Transitive inference (TI) refers to social cognition that facilitates the discernment of unknown relationships between individuals using known relationships. It is extensively reported that TI evolves in animals living in a large group because TI could assess relative rank without deducing all dyadic relationships, which averts costly fights. The relationships in a large group become so complex that social cognition may not be developed adequately to handle such complexity. If members apply TI to all possible members in the (...) group, TI requires extremely highly developed cognitive abilities especially in a large group. Instead of developing cognitive abilities significantly, animals may apply simplified TI we call reference TI in this study as heuristic approaches. The reference TI allows members to recognize and remember social interactions only among a set of reference members rather than all potential members. Our study assumes that information processes in the reference TI comprises (1) the number of reference members based on which individuals infer transitively, (2) the number of reference members shared by the same strategists, and (3) memory capacity. We examined how information processes evolve in a large group using evolutionary simulations in the hawk–dove game. Information processes with almost any numbers of reference members could evolve in a large group as long as the numbers of shared reference member are high because information from the others’ experiences is shared. TI dominates immediate inference, which assesses relative rank on direct interactions, because TI could establish social hierarchy more rapidly applying information from others’ experiences. (shrink)

Transitive inference is claimed to be “deductive”. Yet every group/species ever reported apparently uses it. We asked 58 adults to solve five-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible. Response accuracy and RT (non-discriminative nRT ) were measured as is typically done. We also measured RT confined to correct responses ( cRT ). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to (...) premise recall and was not at all evident for nRT ; suggesting the use of non-deductive end-anchor strategies. For overall performance, and particularly the critical B ? D inference, our findings indicate that deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings suggest at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a “dual process” conception of reasoning. Finally, our differing findings for nRT versus cRT suggest that researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held. (shrink)

A key property of relational representations is their generativity: From partial descriptions of relations between entities, additional inferences can be drawn about other entities. A major theoretical challenge is to demonstrate how the capacity to make generative inferences could arise as a result of learning relations from non-relational inputs. In the present paper, we show that a bottom-up model of relation learning, initially developed to discriminate between positive and negative examples of comparative relations, can be extended to make generative inferences. (...) The model is able to make quasi-deductive transitive inferences and to qualitatively account for human responses to generative questions such as “What is an animal that is smaller than a dog?” These results provide evidence that relational models based on bottom-up learning mechanisms are capable of supporting generative inferences. (shrink)

ABSTRACTThis paper provides a naturalistic account of inference. We posit that the core of inference is constituted by bare inferential transitions, transitions between discursive mental representations guided by rules built into the architecture of cognitive systems. In further developing the concept of BITs, we provide an account of what Boghossian [2014] calls ‘taking’—that is, the appreciation of the rule that guides an inferential transition. We argue that BITs are sufficient for implicit taking, and then, to analyse explicit taking, (...) we posit rich inferential transitions, which are transitions that the subject is disposed to endorse. (shrink)

Transitive inference (TI) plays a part in many aspects of reasoning, and is usually assessed using variants on a particular task dubbed the “IP-paradigm”. Advocates of this paradigm assume it ensures that subjects must use deduction to solve the inferential questions. The present task with 63 adults strengthened this claim by removing all possible perceptual cues and limiting as far as possible all cues from the training procedure itself. Response speed and accuracy were measured as premises were learned. (...) Findings show that when over-training and non-logical cues are avoided, adults nevertheless reach high levels of overall performance. However, key indexes of Lexical Marking, Relative-End-Anchoring, and Symbolic Distance are largely absent or in the opposite direction to the generally accepted view at the start of training, and are present only for response time (RT) at the end of training. The widely accepted strategy of retrieval from an integrated mental representation does emerge; but only after an initial associative process and a deductive process. Regarding three comparisons critical for demonstrating deductive TI, the inference was more demanding than its antecedents both in terms of accuracy and RT, and both after initial and final training. Existing theories of TI account for some of these findings, but what is required is a theory accommodating them all. (shrink)

