstract

Data for analyzing disagreement can be obtained by asking the parties concerned to make short lists of simple statements expressing their own opinions on the topic in dispute. These short lists are combined into a collective list, and the parties are asked to compare each statement in it with every other one in turn, and rate horn far the two agree or disagree. Such tables of ratings, called logical equivalence matrixes (LEMs) can be analyzed by a computer program applying principal coordinate analysis. The results measure both the total amount of disagreement and the relative amounts over the separate issues found to be involved. Repertory grids were found to be unsuitable for the purpose except within narrow limits. The technique is illustrated by analysis of a dispute concerning legalizing abortion.     

Could it be the Case that if I am Right My Opponents will be Pleased? A Rejoinder to Johnson-Laird,Byrne and Girotto

I take up the four issues considered by Johnson-Laird, Byrne and Girotto in their reply to Politzer (2007). Based on the conceptual clarification which they adduce, it seems that the disagreement can be settled about the first one (truth functionality) and can be attenuated about the second one (the paradoxes of material implication). However, I maintain and refine my criticisms on the last two (negation and the probability of conditionals), backed up by considerations borrowed from the perspective of the conditional probability semantics for conditionals.     

The Common Topic in Aristotle’s <Emphasis Type="Italic">Rhetoric</Emphasis>: Precursor of the Argumentation Scheme

In the present article I attribute to the common topic in the Rhetoric a two-fold suggestive function and a guarantee function. These three functions are possible because this type of topic, while often quite abstract, nevertheless contains thought-steering, substantial terms, and formulates a generally empirical or normative endoxon. Assuming that according to Aristotle an enthymeme has at least two premises, it would appear that a common topic is the abstract principle behind the often implicit major premise. This means that the topic may be regarded as the – generalizing – if-then statement in a modern argumentation scheme. Therefore it should be possible to see the enthymemes of Rhetoric 2.23 as a combination of a logical argument form (which can usually be reconstructed as modus ponens) and an argumentation scheme – even though we may not attribute this idea to Aristotle himself.     

Faultless Disagreement and Aesthetic Realism

It has recently been argued that certain areas of discourse, such as discourse about matters of taste, involve a phenomenon of ‘‘faultless disagreement’’ that rules out giving a standard realist or contextualist semantics for them. Thus, it is argued, we are left with no choice but to consider more adventurous semantic alternatives for these areas, such as a semantic account that involves relativizing truth to perspectives or contexts of assessment. I argue that the sort of faultless disagreement present in these cases is in fact compatible with a realist treatment of their semantics. Then I briefly consider other considerations that might be thought to speak against realism about these areas of discourse. I conclude with the tentative suggestion that realism about matters of taste is far more plausible (at least in some cases) than most philosophers believe today.     

Interrupting speculation: The thinking of Heidegger and Greek tragedy

Despite his extended readings of parts of the Antigone of Sophocles, Heidegger nowhere explicitly sets about giving us a theory of tragedy or a detailed analysis of the essence of tragedy. The following paper seeks to piece together Heidegger's understanding of tragedy and tragic experience by looking to themes in his thinking – particularly his analyses of early Greek thinking – and connecting them both to his scattered references to tragedy and actual examples from Greek tragedy. What we find is that, for Heidegger, tragedy is an interruption of speculation, a refusal to philosophize, a way of showing how things are that resonates with the goal of Heidegger's own thinking.