Formal criteria of theoretical equivalence are mathematical mappings between specific sorts of mathematical objects, notably including those objects used in mathematical physics. Proponents of formal criteria claim that results involving these criteria have implications that extend beyond pure mathematics. For instance, they claim that formal criteria bear on the project of using our best mathematical physics as a guide to what the world is like, and also have deflationary implications for various debates in the metaphysics of physics. In this (...) paper, I investigate whether there is a defensible view according to which formal criteria have significant non-mathematical implications, of these sorts or any other, reaching a chiefly negative verdict. Along the way, I discuss various foundational issues concerning how we use mathematical objects to describe the world when doing physics, and how this practice should inform metaphysics. I diagnose the prominence of formal criteria as stemming from contentious views on these foundational issues, and endeavor to motivate some alternative views in their stead. (shrink)

For many years I have maintained that I learned to philosophize by translating Francisco Suárez’s Metaphysical Disputation V from Latin into English. This surely is a claim that must sound extraordinary to the members of this audience or even to most twentieth century philosophers. Who reads Suárez these days? And what could I learn from a sixteenth century scholastic writer that would help me in the twentieth century? I would certainly be surprised if one were to find any references to (...) some of Suárez’s works in any of the works of twentieth-century major philosophers. One of the reasons for my claim is the great difficulty I had in figuring out what Suárez’s text means and how to render it understandable to English readers. Translating the text forced me to think in ways that were quite different from those I was used to think in Spanish, my native tongue, or English, my adoptive tongue. In fact, the translation I produced after having completed many drafts continued, and still continues to this day, to appear to me unsatisfactory, and that dissatisfaction was the key to understanding things I had understood very differently before. I hope to make clear why in what follows. The thesis that I defend is that semantic equivalence between texts of philosophy in different languages is difficult, if not impossible in some cases, to achieve and, therefore, that it is a mistake to restrict doing analytic philosophy to English, as Gustavo Rodríguez-Pereyra argues we should do in a recent article (2013). (shrink)

Frege claims that sentences of the form ‘A’ are equivalent to sentences of the form ‘it is true that A’ (The Equivalence Thesis). Frege also says that there are fictional names that fail to refer, and that sentences featuring fictional names fail to refer as a result. The thoughts such sentences express, Frege says, are also fictional, and neither true nor false. Michael Dummett argues that these claims are inconsistent. But his argument requires clarification, since there are two ways (...) The Equivalence Thesis has been formulated, according as the thesis equates the senses or the referents of the relevant sentences. -/- I have two aims in this paper. The first is to demonstrate that a sameness of sense thesis is inconsistent with Frege’s other theses. The second is to argue that a sameness of reference thesis is consistent with them. Thus, all else being equal, Frege ought to endorse a sameness of reference, rather than a sameness of sense thesis. (shrink)

Goethe's objections to Newton's theory of light and colours are better than often acknowledged. You can accept the most important elements of these objections without disagreeing with Newton about light and colours. As I will argue, Goethe exposed a crucial weakness of Newton's methodological self-assessment. Newton believed that with the help of his prism experiments, he could prove that sunlight was composed of variously coloured rays of light. Goethe showed that this step from observation to theory is more problematic than (...) Newton wanted to admit. By insisting that the step to theory is not forced upon us by the phenomena, Goethe revealed our own free, creative contribution to theory construction. And Goethe's insight is surprisingly significant, because he correctly claimed that all of the results of Newton's prism experiments fit a theoretical alternative equally well. If this is correct, then by suggesting an alternative to a well-established physical theory, Goethe developed the problem of underdete... (shrink)

This paper corrects a mistake I saw students make but I have yet to see in print. The mistake is thinking that logically equivalent propositions have the same counterexamples—always. Of course, it is often the case that logically equivalent propositions have the same counterexamples: “every number that is prime is odd” has the same counterexamples as “every number that is not odd is not prime”. The set of numbers satisfying “prime but not odd” is the same as the set of (...) numbers satisfying “not odd but not not-prime”. The mistake is thinking that every two logically-equivalent false universal propositions have the same counterexamples. Only false universal propositions have counterexamples. A counterexample for “every two logically-equivalent false universal propositions have the same counterexamples” is two logically-equivalent false universal propositions not having the same counterexamples. The following counterexample arose naturally in my sophomore deductive logic course in a discussion of inner and outer converses. “Every even number precedes every odd number” is counterexemplified only by even numbers, whereas its equivalent “Every odd number is preceded by every even number” is counterexemplified only by odd numbers. Please let me know if you see this mistake in print. Also let me know if you have seen these points discussed before. I learned them in my own course: talk about learning by teaching! (shrink)