This paper is about four inferences patterns governing conditionals: Transitivity, Simplification, Contraposition, and Antecedent Strengthening. Transitivity, Simplification, and Contraposition are intuitively compelling. Although Antecedent Strengthening may seem less attractive at first, close attention to the full range of data reveals that it too has considerable appeal. An adequate theory of conditionals should account for these facts. The strict theory does so by validating them. But the variably strict theory invalidates them. So the variably strict theorist faces a question: why do (...) we find these inferences so compelling? In this paper, I suggest an answer on her behalf: that they are reasonable inferences in the sense introduced by Stalnaker (1975). -/- . (shrink)

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Moreover, we prove the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases. Finally, we apply our results to study selected (...) probabilistic versions of classical categorical syllogisms and construct a new version of the square of opposition in terms of defaults and negated defaults. (shrink)

The aim of this article is to show that, just like in recent years Cobreros, Égré, Ripley and van Rooij provided a non-transitive counterpart of classical logic (meaning by this that all classically acceptable inferences are valid, but Cut and other metainferences are not) the same can be done for every Tarskian logic, with full generality. In order to establish this fact, we take a semantic approach, by showing that appropriate structures can be devised to characterize a non-transitive (...) counterpart of every Tarskian logic, starting from the logical matrices that are usually taken to render them. (shrink)

We study probabilistically informative (weak) versions of transitivity by using suitable definitions of defaults and negated defaults in the setting of coherence and imprecise probabilities. We represent p-consistent sequences of defaults and/or negated defaults by g-coherent imprecise probability assessments on the respective sequences of conditional events. Finally, we present the coherent probability propagation rules for Weak Transitivity and the validity of selected inference patterns by proving p-entailment of the associated knowledge bases.

Unconscious logical inference seems to rely on the syntactic structures of mental representations (Quilty-Dunn & Mandelbaum 2018). Other transitions, such as transitions using iconic representations and associative transitions, are harder to assimilate to syntax-based theories. Here we tackle these difficulties head on in the interest of a fuller taxonomy of mental transitions. Along the way we discuss how icons can be compositional without having constituent structure, and expand and defend the “symmetry condition” on Associationism (the idea that associative links (...) and transitions are perfectly symmetric). In the end, we show how a BIT (“bare inferential transition”) theory can cohabitate with these other non-inferential mental transitions. (shrink)

This paper offers an interpretation of multiple-conclusion sequents as a kind of meta-inference rule: just as single-conclusion sequents represent inferences from sentences to sentences, so multiple-conclusion sequents represent a certain kind of inference from single-conclusion sequents to single-conclusion sequents. The semantics renders sound and complete the standard structural rules of reflexivity, monotonicity (or thinning), and transitivity (or cut). The paper is not the first one to attempt to account for multiple-conclusion sequents without invoking notions of truth or falsity—but (...) unlike earlier such efforts, which have typically helped themselves to primitive notions of both acceptance and rejection, the present one makes do with the former alone. For technical reasons, the treatment is limited to sequents with non-empty succedents. (shrink)

John Post has argued that the traditional regress argument against nonfoundational justificatory structures does not go through because it depends on the false assumption that “justifies” is in general transitive. But, says Post, many significant justificatory relations are not transitive. The authors counter that there is an evidential relation essential to all inferential justification, regardless of specific inference form or degree of carried-over justificatory force, which is in general transitive. They respond to attempted counterexamples to transitivity (...) brought by Watkins and Salmon as well as to Post’s, arguing that none of these counterexamples apply to the relation they are describing. Given the revived transitivity assumption using this relation, the regress argument does indeed demonstrate the need for foundational stopping points in inferential justification. (shrink)

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A causes B and B causes (...) C, that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (shrink)

