It is often argued that fully structural theories of truth and related notions are incapable of expressing a nonstratified notion of defectiveness. We argue that recently much-discussed non-contractive theories suffer from the same expressive limitation, provided they identify the defective sentences with the sentences that yield triviality if they are assumed to satisfy structural contraction.

An important question for proponents of non-contractive approaches to paradox is why contraction fails. Zardini offers an answer, namely that paradoxical sentences exhibit a kind of instability. I elaborate this idea using revision theory, and I argue that while instability does motivate failures of contraction, it equally motivates failure of many principles that non-contractive theorists want to maintain.

It has been claimed that contracting connectivesContracting connective are conditionalsConditional. Our modest aim here is to show that the conditional-like features of a contracting connectiveContracting connective depend on the defining features of the conditionalConditional in a particular logic, yes, but they also depend on the underlying notion of logical consequence and the structure of the collection of truth values. More concretely, we will show that under P-consequenceP-consequence and suitable satisfiability conditions for the conditionalConditional, conjunctionsConjunction are contracting connectivesContracting connective for (...) some logics without thereby being conditional-ish. (shrink)

The goal of the paper is to discuss whether substructural non-contractive accounts of the truth-theoretic paradoxes can be philosophically motivated. First, I consider a number of explanations that have been offered to justify the failure of contraction and I argue that they are not entirely compelling. I then present a non-contractive theory of truth that I’ve proposed elsewhere. After looking at some of its formal properties, I suggest an explanation of the failure of structural contraction that (...) is compatible with it. (shrink)

In this article I take up John Rawls's invitation to investigate the capacity of a given comprehensive ethical doctrine to endorse on principled grounds the liberal terms of social cooperation. In the case of Islamic political ethics, however, far more is at stake in affirming citizenship in a (non-Muslim) liberal democracy than state neutrality and individual autonomy. Islamic legal and political traditions have traditionally held that submission to non-Muslim political authority and bonds of loyalty and solidarity with non-Muslim societies are (...) to be avoided. In this article, I examine the Islamic foundations for affirming on principled grounds residence, political obligation and loyalty to a non-Muslim state. My research shows not only that such grounds exist even in classical Islamic legal discourses, but also that the concerns of Islamic scholars vindicate political liberalism's claim to successfully accommodate the adherents of certain non-liberal doctrines by refraining from proclaiming controversial metaphysical truth-claims. (shrink)

The concept of truth arguably plays a central role in many areas of philosophical theorizing. Yet, what seems to be one of the most fundamental principles governing that concept, i.e. the equivalence between P and , is inconsistent in full classical logic, as shown by the semantic paradoxes. I propose a new solution to those paradoxes, based on a principled revision of classical logic. Technically, the key idea consists in the rejection of the unrestricted validity of the structural principle (...) of contraction. I first motivate philosophically this idea with the metaphysical picture of the states-of-affairs expressed by paradoxical sentences as being distinctively . I then proceed to demonstrate that the theory of truth resulting from this metaphysical picture is, in many philosophically interesting respects, surprisingly stronger than most other theories of truth endorsing the equivalence between P and (for example, the theory vindicates the validity of the traditional laws of excluded middle and of non-contradiction, and also vindicates the traditional constraint of truth preservation on logical consequence). I conclude by proving a cutelimination theorem that shows the consistency of the theory. (shrink)

Logicians interested in naive theories of truth or set have proposed logical frameworks in which classical operational rules are retained but structural rules are restricted. One increasingly popular way to do this is by restricting transitivity of entailment. This paper discusses a series of logics in this tradition, in which the transitivity restrictions are effected by a determinacy constraint on assumptions occurring in both the major and minor premises of certain rules. Semantics and proof theory for 3-valued, continuum-valued and (...) surreal-valued semantics are given and the proof theory for the systems outlined. The framework is robust in the sense that no conditional, defined or primitive, which sustains the contraction principles underlying Curry paradoxes can be expressed. Classical recapture is smoothly achievable in the system which however is expressively limited and not semantically closed. The conclusion considers the issue of how to extend the system to capture full naive set theory. (shrink)

