Spinoza's philosophy of mind is thought to lack a serious account of consciousness. In this essay I argue that Spinoza's doctrine of ideas of ideas has been wrongly construed, and that once righted it provides the foundation for an account. I then draw out the finer details of Spinoza's account of consciousness, doing my best to defend its plausibility along the way. My view is in response to a proposal by Edwin Curley and the serious objection leveled against it (...) by Margaret Wilson and Jonathan Bennett. (shrink)

Contributors: Steven Barbone, Laurent Bove, Edwin Curley, Valérie Debuiche, Michael Della Rocca, Simon B. Duffy, Daniel Garber, Pascale Gillot, Céline Hervet, Jonathan Israel, Chantal Jaquet, Mogens Lærke, Jacqueline Lagrée, Martin Lin, Yitzhak Y. Melamed, Pierre-François Moreau, Steven Nadler, Knox Peden, Alison Peterman, Charles Ramond, Michael A. Rosenthal, Pascal Sévérac, Hasana Sharp, Jack Stetter, Ariel Suhamy, Lorenzo Vinciguerra.

The study assessed the conceptual understanding and attitude toward fractions of teacher education students in a socio-constructivist learning environment. Specifically, it determined the students’ level of conceptual understanding before and after instruction; verified the types of conceptual changes that occurred; and ascertained the attitude of students toward fractions before and after instruction and its relationship to their levels of understanding. Descriptive-correlational research method was used. Socio-constructivist context-based teaching method was employed to introduce the concept of fractions. Achievement tests and interviews (...) were administered to determine the students’ level of conceptual understanding. Conceptual analysis based on Jensen and Finley’s (1995) method with Tiberghien’s (1994) classification of changes was utilized to describe students’ conceptual understanding and conceptual changes. In order to determine their attitude on fractions, students were asked to answer the socio-constructivist attitude questionnaire. The level of conceptual understanding of teacher education students in fraction was functional misconception and partial understanding before and after instruction, respectively. The type of conceptual change that occurred among teacher education students was change for the better. Socio-constructivist learning more likely to improve students’ attitudes toward fractions; promoted prosocial behavior among students; and tend to increase students’ activeness in the classroom activities as evidenced. (shrink)

This paper has two aims. First, it sets out an interpretation of the relevant logic E of relevant entailment based on the theory of situated inference. Second, it uses this interpretation, together with Anderson and Belnap’s natural deduc- tion system for E, to generalise E to a range of other systems of strict relevant implication. Routley–Meyer ternary relation semantics for these systems are produced and completeness theorems are proven. -/- .

My real position is that logic is a mere sub-branch of rhetoric, but in this paper I only try to show an area of overlap. Certain usages in logical work are metaphorical, and I argue that this has pernicious effects in a discipline assumed strictly literal. Among these pernicious effects are the bizarre and fruitless focus of philosophy of mathematics on the pseudo-problems of foundations and objects. I mostly examine the locution 'logical construction' and a range of associated metaphors. Some (...) sketchy remarks on the history of rhetoric are offered in explanation. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

The potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students' metacognitive awareness and conceptual understanding of integers. A descriptive-correlational method approach was utilized, and it was carried out on 303 seventh-grade students. The data were obtained using a metacognitive awareness inventory and achievement test on (...) integers. It was further revealed that the students have average metacognitive awareness and performed well in the fundamental operation of integers. Follow-up qualitative analysis revealed that students who were high achievers had the best understanding, average achievers had corrected or incomplete understanding, and low achievers had a functional misconception of integers. Moreover, the student's metacognitive awareness was significantly related to their conceptual understanding of integers. This indicates that student's higher-order thinking skills, such as metacognition, are essential since they are associated with building conceptual skills. Thus, teachers should encourage students' metacognitive awareness to improve students' conceptual understanding of integers. The study provides relevant information for educational managers on the potential factors to be considered in improving mathematics education practices, particularly in promoting metacognition among high school students. (shrink)