Abstract Theories are metaphysically equivalent just if there is no fact of the matter that could render one theory true and the other false. In this paper I argue that if we are judiciously to resolve disputes about whether theories are equivalent or not, we need to develop testable criteria that will give us epistemic access to the obtaining of the relation of metaphysical equivalence holding between those theories. I develop such ?diagnostic? criteria. I argue that correctly inter-translatable theories (...) are metaphysically equivalent, and what we need are ways of determining whether a putative translation is correct or not. To that end I develop a number of tools we can employ to discern whether a translation is a correct one. (shrink)

I investigate syntactic notions of theoretical equivalence between logical theories and a recent objection thereto. I show that this recent criticism of syntactic accounts, as extensionally inadequate, is unwarranted by developing an account which is plausibly extensionally adequate and more philosophically motivated. This is important for recent anti-exceptionalist treatments of logic since syntactic accounts require less theoretical baggage than semantic accounts.

This paper is concerned with the relation between two notions: that of two solutions or models of a theory being related by a symmetry of the theory and that of solutions or models being physically equivalent. A number of authors have recently discussed this relation, some taking an optimistic view, on which there is a suitable concept of the symmetry of a theory relative to which these two notions coincide, others taking a pessimistic view, on which there is no such (...) concept. The present paper arrives at a cautiously pessimistic conclusion. (shrink)

This paper presents a simple pair of first-order theories that are not definitionally (nor Morita) equivalent, yet are mutually conservatively translatable and mutually 'surjectively' translatable. We use these results to clarify the overall geography of standards of equivalence and to show that the structural commitments that theories make behave in a more subtle manner than has been recognized.

In this paper I discuss the rule of inference proposed by Kuipers under the name of Inference to the Best Theory. In particular, I argue that the rule needs to be strengthened if it is to serve realist purposes. I further describe a method for testing, and perhaps eventually justifying, a suitably strengthened version of it.

The open-domain Frame Problem is the problem of determining what features of an open task environment need to be updated following an action. Here we prove that the open-domain Frame Problem is equivalent to the Halting Problem and is therefore undecidable. We discuss two other open-domain problems closely related to the Frame Problem, the system identification problem and the symbol-grounding problem, and show that they are similarly undecidable. We then reformulate the Frame Problem as a quantum decision problem, and show (...) that it is undecidable by any finite quantum computer. (shrink)

We introduce the notions of syntactic synonymy and referential syn- onymy due to Moschovakis. Those notions are capable of accounting for fine- grained aspects of the meaning of linguistic expressions, by formalizing the Fregean distinction between sense and denotation. We integrate Moschovakis’s theory with the theory of concepts developed in the foundational ontology DOLCE, in order to enable a formal treatment of equivalence between concepts.

Answering a question formulated by Halbach (2009), I show that a disquotational truth theory, which takes as axioms all positive substitutions of the sentential T-schema, together with all instances of induction in the language with the truth predicate, is conservative over its syntactical base.

A standard line in the contemporary philosophical literature has it that physical theories are equivalent only when they agree on their empirical content, where this empirical content is often understood as being encoded in the equations of motion of those theories. In this article, we question whether it is indeed the case that the empirical content of a theory is exhausted by its equations of motion, showing that (for example) considerations of boundary conditions play a key role in the empirical (...) equivalence (or otherwise) of theories. Having argued for this, we show that philosophical claims made by Weatherall (2016) that electromagnetism in the Faraday tensor formalism is equivalent to electromagnetism in the vector potential formalism, and by Knox (2011) that general relativity is equivalent to teleparallel gravity, can both be called into question. We then show that properly considering the role of boundary conditions in theory structure can potentially restore these claims of equivalence and close with some remarks on the pragmatics of adjudications on theory identity. (shrink)

