As with mathematics, logic is easier to do if its symbols and their rules are better. In a graphic way, the logic symbols introduced in thís paper show their truth-table values, their composite truth-functions, and how to say them as either ?or? or ?if ? then? propositions. Simple rules make the converse, add or remove negations, and resolve propositions.

Bayesian rationality is an important contribution to syllogistic inference, but it has limitations. The claim that confidence in a conclusion is a function of informativeness of the max-premise is anomalous because this is the least probable premise. A more plausible account is that confidence is inversely related to complexity. Bayesian rationality should be supplemented with principles based on cognitive complexity.

In this response, we clarify several misunderstandings of the understanding/acceptance principle and defend our specific operationalization of that principle. We reiterate the importance of addressing the problem of rational task construal and we elaborate the notion of computational limitations contained in our target article. Our concept of thinking dispositions as variable intentional-level styles of epistemic and behavioral regulation is explained, as is its relation to the rationality debate. Many of the suggestions of the commentators for elaborating two-process models are easily (...) integrated into our generic dual-process account. We further explicate how we view the relation between System 1 and System 2 and evolutionary and normative rationality. We clarify our attempt to fuse the contributions of the cognitive ecologists with the insights of the original heuristics and biases researchers. (shrink)

Cognitive science typically postulates unconscious mental phenomena, computational or otherwise, to explain cognitive capacities. The mental phenomena in question are supposed to be inaccessible in principle to consciousness. I try to show that this is a mistake, because all unconscious intentionality must be accessible in principle to consciousness; we have no notion of intrinsic intentionality except in terms of its accessibility to consciousness. I call this claim the The argument for it proceeds in six steps. The essential point is that (...) intrinsic intentionality has aspectual shape: Our mental representations represent the world under specific aspects, and these aspectual features are essential to a mental state's being the state that it is. (shrink)

Abstracts of each chapter may be found by typing in your browser search bar, "Jeremy Horne, Managing Complexity Through Social Intelligence: Foundations of the Modern Organic Corporatist State", going to the Springer Publishing website and reading the abstracts for each chapter.

Scholars have wrestled with "consciousness", one writer calling it the "hard problem". Some thirty-plus years after the Towards a Science of Consciousness, we do not seem to be any closer to an answer to "What is consciousness?". Seemingly irresolvable metaphysical problems are addressed by bootstrapping, provisional assumptions, not unlike those used by logicians and mathematicians. I bootstrap with the same ontology and epistemology applicable to everything we apprehend. Here, I argue for a version of the unity of opposites, a form (...) of neutral monism. Something exists because of what it is not; nothing can exist by itself, singularities (analogous to monads), expressing the relationship. Applying this most fundamental law to the consciousness problem, the physical (movement) comes into being simultaneously as the mental (stasis), each displayed by a field that is variegated (ranging from creative to entropic processes). Such is in keeping with how the singularity emerged as our universe, the same form that may account for sub-Planck-scale phenomena. Overall, like the most fundamental law, deep structures are imminent in our universe, both as objects and processes. (shrink)

Scholars have wrestled with "consciousness", a major scholar calling it the "hard problem". Some thirty-plus years after the Towards a Science of Consciousness, we do not seem to be any closer to an answer to "What is consciousness?". Seemingly irresolvable metaphysical problems are addressed by bootstrapping, provisional assumptions, not unlike those used by logicians and mathematicians. I bootstrap with the same ontology and epistemology applicable to everything we apprehend. Here, I argue for a version of the unity of opposites, a (...) form of neutral monism. Something exists because of what it is not; nothing can exist by itself, singularities (analogous to monads), expressing the model. Applying this most fundamental law to the consciousness problem, the physical (movement) comes into being simultaneously as the mental (stasis), each displayed by a field that is variegated (ranging from creative to entropic processes). Such is in keeping with how the singularity emerged as our universe, the same form that may account for sub-Planck-scale phenomena. Overall, like the most fundamental law, deep structures are imminent in our universe, both as objects and processes. (shrink)