Mathematics is considered one of the most challenging courses for many elementary pre-service teachers (EPTs). In hopes for improvement, teacher educators have been incorporating a jigsaw strategy to equip future teachers with the necessary competencies. Hence, the study aimed to determine the effectiveness of the jigsaw strategy with EPTs’ level of mathematics achievement and interest in an online cooperative learning environment. The research utilized a pre-experimental design with 40 participants. The researchers used pretest and posttest questions covering fraction operations and (...) a mathematics interest questionnaire before and after the intervention. With the implementation of the jigsaw strategy, results showed that the EPTs’ mathematics achievement improved while their interest in mathematics improved to some extent. Likewise, a significant difference between the pre-and post-intervention concerning the EPTs’ mathematics achievement and interest in mathematics was found. Furthermore, correlation analysis revealed that study time is negatively related to mathematics achievement, as is the overall level of interest in mathematics. These findings imply that a jigsaw strategy is a useful tool in teaching mathematics online. However, several modifications may be considered to recognize that the EPTs’ interest in mathematics varies from one person to another. Teacher education institutions are encouraged to apply this strategy not only for EPTs to increase their mathematical know-hows but also to serve as an example for them to employ in their future teaching careers. (shrink)

There is something puzzling about statistical evidence. One place this manifests is in the law, where courts are reluctant to base affirmative verdicts on evidence that is purely statistical, in spite of the fact that it is perfectly capable of meeting the standards of proof enshrined in legal doctrine. After surveying some proposed explanations for this, I shall outline a new approach – one that makes use of a notion of normalcy that is distinct from the idea of statistical frequency. (...) The puzzle is not, however, merely a legal one. Our unwillingness to base beliefs on statistical evidence is by no means limited to the courtroom, and is at odds with almost every general principle that epistemologists have proposed as to how we ought to manage our beliefs. (shrink)

In this chapter I argue that there are three different senses of 'lie' in Kant's moral philosophy: the lie in the ethical sense (the broadest sense, which includes lies to oneself), the lie in the 'juristic' sense (the narrowest sense, which only includes lies that specifically harm particular others), and the lie in the sense of right (or justice), which is narrower than the ethical sense, but broader than the juristic sense, since it includes all lies told to others, including (...) those who are bent on harming innocent others. (shrink)

A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...) this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more 'big picture' ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics. (shrink)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs’ level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex, socio-economic status, parents’ educational attainment, high school graduated from and subject preference; and their problem-solving skills. The PETs’ problem-solving performance was determined by a problem set consisting of word problems with number sense, measurement, geometry, algebra, and (...) probability. A mixed-method research design was employed. Senior PETs purposively served as a sample where they mostly preferred to teach other subjects than mathematics. PETs who preferred math performed satisfactorily, while prospective teachers who opted for other subjects performed unsatisfactorily. The PETs’ unsatisfactory output indicates the need for remediation to advance the mathematical material skills and enrich the problem-solving abilities of these primary schools' potential teachers. Besides, results showed that subject preference strongly affected and predicted the problem-solving success of the PETs. PETs who preferred to teach mathematics performed significantly better than their counterparts; hence, mathematics as a field of specialization in the Bachelor of Elementary Education program may be considered by teacher education institutions. Further, most PETs displayed lack of problem-solving skills; thus, a Problem-Solving course is recommended for them. (shrink)

According to Kantians, coercion and deception are the two fundamental kinds of wrongdoing. Although this may be true, I wish to argue against two other related assumptions about coercion and deception held by Kantians as well as non-Kantians. One is the assumption that coercion is morally worse than deception, all things being equal. The other is the assumption that whenever coercion is morally permissible, deception is morally permissibe, all things being equal. Both of these assumptions, I argue, are false. Deception (...) is morally worse than coercion, and deception is never morally permissible in virtue of the fact that coercion is morally permissible, whenever coercion is morally permissible. (shrink)

In a recent paper in this journal Duncan Pritchard responds to an objection to the modal account of risk pressed by Ebert, Smith and Durbach ( 2020 ). In this paper, I expand upon the objection and argue that it still stands. I go on to consider a more general question raised by this exchange – whether risk is ‘objective’, or whether it is something that varies from one perspective to another.