The presence of symmetries in physical theories implies a pernicious form of underdetermination. In order to avoid this theoretical vice, philosophers often espouse a principle called Leibniz Equivalence, which states that symmetry-related models represent the same state of affairs. Moreover, philosophers have claimed that the existence of non-trivial symmetries motivates us to accept the Invariance Principle, which states that quantities that vary under a theory’s symmetries aren’t physically real. Leibniz Equivalence and the Invariance Principle are often seen as (...) part of the same package. I argue that this is a mistake: Leibniz Equivalence and the Invariance Principle are orthogonal to each other. This means that it is possible to hold that symmetry-related models represent the same state of affairs whilst having a realist attitude towards variant quantities. Various arguments have been presented in favour of the Invariance Principle: a rejection of the Invariance Principle is inter alia supposed to cause indeterminism, undetectability or failure of reference. I respond that these arguments at best support Leibniz Equivalence. (shrink)

Our evidence can be about different subject matters. In fact, necessarily equivalent pieces of evidence can be about different subject matters. Does the hyperintensionality of ‘aboutness’ engender any hyperintensionality at the level of rational credence? In this paper, I present a case which seems to suggest that the answer is ‘yes’. In particular, I argue that our intuitive notions of independent evidence and inadmissible evidence are sensitive to aboutness in a hyperintensional way. We are thus left with a paradox. While (...) there is strong reason to think that rational credence cannot make such hyperintensional distinctions, our intuitive judgements about certain cases seem to demand that it does. (shrink)

Reformulating a scientific theory often leads to a significantly different way of understanding the world. Nevertheless, accounts of both theoretical equivalence and scientific understanding have neglected this important aspect of scientific theorizing. This essay provides a positive account of how reformulation changes our understanding. My account simultaneously addresses a serious challenge facing existing accounts of scientific understanding. These accounts have failed to characterize understanding in a way that goes beyond the epistemology of scientific explanation. By focusing on cases in (...) which we have differences in understanding without differences in explanation, I show that understanding does not reduce to explanation. (shrink)

According to the standard interpretation of Einstein’s field equations, gravity consists of mass-energy curving spacetime, and an additional physical force or entity—denoted by Λ (the ‘cosmological constant’)—is responsible for the Universe’s metric-expansion. Although General Relativity’s direct predictions have been systematically confirmed, the dominant cosmological model thought to follow from it—the ΛCDM (Lambda cold dark matter) model of the Universe’s history and composition—faces considerable challenges, including various observational anomalies and experimental failures to detect dark matter, dark energy, or inflation-field candidates. This (...) paper shows that Einstein’s Equivalence Principle entails two possible physical interpretations of General Relativity’s field equations. Although the field equations facially appear to support the standard interpretation—that gravity consists of mass-energy curving spacetime—the field equations can be equivalently understood as holding that gravitational effects instead result from mass-energy accelerating the metric-expansion of a second-order spacetime fabric superimposed upon an absolute, first-order Euclidean space, resulting in the observational appearance of spacetime curvature. This alternative interpretation of relativity is shown to be empirically equivalent to the standard interpretation of relativity, albeit with a changing value for Λ (which is similar to how Λ is understood in the conception of Λ as ‘quintessence’, but in this case takes Λ to be gravity). The reconceptualization is then shown to potentially resolve major observational anomalies for the ΛCDM model, including recent observations conflicting with ΛCDM predictions, as well as failures to directly detect dark matter, dark energy, and inflation field/particle candidates. (shrink)

One disturbing but telling demonstration of how definitions of knowledge can go wrong is due to Hawthorne.[1] Although properly intended as an attack on Dretske’s theory of conclusive reasons, it also works against Nozick’s conditional theory. Hawthorne provides a simple example: suppose, he declaims, that salmon induces hallucinations if eaten in great amounts. Suppose that, to be more precise, were you to eat it in amounts greater than 14 pounds at one go (never mind how that is humanly possible), it (...) could cause you to believe that you’ve only had a few tidbits of the savoury fish. Then, on Dretske’s account, if P is the proposition I ate less than 1 pound of salmon, I could know P. On the other hand, let Q be the proposition I ate less than 14 pounds of salmon. Q is not knowable, because were Q to be false, I might still experience the hallucination that I’ve eaten less than a pound of salmon, and therefore I do not have conclusive reasons for Q. (shrink)