It is commonly believed that the role of context cannot be ignored in the analysis of conditionals, and counterfactuals in particular. On truth conditional accounts involving possible worlds semantics, conditionals have been analysed as expressions of relative necessity: “If A, then B” is true at some world w if B is true at all the A-worlds deemed relevant to the evaluation of the conditional at w. A drawback of this approach is that for the evaluation of conditionals with the same (...) antecedents at some world, the same worlds are deemed as relevant for all occasions of utterance. But surely this is inadequate, if shifts of contexts between occasions are to be accounted for. Both the linguistic and logical implications of this defect are discussed, and in order to overcome it a modification of David Lewis’ ordering semantics for counterfactuals is developed for a modified language. I follow Lewis by letting contexts determine comparative similarity assignments, and show that the addition of syntactic context parameters (context indices) to the language gives the freedom required to switch between sets of relevant antecedent worlds from occasion to occasion by choosing the corresponding similarity assignment accordingly. Thus an account that extends Lewis’ analysis of a language containing a single counterfactual connective > to a language containing infinitely many counterfactual connectives >_c, each indexed by a different context name c, overcomes the limitations of traditional analyses. Finally it is also shown that these traditional accounts can be recovered from the modified account if certain contextual restrictions are in place. -/- . (shrink)

This thesis studies the role of conceptual content in inference and reasoning. The first two chapters offer a theoretical and historical overview of the relation between inference and meaning in philosophy and psychology. In particular, a critical analysis of the formality thesis, i.e., the idea that rational inference is a rule-based and topic-neutral mechanism, is advanced. The origins of this idea in logic and its influence in philosophy and cognitive psychology are discussed. Chapter 3 consists of an analysis of the (...) relationship between inference and representation. It is argued that inference has to be studied from a pluralistic per- spective due to its dependence on different formats of representing information. The following four chapters apply conceptual spaces, a formal theory of concepts within cognitive semantics, to three concept-based inference-types. First, an explication of Sellars notion of material inference is advanced. Later, the model is extended to account for nonmonotonic inference by studying the role expectations in reasoning. Finally, a conceptual space-model of category-based induction is presented. This model predicts most of the empirical properties of this psychological phenomenon and subsumes some of the previous theories in psychology. It is stated that the explanatory fruitfulness of this new approach is evidence for the failure of the formality thesis and calls for a unified model of rational inference that puts semantics at center stage. The last chapter of the thesis discusses how inference and concepts interact in scientific reasoning, which makes constant use of hybrid symbolic structures for representing conceptual information. Stephen Toulmin’s notions of method of representation and inferential technique are developed and applied in a case study about the emergence of the notion of instantaneous speed during the passage from geometrical physics to analytical mechanics. It is claimed that this analysis provides support to the pluralistic perspective for theorizing about reasoning. (shrink)

Perhaps there has been no greater opportunity than in this “VOLUME FIFTEEN of our Death And Anti-Death set of anthologies” to write about how might think about life and how to avoid death. There are two reasons to discuss “life”, the first being enhancing our understanding of who we are and why we may be here in the Universe. The second is more practical: how humans meet the physical challenges brought about by the way they have interacted with their environment. (...) Many persons discussing “life” beg the question about what “life” is. Surely, when one discusses how to overcome its opposite, death, they are not referring to another “living” thing such as a plant. There seems to be a commonality, though, and it is this commonality is one needing elaboration. It ostensibly seems to be the boundary condition separating what is completely passive (inert) from what attempts to maintain its integrity, as well as fulfilling other conditions we think “life” has. In our present discussion, there will be a reminder that it by no means has been unequivocally established what life really is by placing quotes around the word, namely, “life”. Consider it a tag representing a bundle of philosophical ideas that will be unpacked in this paper. (shrink)