In ‘The normative role of knowledge’ (2012), Declan Smithies defends a ‘JK-rule’ for belief: One has justification to believe that P iff one has justification to believe that one is in a position to know that P. Similar claims have been defended by others (Huemer, 2007, Reynolds, forthcoming). In this paper, I shall argue that the JK-rule is false. The standard and familiar way of arguing against putative rules for belief or assertion is, of course, to describe putative counterexamples. My (...) argument, though, won’t be like this – indeed I doubt that there are any intuitively compelling counterexamples to the JK-rule. Nevertheless, the claim that there are counterexamples to the JK-rule can, I think, be given something approaching a formal proof. My primary aim here is to sketch this proof. I will briefly consider some broader implications for how we ought to think about the epistemic standards governing belief and assertion. (shrink)

In the Philippines, improving pre-service math teachers’ critical thinking is receiving increasing attention, emphasizing the importance of tailoring instructional methods to students’ learning approaches for a more equitable environment and enhanced mathematics performance. Thus, this study aimed to determine if the critical thinking disposition subscales (reflective, attentiveness, open-mindedness, organization, perseverance, and intrinsic motivation) and learning approach (deep approach and surface approach) predict the mathematics performance of pre-service math teachers. This study employed a descriptive-correlational research design to randomly selected 125 pre-service (...) math teachers from Central Luzon, Philippines. The survey instruments are administered through the student-educator negotiated CTDs scale, the revised two-factor study process questionnaire, and the 40-item validated test. Using descriptive analysis, findings revealed that preservice mathematics teachers have moderate levels of CTD, most of which use a deep approach and have average mathematics performance. Regression analysis showed that CTD and the deep approach were predictors. Therefore, pre-service mathematics teachers with a higher CTD and a deep approach are likelier to perform better in mathematics. These findings provide valuable insights into enhancing mathematics teacher education. (shrink)

In this paper I investigate whether there are any cases in which it is rational for a person to hold inconsistent beliefs and, if there are, just what implications this might have for the theory of epistemic justification. A number of issues will crop up along the way – including the relation between justification and rationality, the nature of defeat, the possibility of epistemic dilemmas, the importance of positive epistemic duties, and the distinction between transitional and terminal attitudes.

Modal phenomena in general, and modal claims in particular, present a problem for contemporary philosophers. The truth conditions of modal claims differ from those of nonemodal claims. I discuss a widely accepted strategy that posits possible and impossible worlds in order to analyze modal claims and thus systematize our intuitions about modal reality.

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (shrink)

In this paper I draw attention to a peculiar epistemic feature exhibited by certain deductively valid inferences. Certain deductively valid inferences are unable to enhance the reliability of one's belief that the conclusion is true—in a sense that will be fully explained. As I shall show, this feature is demonstrably present in certain philosophically significant inferences—such as GE Moore's notorious 'proof' of the existence of the external world. I suggest that this peculiar epistemic feature might be correlated with the much (...) discussed phenomenon that Crispin Wright and Martin Davies have called 'transmission failure'—the apparent failure, on the part of some deductively valid inferences to transmit one's justification for believing the premises. (shrink)

Recent developments in Continental philosophy have included the emergence of a school of “speculative realism,” which rejects the human-centered orientation that has long dominated Continental thought. Proponents of speculative realism differ on several issues, but many agree on the need for an object-oriented ontology. Some speculative realists identify realism with materialism, while others accord equal reality to objects that are non-material, even fictional. Several thinkers retain a focus on difference, a well-established theme in Continental thought. This paper looks at speculative (...) realism from the perspective of systems theory. Many of the tenets of speculative realism have long been features of systems metaphysics and are expressed clearly in a systems framework. However, some views of some speculative realists differ substantially from systems theoretic ideas. (shrink)