With catastrophic events of «nature» like global warming, arguments emerge that insinuate an equivalence of vulnerability, responsibility or being affected by these catastrophes. Such an alleged equivalence when facing climate catastrophe is already visible, for example, in the notion of the «Anthropocene» itself, which obscures both causes and various vulnerabilities in a homogenized as well as universalized concept of humanity (anthropos). Taking such narratives as a starting point, the paper explores questions about the connection between catastrophe, temporality, and (...) history, following mainly Walter Benjamin, Dipesh Chakrabarty and Jean-Luc Nancy with the goal to provide (1) a critique of the concept «Anthropocene» on the basis of nonequivalence while retaining its key features to still grasp the catastrophic present, (2) an analysis of anthropocenic time and the chronical structure of catastrophe, (3) philosophical considerations on the intersection of catastrophe and history. (shrink)

This paper argues for a particular view about in what metaphysical equivalence consists: namely, that any two metaphysical theories are metaphysically equivalent if and only if those theories are strongly hyperintensionally equivalent. It is consistent with this characterisation that said theories are weakly hyperintensionally distinct, thus affording us the resources to model the content of propositional attitudes directed towards metaphysically equivalent theories in such a way that non-ideal agents can bear different propositional attitudes towards metaphysically equivalent theories.

When are two formal theories of broadly logical concepts, such as truth, equivalent? The paper investigates a case study, involving two well-known variants Kripke-Feferman truth. The first, KF+CONS, features a consistent but partial truth predicate. The second, KF+COMP, an inconsistent but complete truth predicate. It is well-known that the two truth predicates are dual to each other. We show that this duality reveals a much stricter correspondence between the two theories: they are intertraslatable. Intertranslatability under natural assumptions coincides with definitional (...) equivalence, and is arguably the strictest notion of theoretical equivalence different from logical equivalence. The case of KF+CONS and KF+COMP raises a puzzle: the two theories can be proved to be strictly related, yet they appear to embody remarkably different conceptions of truth. We discuss the significance of the result for the broader debate on formal criteria of conceptual reducibility for theories of truth. (shrink)

The equivalence principle between the gravitational motion and the inertial motion is false because a particle or body successively in two any contiguous points while in a gravitational frame they have different kinetic energy, instead they always have equal kinetic energy in an inertial frame.

Context: Consistency of mathematical constructions in numerical analysis and the application of computerized proofs in the light of the occurrence of numerical chaos in simple systems. Purpose: To show that a computer in general and a numerical analysis in particular can add its own peculiarities to the subject under study. Hence the need of thorough theoretical studies on chaos in numerical simulation. Hence, a questioning of what e.g. a numerical disproof of a theorem in physics or a prediction in numerical (...) economics could mean. Method: An algebraic simple model system is subjected to a deeper structure of underlying variables. With an algorithm simulating the steps in taking a limit of second order difference quotients the error terms are studied at the background of their algebraic expression. Results: With the algorithm that was applied to a simple quadratic polynomial system we found unstably amplified round-off errors. The possibility of numerical chaos is already known but not in such a simple system as used in our paper. The amplification of the errors implies that it is not possible with computer means to constructively show that the algebra and numerical analysis will ‘on the long run’ converge to each other and the error term will vanish. The algebraic vanishing of the error term cannot be demonstrated with the use of the computer because the round-off errors are amplified. In philosophical terms, the amplification of the round-off error is equivalent to the continuum hypothesis. This means that the requirement of (numerical) construction of mathematical objects is no safeguard against inference-only conclusions of qualities of (numerical) mathematical objects. Unstably amplified round-off errors are a same type of problem as the ordering in size of transfinite cardinal numbers. The difference is that the former problem is created within the requirements of constructive mathematics. This can be seen as the reward for working numerically constructive. (shrink)

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these (...) paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other. (shrink)