John Post has argued that the traditional regress argument against nonfoundational justificatory structures does not go through because it depends on the false assumption that “justifies” is in general transitive. But, says Post, many significant justificatory relations are not transitive. The authors counter that there is an evidential relation essential to all inferential justification, regardless of specific inference form or degree of carried-over justificatory force, which is in general transitive. They respond to attempted counterexamples to transitivity (...) brought by Watkins and Salmon as well as to Post’s, arguing that none of these counterexamples apply to the relation they are describing. Given the revived transitivity assumption using this relation, the regress argument does indeed demonstrate the need for foundational stopping points in inferential justification. (shrink)

John Post has argued that the traditional regress argument against nonfoundational justificatory structures does not go through because it depends on the false assumption that “justifies” is in general transitive. But, says Post, many significant justificatory relations are not transitive. The authors counter that there is an evidential relation essential to all inferential justification, regardless of specific inference form or degree of carried-over justificatory force, which is in general transitive. They respond to attempted counterexamples to transitivity (...) brought by Watkins and Salmon as well as to Post’s, arguing that none of these counterexamples apply to the relation they are describing. Given the revived transitivity assumption using this relation, the regress argument does indeed demonstrate the need for foundational stopping points in inferential justification. (shrink)

A thought process is an unfolding causal chain. Some thoughts cause others in virtue of their contents. Paradigmatic cases of personal level inference involve something more, some kind of appreciation or feeling that the conclusion follows from the premises. First- order processes are inadequate to account for the phenomenon. Attempts to capture the additional ingredient in terms of second-order beliefs have proven problematic. An intermediate position has, however, been overlooked. The extra ingredient could be an epistemic feeling, a form (...) of procedural metacognition. Extensive psychological research has shown that epistemic feelings are involved in monitoring many kinds of cognitive process, affecting how the processes unfold. Inferences may be no different. Inferences are also plausibly accompanied by an epistemic feeling, something like a feeling of reliability or unreliability. Such a feeling accounts for the phenomenological datum. It can also play a significant epistemic role for the thinker. (shrink)

This paper is about two controversial inference-patterns involving counterfactual or subjunctive conditionals. Given a plausible assumption about the truth-conditions of counterfactuals, it is shown that one can't go wrong in applying hypothetical syllogism (i.e., transitivity) so long as the set of worlds relevant for the conclusion is a subset of the sets of worlds relevant for the premises. It is also shown that one can't go wrong in applying antecedent strengthening so long as the set of worlds relevant for (...) the conclusion is a subset of that for the premise. These results are then adapted to Lewis's theory of counterfactuals. (shrink)

The ‘Major Transitions in Evolution’ framework has emerged as the dominant paradigm for understanding the origins of life's hierarchical organization, but it has been criticized on the grounds that it lacks theoretical unity, that is, that the events included in the framework do not constitute a coherent category. I agree with this criticism, and I argue that the best response is to modify the framework so that the events it includes do comprise a coherent category, one whose members share fundamental (...) similarities. Specifically, I recommend defining major transitions as all those, and only those, events and processes that result in the emergence of a new population of evolutionary individuals. Two sorts of change will be required to achieve this. First, events and processes that do not meet this criterion, such as the origins of the genetic code and of human language, should be excluded. Second, events and processes that do meet the criterion, but which have generally been neglected, should be included. These changes would have the dual benefits of making MTEs a philosophically coherent category and of increasing the sample size on which we may infer trends and general principles that may apply to all MTEs. (shrink)

The present paper focuses on the heuristic selection process preceding the actual transitive reasoning process. A part of the difficulty of transitive reasoning lies in the selection of the relevant problem aspects. Two experiments are presented using the paradigm introduced by Markovits, Dumas, and Malfait (1995), in which children were asked to make “higher than” inferences about arrays of coloured blocks. In order to discriminate between genuine transitive inference and a simple strategy of relative position, Markovits (...) et al. interspersed white blocks with the coloured blocks, such that the relative position strategy leads to erroneous responses. However, we argue that the white blocks cause confusion due to their ambiguity, which interferes with the heuristic selection process. Two methodological adaptations were introduced, which are hypothesised to facilitate the selection process and improve transitive reasoning: (1) the white blocks were replaced by coloured blocks, and (2) a less abstract context was added to the experimental design. The colour manipulation leads to a clear increase in the use of a transitive strategy by 9-year-old children; 8-year-old children mainly used the relative position strategy. When adding a context story, 9-year-old children used the transitive strategy regardless of the colour of the interspersed blocks. The overall performance of 8-year-olds improved slightly. These results are interpreted as support for a dual-process model of transitive reasoning. (shrink)