Some random processes, like a series of coin flips, can produce outcomes that seem particularly remarkable or striking. This paper explores an epistemic puzzle that arises when thinking about these outcomes and asking what, if anything, we can justifiably believe about them. The puzzle has no obvious solution, and any theory of epistemic justification will need to contend with it sooner or later. The puzzle proves especially useful for bringing out the differences between three prominent theories; the probabilist theory, the (...) normic theory and a theory recently defended by Goodman and Salow. (shrink)

Recent years have seen an explosion of interest in metaphysical explanation, and philosophers have fixed on the notion of ground as the conceptual tool with which such explanation should be investigated. I will argue that this focus on ground is myopic and that some metaphysical explanations that involve the essences of things cannot be understood in terms of ground. Such ‘essentialist’ explanation is of interest, not only for its ubiquity in philosophy, but for its being in a sense an ultimate (...) form of explanation. I give an account of the sense in which such explanation is ultimate and support it by defending what I call the inessentiality of essence. I close by suggesting that this principle is the key to understanding why essentialist explanations can seem so satisfying. (shrink)

Mathematical modeling offers a promising approach to improving mathematics education. This study aims to determine if the concept of metacognitive awareness in the learning process is associated with mathematical modeling. This study also considers the interaction effect of sex and academic year level on both variables. Focusing the study on preservice elementary teachers might address potential issues and targeted intervention in their preparation program concerning their ability to teach and guide young learners in modeling activities. The research sample includes 140 (...) preservice elementary teachers at Central Luzon State University, Philippines. Data collection used an adapted metacognitive awareness inventory and a validated researcher-made mathematical modeling competency test aligned with the K-12 mathematics curriculum in the Philippines. Results revealed that the preservice elementary teachers had a high metacognitive awareness and mathematical modeling competency, ranging from 22 to 31 out of 36 points. Besides, Factorial ANOVA indicates that academic year level positively affects both variables regardless of sex, and stepwise regression analysis unveiled that information management, declarative knowledge, and planning significantly predict 41.4% of the mathematical modeling competency variance. This suggests that developing metacognitive awareness supports preservice elementary teachers in performing modeling tasks that improve their competency level in mathematics. (shrink)

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. (shrink)

Is it right to convict a person of a crime on the basis of purely statistical evidence? Many who have considered this question agree that it is not, posing a direct challenge to legal probabilism – the claim that the criminal standard of proof should be understood in terms of a high probability threshold. Some defenders of legal probabilism have, however, held their ground: Schoeman (1987) argues that there are no clear epistemic or moral problems with convictions based on purely (...) statistical evidence, and speculates that our aversion to such convictions may be nothing more than an irrational bias. More recently, Hedden and Colyvan (2019, section VI) describe our reluctance to convict on the basis of purely statistical evidence as an ‘intuition’, but suggest that there may be no ‘in principle’ problem with such convictions (see also Papineau, forthcoming, section 6). In this paper, I argue that there is, in some cases, an in principle problem with a conviction based upon statistical evidence alone – namely, it commits us to a precedent which, if consistently followed through, could lead to the deliberate conviction of an innocent person. I conclude with some reflections on the idea that the criminal justice system should strive to maximise the accuracy of its verdicts – and the related idea that we should each strive to maximise the accuracy of our beliefs. (shrink)

In this paper I respond to Marcello Di Bello’s criticisms of the ‘normic account’ of the criminal standard of proof. In so doing, I further elaborate on what the normic account predicts about certain significant legal categories of evidence, including DNA and fingerprint evidence and eyewitness identifications.