In this article I attempt to show conclusively that the apparent intrinsic difference between causing collateral damage and directly attacking innocents is an illusion. I show how eleven morally irrelevant alterations can transform an apparently permissible case of harming as a side-effect into an apparently impermissible case of harming as a means. The alterations are as obviously irrelevant as the victims’ skin colour, and consistently treating them as relevant would have unacceptable implications for choices between more and less harmful ways (...) of securing greater goods. This shows not only how the principles philosophers have proposed for distinguishing between these cases cannot withstand scrutiny, but how we can be sure that there are no relevant differences yet to be discovered. I conclude by considering reasons to think that there are deontological constraints against harming, but that they apply just as forcefully against collateral harms as they do against intended harms. (shrink)

Purpose of the study: Not all languages have a universal concept of the same object, and this creates problems in translation. This paper aims to examine the semiotic model for equivalence or non-equivalence in translation which attempts to define the semiotic model, to use the model for translation, and to offer the benefits of this model to solving translation’s problem in equivalence and non-equivalence. Methodology: The data of this research are derived from the novel Lelaki Harimau, (...) as the source language and L'homme Tigre, as the target language. This model is used in the Indonesian novel which has been translated into 14 languages, one of which is in French. The authors use a semiotic approach to analyze the equivalence and non-equivalence in the translation. Main Findings: This study reveals that the concept of signified in the semiotic theory proposes two models: the first: translation using the same concept in the source text (ST) and target text (TT), which is broadly known as equivalence, the second: translation using different concept between ST and TT, this called non-equivalence. This article not only explores the issue of meaning contextually in translation, but also the use of the semiotic model in translation which shows that the language perspective depends on the relationship between the sign and the object. Applications of this study: The model for this study can be used not only in translation studies at universities but also in providing supporting data for applied linguistic studies. Novelty/Originality of this study: This study provides a novelty in translation research with a semiotic approach. The contribution of this study is that the semiotics perspective suggests that a sign in the concept level (signified) will not be universal due to different cultural backgrounds. (shrink)

William James declared a moral war, Charles Peirce a metaphysical one: "fall into the ranks then" was his battle cry, follow your colonel. Keep your one purpose steadily and alone in view, and you may promise yourself the attainment of your sole desire, which is to hasten the chariot wheels of redeeming love. (6.448:1893) Peirce's was a war not against war, but against the metaphysical equivalent of war, individuation. In the field of social philosophy, Peirce's enemy appeared under the alias (...) of Darwinism, which Peirce fought with Christian Love. In the field of metaphysics, it appeared under the alias of nominalism, which Peirce fought with his special brand of pragmatic realism. But most challenging of all, the enemy appeared within Peirce's own thought under the alias of what I call Kantian conceptualism, and it took Peirce most of his career to win the battle. (shrink)

Many differences exist between the logical relations “equality” and “equivalence”. In this monograph I point out differences that concern definition, linguistics, computational gates and tables, denotation, application, negation of terms, negation of the relation, relations to other relations, the laws of symmetry, transitivity and reflexivity, the laws of commutation and permutation, the law of tautology, the law of distribution, the law of association, propositional meaning, and “genesis”. I also point out a form of “symmetry breaking”: the negation of some (...) equality may yield some non-equality, while the negation of that non-equality might not yield the same equality. (For full access: use the website link of the title page. -- Copyright License: CC BY-NC-ND. -- DOI: 10.17026/dans-zh3-h2b2 --). (shrink)

This paper is the first part of a three-part project ‘How the principle of energy conservation evolved between 1842 and 1870: the view of a participant’. This paper aims at showing how the new ideas of Mayer and Joule were received, what constituted the new theory in the period under study, and how it was supported experimentally. A connection was found between the new theory and thermodynamics which benefited both of them. Some considerations are offered about the desirability of taking (...) a historical approach to teaching energy and its conservation. (shrink)

We give a complete axiomatization of the identities of the basic game algebra valid with respect to the abstract game board semantics. We also show that the additional conditions of termination and determinacy of game boards do not introduce new valid identities.En route we introduce a simple translation of game terms into plain modal logic and thus translate, while preserving validity both ways, game identities into modal formulae.The completeness proof is based on reduction of game terms to a certain ‘minimal (...) canonical form’, by using only the axiomatic identities, and on showing that the equivalence of two minimal canonical terms can be established from these identities. (shrink)

Review of Meta-Metaphysics: On Metaphysical Equivalence, Primitiveness, and Theory Choice (Springer, Synthese Library, 2016). By Jiri Benovsky.