In this work we review the formalism used in describing the thermodynamics of first-order phase transitions from the point of view of maximum entropy inference. We present the concepts of transition temperature, latent heat and entropy difference between phases as emergent from the more fundamental concept of internal energy, after a statistical inference analysis. We explicitly demonstrate this point of view by making inferences on a simple game, resulting in the same formalism as in thermodynamical phase transitions. We (...) show that analogous quantities will inevitably arise in any problem of inferring the result of a yes/no question, given two different states of knowledge and information in the form of expectation values. This exposition may help to clarify the role of these thermodynamical quantities in the context of different first-order phase transitions such as the case of magnetic Hamiltonians. (shrink)

This paper offers a brief analysis of the unification problem in modal transitive logics related to the logic S4 : S4 itself, K4, Grz and Gödel-Löb provability logic GL . As a result, new, but not the first, algorithms for the construction of ‘best’ unifiers in these logics are being proposed. The proposed algorithms are based on our earlier approach to solve in an algorithmic way the admissibility problem of inference rules for S4 and Grz . The first (...) algorithms for the construction of ‘best’ unifiers in the above mentioned logics have been given by S. Ghilardi in [ 16 ]. Both the algorithms in [ 16 ] and ours are not much computationally efficient. They have, however, an obvious significant theoretical value a portion of which seems to be the fact that they stem from two different methodological approaches. (shrink)

ABSTRACTWhile extant replies to Jonathan Schaffer’s putative counterexamples to the transitivity of grounding have made significant strides against the charge of transitivity failure, the replies pay insufficient attention to the common structure of the counterexamples, overlooking a deeper structural feature that contributes to their prima facie plausibility. Putative counterexamples to the transitivity of grounding, I argue, trade on the distinction between what I call ‘rigid’ and ‘non-rigid’ grounding, and confusion over how rigid and non-rigid grounding react when combined pumps the (...) intuition that the counterexamples’ chained conclusions are false. The rigid/non-rigid grounding distinction also reveals plausible weakening inference rules that have been overlooked in treatments of the logic of grounding. (shrink)

The idea that reasoning is a singular accomplishment of the human species has an ancient pedigree.Yet this idea remains as controversial as it is ancient. Those who would deny reasoning to nonhuman animals typically hold a language-based conception of inference which places it beyond the reach of languageless creatures. Others reject such an anthropocentric conception of reasoning on the basis of similar performance by humans and animals in some reasoning tasks, such as transitive inference. Here, building on (...) the modal similarity theory of Vigo [J Exp Theor Artif Intell, 2008 (in press)], we offer an account in which reasoning depends on a core suite of subsymbolic processes for similarity assessment, discrimination, and categorization. We argue that premise-based inference operates through these subsymbolic processes, even in humans. Given the robust discrimination and categorization abilities of some species of nonhuman animals, we believe that they should also be regarded as capable of simple forms of inference. Finally, we explain how this account of reasoning applies to the kinds of transitive inferences that many nonhuman animals display. (shrink)

This paper in revised form appears in Facta Philosophica 5:1 (2003) 49­75. It addresses some problems about intensional transitives raised by Moltmann and Zimmerman, corrects some oversights in my paper in The Proceedings of the Aristotelian Society (S.V. for 2002), and adds new material on binary vs. tripartite construals of “relational/notional”, bridge inferences, weakening inferences, and the relevance problem. Its other sections are, like the PASS paper, concerned with the conjunctive force of disjunctive NP complements of intensional transitive verbs: (...) “Smith needs a good lawyer or a friendly judge” on its normal reading implies both “a good lawyer could help him” AND “a friendly judge could help him”. The reading on which “Smith needs a good lawyer or a friendly judge” is implied just by “Smith needs a good lawyer” (and so doesn’t imply a friendly judge could help him) is much less preferred, except when the disjunction is followed by a coda such as “and he doesn’t care which”. (shrink)