In today’s fast-changing educational settings, technology integration offers the opportunity to enhance mathematics instruction. This study determines the significant socio-cognitive factors among preservice mathematics teachers (PMTs) affecting their behavioral intention toward the use of technology. A descriptive-correlational research design was employed with 130 participants. Revised UTAUT construct items and behavioral intention scales were utilized through survey forms. Findings revealed that the participants were more inclined to use technology in their pedagogical approach. The only socio-cognitive factors significantly affecting the participants’ positive (...) inclination to utilize educational technology were performance expectancy, effort expectancy, and social influence. However, when controlling for the effects of the participants’ willingness to use technology, social influence became insignificant. Developing favorable impressions of technology’s effectiveness and ease of use may encourage greater technology integration in mathematics education. (shrink)

In Groenendijk & Stokhof [1989] a system of dynamic predicate logic (DPL) was developed, as a compositional alternative for classical discourse representation theory (DRT ). DPL shares with DRT the restriction of being a first-order system. In the present paper, we are mainly concerned with overcoming this limitation. We shall define a dynamic semantics for a typed language with λ-abstraction which is compatible with the semantics DPL specifies for the language of first-order predicate logic. We shall propose to use this (...) new logical system as the semantic component of a Montague-style grammar (referred to as dynamic Montague grammar, DMG), which will enable us to extend the compositionality of DPL to the subsentential level. Furthermore, we shall extend this analysis also in this sense that we shall add new, dynamic interpretations for logical constants which in DPL were treated in a static fashion. This will substantially increase the descriptive coverage of DMG. (shrink)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox as an argument against the (...) second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

A de minimis risk is defined as a risk that is so small that it may be legitimately ignored when making a decision. While ignoring small risks is common in our day-to-day decision making, attempts to introduce the notion of a de minimis risk into the framework of decision theory have run up against a series of well-known difficulties. In this paper, I will develop an enriched decision theoretic framework that is capable of overcoming two major obstacles to the modelling (...) of de minimis risk. The key move is to introduce, into decision theory, a non-probabilistic conception of risk known as normic risk. (shrink)

In a recent paper, Björn Lundgren and H. Orri Stefánsson (forthcoming) present three objections to normic de minimis expected utility theory (NDEUT) – a decision theoretic framework defended in Smith (2024). In this paper, I respond to these objections and outline some possible ways in which NDEUT might be modified or further developed. Like any de minimis framework, NDEUT employs a risk threshold to sort possibilities into those that must be considered when making a decision, and those that can be (...) legitimately ignored – the so-called ‘de minimis risks’. While this threshold would usually take the form of a probability value, in NDEUT the de minimis risks are identified instead on the basis of their abnormality. In the first section I will set up some of the formalism used in NDEUT and consider Lundgren and Stefánsson’s first objection – which is essentially formal in nature. In the second section I will delve further into the interpretation of NDEUT and consider the second and third objections, which turn on particular examples. (shrink)

I develop a puzzle, the resolution of which, I argue, requires an unfamiliar distinction between two forms or senses of metaphysical modality, each bearing a different relationship to time. In one sense of ‘metaphysically possible’, it is metaphysically possible for it to be a time other than the time it is now; in another sense, this is not metaphysically possible.

This paper outlines a novel solution to the Ship of Theseus puzzle. The solution relies on situations, a philosophical tool used in natural language semantics among other places. The core idea is that what is true is always relative to the situation under consideration. I begin by outlining the problem before briefly introducing situations. I then present the solution: in smaller situations the candidate is identical to Theseus’s ship. But in larger situations containing both candidates these identities are neither true (...) nor false. Finally, I discuss some worries for the view that arise from the nature of identity, and suggest responses. It is concluded that the solution, and the theory that underpins it, are worth further investigation. (shrink)

One of the most intriguing claims in Sven Rosenkranz’s Justification as Ignorance is that Timothy Williamson’s celebrated anti-luminosity argument can be resisted when it comes to the condition ~K~KP—the condition that one is in no position to know that one is in no position to know P. In this paper, I critically assess this claim.

In this paper I defend the claim that justification is closed under conjunction, and confront its most alarming consequence — that one can have justification for believing propositions that are unlikely to be true, given one's evidence.