What is the quantum state of the universe? Although there have been several interesting suggestions, the question remains open. In this paper, I consider a natural choice for the universal quantum state arising from the Past Hypothesis, a boundary condition that accounts for the time-asymmetry of the universe. The natural choice is given not by a wave function but by a density matrix. I begin by classifying quantum theories into two types: theories with a fundamental wave function and theories with (...) a fundamental density matrix. The Past Hypothesis is compatible with infinitely many initial wave functions, none of which seems to be particularly natural. However, once we turn to density matrices, the Past Hypothesis provides a natural choice---the normalized projection onto the Past Hypothesis subspace in the Hilbert space. Nevertheless, the two types of theories can be empirically equivalent. To provide a concrete understanding of the empirical equivalence, I provide a novel subsystem analysis in the context of Bohmian theories. Given the empirical equivalence, it seems empirically underdetermined whether the universe is in a pure state or a mixed state. Finally, I discuss some theoretical payoffs of the density-matrix theories and present some open problems for future research. (Bibliographic note: the thesis was submitted for the Master of Science in mathematics at Rutgers University.). (shrink)

Philosophers of science often assume that logically equivalent theories are theoretically equivalent. I argue that two theses, anti-exceptionalism about logic (which says, roughly, that logic is not a priori, that it is revisable, and that it is not special or set apart from other human inquiry) and logical realism (which says, roughly, that differences in logic reflect genuine metaphysical differences in the world), make trouble for both this commitment and the closely related commitment to theories being closed under logical consequence. (...) I provide three arguments. The first two show that anti-exceptionalism about logic provides an epistemic challenge to both the closure and the equivalence claims; the third shows that logical realism provides a metaphysical challenge to both the closure and the equivalence claims. Along the way, I show that there are important methodological upshots for metaphysicians and philosophers of logic. In particular, there are lessons to be drawn about certain conceptions of naturalism as constraining the possibilities for metaphysics and the philosophy of logic. (shrink)

Henry Shevlin’s paper—“How could we know when a robot was a moral patient?” – argues that we should recognize robots and artificial intelligence (AI) as psychological moral patients if they are cognitively equivalent to other beings that we already recognize as psychological moral patients (i.e., humans and, at least some, animals). In defending this cognitive equivalence strategy, Shevlin draws inspiration from the “behavioral equivalence” strategy that I have defended in previous work but argues that it is flawed in (...) crucial respects. Unfortunately—and I guess this is hardly surprising—I cannot bring myself to agree that the cognitive equivalence strategy is the superior one. In this article, I try to explain why in three steps. First, I clarify the nature of the question that I take both myself and Shevlin to be answering. Second, I clear up some potential confusions about the behavioral equivalence strategy, addressing some other recent criticisms of it. Third, I will explain why I still favor the behavioral equivalence strategy over the cognitive equivalence one. (shrink)

In this article I examine two mathematical definitions of observational equivalence, one proposed by Charlotte Werndl and based on manifest isomorphism, and the other based on Ornstein and Weiss’s ε-congruence. I argue, for two related reasons, that neither can function as a purely mathematical definition of observational equivalence. First, each definition permits of counterexamples; second, overcoming these counterexamples will introduce non-mathematical premises about the systems in question. Accordingly, the prospects for a broadly applicable and purely mathematical definition of (...) observational equivalence are unpromising. Despite this critique, I suggest that Werndl’s proposals are valuable because they clarify the distinction between provable and unprovable elements in arguments for observational equivalence. (shrink)

David Builes presents a paradox concerning how confident you should be that any given member of an infinite collection of fair coins landed heads, conditional on the information that they were all flipped and only finitely many of them landed heads. We argue that if you should have any conditional credence at all, it should be 1/2.