[Graeme Forbes] In I, I summarize the semantics for the relational/notional distinction for intensional transitives developed in Forbes. In II-V I pursue issues about logical consequence which were either unsatisfactorily dealt with in that paper or, more often, not raised at all. I argue that weakening inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a gorgon', are valid, but that disjunction inferences, such as 'Perseus seeks a mortal gorgon, therefore Perseus seeks a mortal gorgon or an immortal (...) gorgon', are invalid. Since 'a gorgon' and 'a mortal gorgon or an immortal gorgon' are extensionally and intensionally the same quantifier, it is not completely trivial to arrange the semantics of intensional transitives so that this classification of the inferences is obtained. ; the latter will be incorporated into a forthcoming monograph, Attitude Problems.) /// [Jennifer Saul ] This paper discusses the question of which verbs are intensional transitives. In particular, I ask which verbs Forbes should take to be intensional transitives. I argue that it is very difficult to arrive at a clear and plausible understanding of what an intensional transitive is-making it difficult to answer these questions. I end by briefly raising some questions about the usefulness of the category of intensional transitives. (shrink)

In the recent paper “Naive modus ponens”, Zardini presents some brief considerations against an approach to semantic paradoxes that rejects the transitivity of entailment. The problem with the approach is, according to Zardini, that the failure of a meta-inference closely resembling modus ponens clashes both with the logical idea of modus ponens as a valid inference and the semantic idea of the conditional as requiring that a true conditional cannot have true antecedent and false consequent. I respond on (...) behalf of the non-transitive approach. I argue that the meta-inference in question is independent from the logical idea of modus ponens, and that the semantic idea of the conditional as formulated by Zardini is inadequate for his purposes because it is spelled out in a vocabulary not suitable for evaluating the adequacy of the conditional in semantics for non-transitive entailment. I proceed to generalize the semantic idea of the conditional and show that the most popular semantics for non-transitive entailment satisfies the new formulation. (shrink)

In 2006, Perruchet and Pacton (2006) asked whether implicit learning and statistical learning represent two approaches to the same phenomenon. This article represents an important follow‐up to their seminal review article. As in the previous paper, the focus is on the formation of elementary cognitive units. Both approaches favor different explanations on what these units consist of and how they are formed. Perruchet weighs up the evidence for different explanations and concludes with a helpful agenda for future research.

According to William Craig, the notion of explanatory priority is the Achilles' heel of Robert Adams' argument against Molinism. Specifically, Craig contends that (1) the notion of explanatory priority is employed equivocally in the argument; (2) Adams is guilty of conflating reasons and causes; and (3) one of the intermediate conclusions of the argument is invalidly inferred, as can be seen by a counterexample. I argue that Craig is mistaken on all counts, and that Adams' argument emerges unscathed.

I present a novel approach to the scholarly debate that has arisen with respect to the philosophical import one should infer from scientific accounts of phase transitions by appealing to a distinction between representation understood as denotation, and faithful representation understood as a type of guide to ontology. It is argued that the entire debate is misguided, for it stems from a pseudo-paradox that does not license the type of claims made by scholars and that what is really interesting about (...) phase transitions is the manner by which they force us to rethink issues regarding scientific representation, idealizations, and realism. (shrink)