Causal contextualism holds that sentences of the form ‘c causes e’ have context-sensitive truth-conditions. We consider four arguments invoked by Jonathan Schaffer in favor of this view. First, he argues that his brand of contextualism helps solve puzzles about transitivity. Second, he contends that how one describes the relata of the causal relation sometimes affects the truth of one’s claim. Third, Schaffer invokes the phenomenon of contrastive focus to conclude that causal statements implicitly designate salient alternatives to the cause and (...) effect. Fourth, he claims that the appropriateness of a causal statement depends on what is contextually taken for granted or made salient. We show that causal invariantism can explain these linguistic data at least as well as contextualism. We then argue that pace Schaffer, some causal sentences are always correct and can never be plausibly denied, regardless of the context. (shrink)

In this paper, I list various kinds of ‘plurality’ in philosophical investigations. By plurality, I mean a plurality of methodological criteria which we apply to philosophical phenomena and which are very often incompatible with each other. Any philosophical phenomenon can be approached from different methodological viewpoints and result in utterly different ontological and ideological commitments. In other words, I assume that one philosophical problem can have different solutions which depend on different methodological and theoretical presuppositions. Instead of considering this feature (...) of philosophical theories as a problem, I take this plurality as a natural meta-philosophical result. As an example, I consider impossible phenomena and ways of treating them systematically. (shrink)

Using the KenKen puzzle may improve students’ performance in operating integers. Quasi-experimental research was conducted to determine the effectiveness of this intervention on the performance and attitude of students in a collaborative learning environment. One hundred four purposively selected Grade 7 students in Nueva Ecija served as respondents and the experimentation lasted four days following the K to 12 Learners Manual. An increase in the student’s performance was found after utilizing the KenKen puzzle, where a significant difference between the posttest (...) and pretest was recorded after the four days of utilization of the puzzle. Besides, students’ attitude toward operating integers showed positivity as it is enjoyable, interesting, challenging, and developing creativity and critical thinking. Moreover, a strong relationship was found between the students’ performance and attitude in operating integers. This suggests that the KenKen puzzle helped improve the students’ performance and attitude in operating integers in a collaborative learning environment. (shrink)

Our understanding of subjunctive conditionals has been greatly enhanced through the use of possible world semantics and, more precisely, by the idea that they involve variably strict quantification over possible worlds. I propose to extend this treatment to ceteris paribus conditionals – that is, conditionals that incorporate a ceteris paribus or ‘other things being equal’ clause. Although such conditionals are commonly invoked in scientific theorising, they traditionally arouse suspicion and apprehensiveness amongst philosophers. By treating ceteris paribus conditionals as a species (...) of variably strict conditional I hope to shed new light upon their content and their logic. (shrink)

Any explanation of one fact in terms of another will appeal to some sort of connection between the two. In a causal explanation, the connection might be a causal mechanism or law. But not all explanations are causal, and neither are all explanatory connections. For example, in explaining the fact that a given barn is red in terms of the fact that it is crimson, we might appeal to a non-causal connection between things’ being crimson and their being red. Many (...) such connections, like this one, are general rather than particular. I call these general non-causal explanatory connections 'laws of metaphysics'. In this paper I argue that some of these laws are to be found in the world at its most fundamental level, forming a bridge between fundamental reality and everything else. It is only by admitting fundamental laws, I suggest, that we can do justice to the explanatory relationship between what is fundamental and what is not. And once these laws are admitted, we are able to provide a nice resolution of the puzzle of why there are any non-fundamental facts in the first place. (shrink)

If people believe that some property is true of all members of a class such as sofas, then they should also believe that the same property is true of all members of a conjunctively defined subset of that class such as uncomfortable handmade sofas. A series of experiments demonstrated a failure to observe this constraint, leading to what is termed the inverse conjunction fallacy. Not only did people often express a belief in the more general statement but not in the (...) more specific, but also when they accepted both beliefs, they were inclined to give greater confidence to the more general. It is argued that this effect underlies a number of other demonstrations of fallacious reasoning, particularly in category-based induction. Alternative accounts of the phenomenon are evaluated, and it is concluded that the effect is best interpreted in terms of intensional reasoning [Tversky, A., & Kahneman, D.. Extensional versus intuitive reasoning: the conjunction fallacy in probability judgment. Psychological Review, 90, 293-315.]. (shrink)