This chapter explores the relationship between knowing-how and skill, as well other success-in-action notions like dispositions and abilities. I offer a new view of knowledge-how which combines elements of both intellectualism and Ryleanism. According to this view, knowing how to perform an action is both a kind of knowing-that (in accord with intellectualism) and a complex multi-track dispositional state (in accord with Ryle’s view of knowing-how). I argue that this new view—what I call practical attitude intellectualism—offers an attractive set of (...) solutions to various puzzles concerning the connections between knowing-how and abilities and skills to perform intentional actions. (shrink)

The theme of this study is about establishing a purely logical theory about the Universe. Logic is the premier candidate for the reality behind phenomena. If there is a final theory, the Universe must be logic itself, called pure logic, elements of which include not only logic and illogic but also logical and illogical manipulations between them. The kernel is the revised law of the excluded middle: between two basic concepts are four possible manipulations, three logical and one illogical, whereas (...) only one is realized. The key parameter for an element is aim, including reason, outcome, and neutrality. When an element is a contradiction, it can be located at three positions: reason, outcome, and manipulation, corresponding to three colors of quark. Thus, there is interaction with the SU(3) symmetry keeping the number of the three elements balanced locally. A proposition without contradiction has two independent aims. When one aim changes, there is interaction with the U(1) symmetry. When two aims change together, there is interaction with the SU(2) symmetry. (shrink)

The Concept of Life and Death of Chuang-tzu have inherited and developed Confucianism and Taoism thoughts, establishing Ontological foundation of "Life - Body", distinguishing the transcendental concept of "Dead Heart" and the empirical concept of "Death Body", as well as proposing the thought of "Equivalence of Life and Death" finally. The logic Reasoning of Chuang-tzu "Equivalence of Life and Death", start from constructing the equal status of "Life" and “Death" from ontological argument. Life and Death then are reduced (...) to be a natural phenomenon to dispel its mystery. With emphasizing the social connotation of life and death, the difference between them has been removed, and finally the Thought experiment of "Chuang-tzu dreaming butterfly" has deepened the idea of "Equivalence of Life and Death". The Ideological Characteristic of the Concept of Life and Death of Chuang-tzu mainly reflects in the aspects of Ontology, Epistemology and Ethical practice. (shrink)

The aim of this paper is to describe and analyze the epistemological justification of a proposal initially made by the biomathematician Robert Rosen in 1958. In this theoretical proposal, Rosen suggests using the mathematical concept of “category” and the correlative concept of “natural equivalence” in mathematical modeling applied to living beings. Our questions are the following: According to Rosen, to what extent does the mathematical notion of category give access to more “natural” formalisms in the modeling of living beings? (...) Is the so -called “naturalness” of some kinds of equivalences (which the mathematical notion of category makes it possible to generalize and to put at the forefront) analogous to the naturalness of living systems? Rosen appears to answer “yes” and to ground this transfer of the concept of “natural equivalence” in biology on such an analogy. But this hypothesis, although fertile, remains debatable. Finally, this paper makes a brief account of the later evolution of Rosen’s arguments about this topic. In particular, it sheds light on the new role played by the notion of “category” in his more recent objections to the computational models that have pervaded almost every domain of biology since the 1990s. (shrink)

We approach the topic of solution equivalence of propositional problems from the perspective of non-constructive procedural theory of problems based on Transparent Intensional Logic (TIL). The answer we put forward is that two solutions are equivalent if and only if they have equivalent solution concepts. Solution concepts can be understood as a generalization of the notion of proof objects from the Curry-Howard isomorphism.

It is shown how the schema of equivalence can be used to obtain short proofs of tautologies A , where the depth of proofs is linear in the number of variables in A .

The notion of space is one of the most discussed within classical physics concepts. The works of Copernicus and Galileo, as well as Gassendi´s ideas led to Newton to regard it as substance. This conception of space, allows the notion of symmetry is present in an indirect or implied, within the laws of physics, formed through the notions of equivalence and balance. The aim of this study is to identify the symmetry, through such notions, under the study of indistinction (...) between the repose state and the state of uniform translational movement known as the law of inertia. The philosophical approach is framed in the link between these notions and the problem of indistinguishability between states of different movement. We will discuss first the conception of space Telesio and Gassendi that led Newton to his absolutist conception of space. The conception of space and its relationship with Newton symmetry is the second part of our work. As a third part present linking of the Newtonian space with notions of balance, symmetry and equivalence. Subsequently they give our conclusions. (shrink)

It is known, despite special theory of relativity has been widely accepted, in our recent draft submitted to this journal it is shown that some experiments have been carried out suggesting superluminal wave propagation, which make Minkowski lightcone not valid anymore. Therefore, it seems worth to reconsider the connection between elastic wave and electromagnetic wave equations, as in their early development. In this paper we will start with Maxwell-Dirac isomorphism, then we will find its connection with elastic wave equations.