We investigate the general properties of general Bayesian learning, where “general Bayesian learning” means inferring a state from another that is regarded as evidence, and where the inference is conditionalizing the evidence using the conditional expectation determined by a reference probability measure representing the background subjective degrees of belief of a Bayesian Agent performing the inference. States are linear functionals that encode probability measures by assigning expectation values to random variables via integrating them with respect to the probability (...) measure. If a state can be learned from another this way, then it is said to be Bayes accessible from the evidence. It is shown that the Bayes accessibility relation is reflexive, antisymmetric and non-transitive. If every state is Bayes accessible from some other defined on the same set of random variables, then the set of states is called weakly Bayes connected. It is shown that the set of states is not weakly Bayes connected if the probability space is standard. The set of states is called weakly Bayes connectable if, given any state, the probability space can be extended in such a way that the given state becomes Bayes accessible from some other state in the extended space. It is shown that probability spaces are weakly Bayes connectable. Since conditioning using the theory of conditional expectations includes both Bayes’ rule and Jeffrey conditionalization as special cases, the results presented generalize substantially some results obtained earlier for Jeffrey conditionalization. (shrink)

Young children routinely display a naturalistic understanding of the world. When asked for explanations, they rarely invoke supernatural or religious explanations even when confronted by puzzling or unexpected phenomena. Nevertheless, depending on the surrounding culture, children are eventually prone to accept God as a creator, to believe in the power of prayer and to expect there to be an afterlife. A plausible interpretation of this dual stance is that children adopt two different cognitive routes to understanding: one grounded in empirical (...) observation and in trusted testimony about the observable world. Based on this route, children gradually build up a common-sense understanding of various natural domains, including the physical, the biological and the psychological. The second route is grounded in children’s early emerging ability to engage in shared pretense. As members of a religious community, children will routinely observe community members engage in activities, such as prayer, which cannot be readily understood in terms of their standard, common-sense framework. Nevertheless, children can charitably interpret prayer as special form of communication, directed at an imagined interlocutor. Cumulative exposure to such belief-based activities is likely to encourage children to transition from charitable interpreters of religious activities to participant believers. (shrink)

Applying Snyder and Feldman's 1984 consolidation‐transition model to moral judgement development has enabled further understanding of how moral judgement translates to moral functioning. In this study, 178 college students were identified as being in consolidated versus transitional phases of moral judgement development using Rest's Defining Issues Test (DIT). Participant moral functioning was inferred through an honest decision‐making index along with Attitudes Towards Human Rights Inventory (ATHRI) and Volunteer Functions Inventory (VFI) scores. Multivariate Analyses of Variance revealed that the consolidated group (...) was significantly more honest than the transitional group. No differences attributable to moral judgement phase were seen for ATHRI and VFI scores. Findings support the claim that consolidated phases improve the explanatory power of moral judgement for certain moral functional outcomes—particularly those involving ambiguity and minimal time for decision‐making. (shrink)

Inductive reasoning is fundamental to human cognition, yet it remains unclear how we develop this ability and what might influence our inductive choices. We created novel categories in which crucial factors such as domain and category structure were manipulated orthogonally. We trained 403 4–9-year-old children to categorise well-matched natural kind and artefact stimuli with either featural or relational category structure, followed by induction tasks. This wide age range allowed for the first full exploration of the developmental trajectory of inductive reasoning (...) in both domains. We found a gradual transition from perceptual to categorical induction with age. This pattern was stable across domains, but interestingly, children showed a category bias one year later for relational categories. We hypothesise that the ability to use category information in inductive reasoning develops gradually, but is delayed when children need to process and apply more complex category structures. (shrink)

According to neoclassical growth theory, there are two main patterns of economic growth, namely, intensive growth, which depends on total factor productivity, and extensive growth, which relies on factor input. This study explores the impacts of property taxes on growth patterns by considering the property tax pilots in Shanghai and Chongqing as a quasi-natural experiment. For evaluation, we applied multiple causal inference methods, including DID, PSM-DID, and a panel data approach for program evaluation. We found that the pilot of (...) Shanghai contributed to intensive growth, while the pilot of Chongqing reinforced the prevailing extensive growth. Specifically, Shanghai's property taxes restricted the buying of multiple homes and oversized homes, thereby reducing house prices and increasing TFP. Chongqing's property taxes are mainly for high-end houses, causing the substitution effect between high-end homes and ordinary houses; thus, the pilot increased the prices of ordinary houses and the average house price, which stimulated factor input and economic growth but decreased TFP. This study provides empirical evidence of the causal relationships between property taxes and growth patterns, indicating that transitional economies should avoid narrow tax bases during property tax reform for intensive growth. (shrink)