The representational nature of human cognition and thought in general has been a source of controversies. This is particularly so in the context of studies of unconscious cognition, in which representations tend to be ontologically and structurally segregated with regard to their conscious status. However, it appears evolutionarily and developmentally unwarranted to posit such segregations, as,otherwise, artifact structures and ontologies must be concocted to explain them from the viewpoint of the human cognitive architecture. Here, from a by-and-large Classical cognitivist viewpoint, (...) I show why this segregation is wrong, and elaborate on the need to postulate an ontological and structural continuity between unconscious and conscious representations. Specifically, I hypothesize that this continuity is to be found in the symbolic-based interplay between the syntax and the semantics of thought, and I propose a model of human information processing characterized by the integration of syntactic and semantic representations. (shrink)

Human cognition requires coping with a complex and uncertain world. This suggests that dealing with uncertainty may be the central challenge for human reasoning. In Bayesian Rationality we argue that probability theory, the calculus of uncertainty, is the right framework in which to understand everyday reasoning. We also argue that probability theory explains behavior, even on experimental tasks that have been designed to probe people's logical reasoning abilities. Most commentators agree on the centrality of uncertainty; some suggest that there is (...) a residual role for logic in understanding reasoning; and others put forward alternative formalisms for uncertain reasoning, or raise specific technical, methodological, or empirical challenges. In responding to these points, we aim to clarify the scope and limits of probability and logic in cognitive science; explore the meaning of the explanation of cognition; and re-evaluate the empirical case for Bayesian rationality. (shrink)

Objections to Searle's argument for the Connection Principle and its consequences (Searle 1990a) fall roughly into three categories: (1) those that focus on problems with the _argument_ for the Connection Principle; (2) those that focus on problems in understanding the _conclusion_ of this argument; (3) those that focus on whether the conclusion has the _consequences_ Searle claims for it. I think the Connection Principle is both true and important, but I do not think that Searle's argument establishes it. The problem (...) with the argument is that it either begs the question or proves too much. (shrink)

Contemporary psychologism has been amended for most of the objections by its opponents over a century ago. However, some authors still raise doubts about its ability to account for some peculiar properties of logic. In particular, it is argued that the psychological universality of patterns of inferential behavior is not sufficient to account for the normativity of logic. In this paper, I deal with the issue and offer three alternative solutions that do not rely on mere empirical universality. I will (...) use the works of Laurence Jonathan Cohen, Diego Marconi and Marcello D'Agostino, adapting them for the purpose of defending logical psychologism. I will therefore argue that, although more refined work on the subject is needed, contemporary psychologism has the key resources to retain its place in the philosophical debate on the foundations of logic. (shrink)

Metalogic is an open-ended cognitive, formal methodology pertaining to semantics and information processing. The language that mathematizes metalogic is known as metalanguage and deals with metafunctions purely by extension on patterns. A metalogical process involves an effective enrichment in knowledge as logical statements, and, since human cognition is an inherently logic–based representation of knowledge, a metalogical process will always be aimed at developing the scope of cognition by exploring possible cognitive implications reflected on successive levels of abstraction. Indeed, it is (...) basically impracticable to maintain logic–and–metalogic without paying heed to cognitive theorizing. For it is cognitively irrelevant whether possible conclusions are deduced from some premises before the premises are determined to be true or whether the premises themselves are determined to be true first and, then, the conclusions are deduced from them. In this paper we consider the term metalogic as inherently embodied under the framework referred to as cognitive science and mathematics. We propose a metalogical interpretation of Arrow’s impossibility theorem and, to that end, choice theory is understood as a mental course of action dealing with logic and metalogic issues, in which a possible mathematical approach to model a mental course of action is adopted as a systematic operating method. Nevertheless, if we look closely at the core of Arrow’s impossibility theorem in terms of metalogic, a second fundamental contribution to this framework is represented by the Nash equilibrium. As a result of the foregoing, therefore, we prove the metalogical equivalence between Arrow’s impossibility theorem and the existence of the Nash equilibrium. More specifically, Arrow’s requirements correspond to the Nash equilibrium for finite mixed strategies with no symmetry conditions. To demonstrate this proof, we first verify that Arrow’s set and Nash’s set are isomorphic to each other, both sets being under stated conditions of non–symmetry. Then, the proof is completed by virtue of category theory. Indeed, the two sets are categories that correspond biuniquely to one another and, thus, it is possible to define a covariant functor that preserves their mutual structures. According to this, we show the proof–dedicated metalanguage as a precursor to a special equivalence theorem. (shrink)