The notion of “worth” and “value” throughout human history was only partly dependent on economic reasons. Arrangements about what is considered an equivalent value/measure of wealth are the result of complex interdependencies of economic, social and cultural factors. For thousands of years people have used precious metals as universal equivalent and main measure of wealth; full-value metal money was, in fact, only reinforced by the authority of state (ruler) evidence of presence certain amount of precious metal. The rejection of valuable (...) coins and the provision of banknotes with precious metals (that is, the rejection of the gold and the silver standard) led to the fact that the circulating money signs in the society ceased to denote a concrete value, becoming an abstraction, putting the population in dependence on state’s monetary policy and financial stability of national economy. Bitcoin and its numerous alternatives arose as a response to the challenge of informatization, globalization and individualization of economic activity. This is an attempt to escape from control of state structures that are inclined to abuse their right to issue banknotes and to voluntaristic methods of managing the economy. To some extent, the cryptocurrencies reflect the nostalgia of market participants on the gold standard, which is surprisingly transformed into a complete denial of the materiality (including the metal substance) of money. This situation stimulates the search for new models for designation the equivalent value in the information society. (shrink)

The author has established a mathematical theory about the system of freedom in which components of freedom are ruled by the largest freedom principle, explaining how one invariant reality can be equated with the dynamical universe. Freedom as a whole is the reality, and components of freedom show variable phenomena and become a dynamic system. In freedom, component equality leads to sequence equality; therefore, various sequences coexist in the system. Because there are incompatible sequences for any sequence, the interior of (...) freedom cannot be a static sequence. In order for the system to be a whole, there must be some connecting sequences between any two sequences. Then, at every part of freedom, it is always possible to find a group of three independent sequences that, for most components, is located inside. For the sequence group, there is a sequence through which most components flow in and out. The most abundant three - sequence group and most abundant connecting sequence correspond to the space - time structure. Other incompatible sequences correspond to particles, and interactions between these sequences correspond to interactions between particles. The interactions have some symmetries similar to those in physics, such as SU (3) AND SU (2)×U (1), thus proving the feasibility of the hypothesis: the universe is equivalent with the system of freedom. (shrink)

This paper deals with Austinian ifs of every stripe within classical logic. It is argued that they are truth-functional and the theory of conditional elements is used. Ellipsis is key. Corrects an error in Fulda (2010) in translation and therefore scope. -/- The PDF is made available gratis by the Publisher.

We show in this paper that the answer to the question in the title is in the negative. In modern optics, Snell’s law of reflection is derived using Leibniz’s calculus method that identifies the least time path, chosen by rays of light in going from a given point A, to another given point B, undergoing reflection at a point P on their way. We demonstrate, taking two examples of reflection: (1) at a plane reflector and (2) at elliptical reflector, that (...) Snell’s law of reflection is not a consequence of least time path principle and, that Leibniz’s method of derivation of Snell’s law of reflection is invalid. In (1), we prove that, if a light ray is reflected at point P on a line, along the least time path APB, then at every point Pi on that line, rays from A are reflected to point B, satisfying Snell’s law. However, paths, APB and APiB do not have equal travel times. In (2), we prove that, if a light ray is reflected along the least time path APB, from focus A to focus B incident at point P on an ellipse, satisfies Snell’s law, then points Pi, not lying on the ellipse, also reflect light rays from A to B, satisfying Snell’s law. However, the paths APB and APiB do not have equal travel times. Thus, both examples prove that least time path is not a criterion for reflection and, that Snell’s law of reflection is not a consequence of least time path principle. (shrink)

Realism about quantum theory naturally leads to realism about the quantum state of the universe. It leaves open whether it is a pure state represented by a wave function, or an impure one represented by a density matrix. I characterize and elaborate on Density Matrix Realism, the thesis that the universal quantum state is objective but can be impure. To clarify the thesis, I compare it with Wave Function Realism, explain the conditions under which they are empirically equivalent, consider two (...) generalizations of Density Matrix Realism, and answer some frequently asked questions. I end by highlighting an implication for scientific realism. (shrink)