1. There is only one rule of inference, modus ponens. This is true both in the presentations of Begriffsschrift and Grundgesetze. There are other ways of making transitions between propositions in proofs, but these are never labeled by Frege “rules of inference.” These pertain to scope of quantification, parsing of formulas, introduction of definitions, conventions for the use and replacement of the various letters, and certain structural reorganizations, ; cf. the list in Gg §48.

In a series of publications E.J. Lowe has advocated an attractive alternative to the orthodox view about conditionals embodied in the Stalnaker-Lewis approach. One alleged advantage of Lowe’s approach over its rival is that it offers the prospect of a simpler conditional logic. Another related advantage is that it appears to treat inference by transitivity more plausibly than does the Stalnaker-Lewis approach. One central goal of this paper is to call into question Lowe’s success in providing an account that (...) is better than the Stalnaker-Lewis account in these respects. As part of this, I develop a Loweian-inspired account of sufficient condition sentences such as ‘Harry’s eating this apple is a sufficient condition for his getting sick’, which is another central goal of the paper. (shrink)

In a series of publications E.J. Lowe has advocated an attractive alternative to the orthodox view about conditionals embodied in the Stalnaker-Lewis approach. One alleged advantage of Lowe’s approach over its rival is that it offers the prospect of a simpler conditional logic. Another related advantage is that it appears to treat inference by transitivity more plausibly than does the Stalnaker-Lewis approach. One central goal of this paper is to call into question Lowe’s success in providing an account that (...) is better than the Stalnaker-Lewis account in these respects. As part of this, I develop a Loweian-inspired account of sufficient condition sentences such as ‘Harry’s eating this apple is a sufficient condition for his getting sick’, which is another central goal of the paper. (shrink)

Protein redox reactions are one of the most basic and important biochemical actions. As amino acids are weak redox mediators, most protein redox functions are undertaken by protein cofactors, which include organic ligands and transition metal ions. Since both kinds of redox cofactors were available in the pre‐protein RNA world, it is challenging to explore which one was more involved in redox processes of primitive proteins? In this paper, using an examination of the redox cofactor usage of putative ancient proteins, (...) we infer that organic ligands participated more frequently than transition metals in redox reactions of primitive proteins, at least as protein cofactors. This is further supported by the relative abundance of amino acids in the primordial world. Supplementary material for this article can be found on the BioEssays website. BioEssays 30:766–771, 2008. © 2008 Wiley Periodicals, Inc. (shrink)

Logically, weighting is transitive, but similarity is not, so clustering cannot be either. Entailments must help a child to review attribute lists more efficiently. Children's understanding of exceptions to generic claims precedes their ability to articulate explanations. So agency, as enabling constraint, may show coherent covariation with attributes, as mere extensional, observable effect of intensional entailments.

Logically, weighting is transitive, but similarity is not, so clustering cannot be either. Entailments must help a child to review attribute lists more efficiently. Children's understanding of exceptions to generic claims precedes their ability to articulate explanations. So agency, as enabling constraint, may show coherent covariation with attributes, as mere extensional, observable effect of intensional entailments.

Probability updating via Bayes' rule often entails extensive informational and computational requirements. In consequence, relatively few practical applications of Bayesian adaptive control techniques have been attempted. This paper discusses an alternative approach to adaptive control, Bayesian in spirit, which shifts attention from the updating of probability distributions via transitional probability assessments to the direct updating of the criterion function, itself, via transitional utility assessments. Results are illustrated in terms of an adaptive reinvestment two-armed bandit problem.