The algebra of sets has, basically, two different types of symbols. One type of symbol (∩, ?, +, ?) defines another set from two other sets. A second type of symbol (?, ?, =, ?) makes a proposition about two sets. When the construction of these two types of symbols is based on the same four-dot matrix as the logic symbols described in a previous paper, the three symbol types then dovetail together into a harmonious whole that greatly simplifies derivation (...) in the algebra of sets. (shrink)

Mathematics and logic are indispensable in science, yet how they are deployed and why they are so effective, especially in the natural sciences, is poorly understood. In this paper, I focus on the how by analysing Jean Piaget’s application of mathematics to the empirical content of psychological experiment; however, I do not lose sight of the application’s wider implications on the why. In a case study, I set out how Piaget drew on the stock of mathematical structures to model psychological (...) content, namely, the operations of thought involved in reasoning. In particular, I show how operations of thought form structured wholes that initially resisted modelling by either lattices or groups but could be modelled adequately by modifications of these mathematical structures. Piaget coined the term ‘grouping’ for the modified structure, and I conclude that it represents a non-canonical application of mathematics to the empirical content of experimental psychology. I also touch on the role external factors played in Piaget’s development of the grouping. According to the genetic epistemology conceived by Piaget, the origin of intelligence lies in the biological organism and develops in stages over time, and, via the grouping, Piaget established a genetic relationship between two stages of reasoning. I show how this relationship explains why mathematics and logic fit the psychological content of reasoning whilst simultaneously making their successful deployment in the natural sciences more mysterious. Finally, I turn to the explanation Piaget envisaged for the unreasonable effectiveness of mathematics in the natural sciences and consider some consequences for naturalism and Pythagoreanism. (shrink)

Many contemporary logicians acknowledge a plurality of logical theories and accept that theory choice is in part motivated by logical evidence. However, just as there is no agreement on logical theories, there is also no consensus on what constitutes logical evidence. In this paper, I outline Jean Piaget’s psychological theory of reasoning and show how he used it to diagnose and solve one of the paradoxes of material implication. I assess Piaget’s use of psychology as a source of evidence for (...) logical theory in light of reservations raised by psychologism, and I highlight some ramifications for exceptionalism and anti-exceptionalism about logic by considering his use of psychology as logical evidence in the framework of genetic epistemology, Piaget’s research programme. I conclude that Piaget’s psychological theory of reasoning not only plausibly serves as a source of evidence for logical theory but also makes a strong case for anti-exceptionalism about logic. (shrink)

(2013). Is scientific theory change similar to early cognitive development? Gopnik on science and childhood. Philosophical Psychology: Vol. 26, No. 1, pp. 109-128. doi: 10.1080/09515089.2011.625114.

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal (...) foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

Severity of Test (SoT) is an alternative to Popper's logical falsification that solves a number of problems of the logical view. It was presented by Popper himself in 1963. SoT is a less sophisticated probabilistic model of hypothesis testing than Oaksford & Chater's (O&C's) information gain model, but it has a number of striking similarities. Moreover, it captures the intuition of everyday hypothesis testing.

This paper attempts to investigate five and six-year old children’s ability to formulate logical reasoning. More specifically, our interest focuses on the investigation of young children’s ability to use arguments based on logical reasoning. Can pre-school children build arguments based on logical reasoning such as deductive reasoning, or forms of indirect reasoning? Can teaching contribute to the development of you children’s ability to manipulate logical reasoning in the forms previously mentioned? These are the basic questions we attempt to answer in (...) this paper. Thirteen pre-school children participated in the study. The children were involved in organized dialogues in order to investigate their ability to build logical argumentation. Our findings showed that the children had the ability to use arguments with structures, resembling reasoning found in formal logic such as deductive reasoning, inductive reasoning, as well as reasoning based on the law of excluded middle. (shrink)