Say that two goals are normatively coincident just in case one cannot aim for one goal without automatically aiming for the other. While knowledge and justification are distinct epistemic goals, with distinct achievement conditions, this paper begins from the suggestion that they are nevertheless normatively coincident—aiming for knowledge and aiming for justification are one and the same activity. A number of surprising consequences follow from this—both specific consequences about how we can ascribe knowledge and justification in lottery cases and more (...) general consequences about the nature of justification and the relationship between justification and evidential probability. Many of these consequences turn out to be at variance with conventional, prevailing views. (shrink)

Graham Harman writes that the “basic dualism in the world lies…between things in their intimate reality and things as confronted by other things.” However, dualism implies irreconcilable difference; what Harman points to is better expressed as a dyad, where the two components imply one another and interact. This article shows that systems theory has long asserted the fundamental character of Harman’s dyad, expressing it as the union of internal structure and external function, which correspond exactly to what Levi Bryant, characterizing (...) Harman’s views, refers to as the intra-ontic and the inter-ontic, respectively. After interpreting Harman’s dyad in terms of the ontology of systems theory, the article illustrates his dyad with a variety of examples, including conceptions about truth, ethics, value, and intelligence. The structure–function dyad is a spatial conception of a system as an object. It is usefully augmented with a temporal dimension, expressed in a third component or with an additional orthogonal dyad. Adding a temporal dyad to the structure–function dyad joins the idea of an event and/or process to the idea of an object. (shrink)

This chapter both explains the origins of emotivism in C. K. Ogden and I. A. Richards, R. B. Braithwaite, Austin Duncan-Jones, A. J. Ayer and Charles Stevenson (along with the endorsement by Frank P. Ramsey, and the summary of C. D. Broad), and looks at MacIntyre's criticisms of emotivism as the inevitable result of Moore's attack on naturalistic ethics and his ushering in the fact/value, which was a historical product of the Enlightenment.

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In (...) this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

What might a contemporary philosophical practice after and following Foucault look like? After briefly analyzing Foucault’s rather ambiguous stance towards academic philosophy in his posthumously published Le discours philosophique, we argue for continuing his historico-philosophical practice of diagnosing the present. This means taking up his analytic heuristic (with its three dimensions of power, knowledge and subjectivity) rather than his more concrete diagnostic concepts and the specific historical results they yield. We argue that the common methodological operation on each of the (...) three axis is to shift the perspective from the given legitimacies, norms, identities and selves to their historical, conflict-ridden emergence. Practicing philosophy in this way allows developing Foucauldian contributions in two contemporary philosophical debates: critical ontology and political epistemology. While ontology and epistemology might seem surprising fields to work in for philosophers inspired by and critically loyal to Foucault, we attempt to dispel these reservations and illustrate the stakes in both debates, pointing to the urgent issues of ecological questions and of the problematization of untruths in politics respectively. (shrink)

Are the workings of the international world to be explained scientifically, or are they to be understood through their inward meaning? In Explaining and Understanding International Relations philosopher Martin Hollis and international relations scholar Steve Smith join forces to analyse the dominant theories of international relations and to examine the philosophical issues underlying them. The book has three parts. In the first the authors review the growth of the discipline since 1918, pose the 'level of analysis' problem of whether (...) to account for a sytem in terms of its units or vice versa, and contrast the demand of scientific method with those of interpretative understanding. In the second they apply the contrast to four factors often cited in accounting for international behaviour - the international system, the state, bureaucracies, and decision-making individuals. Rival accounts of the games nations play are offered in readiness for the final part, where the authors propose a theoretical agenda, air their differences, and invite readers to take sides. By tackling deep theoretical issues with lucidity and verve this book will excite debate among theorists and students of international relations while also engaging thought about the philosophical character of the social sciences. (shrink)