A logic is said to be contraction free if the rule from A→(A→B) to A→B is not truth preserving. It is well known that a logic has to be contraction free for it to support a non-trivial naïve theory of sets or of truth. What is not so well known is that if there is another contracting implication expressible in the language, the logic still cannot support such a naïve theory. A logic is said to be robustly contraction (...) free if there is no such operator expressible in its language. We show that a large class of finitely valued logics are each not robustly contraction free, and demonstrate that some other contraction free logics fail to be robustly contraction free. Finally, the sublogics of Łω (with the standard connectives) are shown to be robustly contraction free. (shrink)

This article outlines two models of constructing contract theory: The impinging model (based on metaethical cognitivism), which gives central place to truth and justification; and the projectivist model (based on metaethical non-cognitivism), which gives central place to attitudes and motivation. It is argued that modern contract theories which typically seek to present the whole body of contract doctrine as deducible from, and morally justifiable by, one or a small number of apex principles, presuppose the impinging model. By contrast, a (...) projectivist approach to theory creation does not purport to offer justificatory apex principles, but rather argues for propositions that are likely to have maximum motivational purchase in the practical reasoning of contract law’s subjects. The article then goes on to point out the theoretical cost of the impinging model and argues that projectivist accounts do a better job of accommodating the internal point of view of contract law’s subjects. (shrink)

This article connects François Laruelle's non-philosophical experiments with the axiomatic method to non-philosophy's anti-hermeneutic stance. Focusing on two texts from 1987 composed using the axiomatic method, "The Truth According to Hermes" and "Theorems on the Good News," I demonstrate how non-philosophy utilizes structural mechanisms to both expand and contract the field of potential models allowed by non-philosophy. This demonstration involves developing a notion of interpretation, which synthesizes Rocco Gangle's work on model theory with respect to non-philosophy with Laruelle's critique (...) of hermeneutics. I use Alexander Galloway's interpretation of "The Truth According to Hermes" as a case study of the limits non-philosophy sets upon its use as a basis for philosophical models, in contrast to arguments by Gangle regarding non-philosophy's greater genericity in comparison to philosophy. (shrink)

Closure is the idea that what is true about a theory of truth should be true in it. Commitment to closure under truth motivates non-classical logic; commitment to closure under validity leads to substructural logic. These moves can be thought of as responses to revenge problems. With a focus on truth in mathematics, I will consider whether a noncontractive approach faces a similar revenge problem with respect to closure under provability, and argue that if a noncontractive theory (...) is to be genuinely closed, then it must be free of all contraction, even in the metatheory. (shrink)

In this note, we show that the first-order logic IKω is sound with regard to the models obtained from continuum-valued Łukasiewicz-models for first-order languages by treating the quantifiers as infinitary strong disjunction/conjunction rather than infinitary weak disjunction/conjunction. Moreover, we show that these models cannot be used to provide a new consistency proof for the theory of truth IKTω obtained by expanding IKω with transparent truth, because the models are inconsistent with transparent truth. Finally, we show that whether (...) or not this inconsistency can be reproduced in the sequent calculus for IKTω depends on how vacuous quantification is treated. (shrink)

The paper is concerned with a logical difficulty which Lionel Shapiro’s deflationist theory of logical consequence (as well as the author’s favoured, non-deflationist theory) gives rise to. It is argued that Shapiro’s non-contractive approach to solving the difficulty, although correct in its broad outlines, is nevertheless extremely problematic in some of its specifics, in particular in its failure to validate certain intuitive rules and laws associated with the principle of modus ponens. An alternative non-contractive theory is offered which (...) does not suffer from the same problem. (shrink)

In this paper a logic for reasoning disquotationally about truth is presented and shown to have a standard model. This work improves on Hartry Field's recent results establishing consistency and omega-consistency of truth-theories with strong conditional logics. A novel method utilising the Banach fixed point theorem for contracting functions on complete metric spaces is invoked, and the resulting logic is shown to validate a number of principles which existing revision theoretic methods have heretofore failed to provide.

A new semantic paradox developed by Richard Heck and relying on very minimal logical and truth-theoretic resources is rehearsed. A theory of truth restricting the structural metarule of contraction is presented and some of the theory's relevant features are made explicit. It is then shown how the theory provides a principled solution to the paradox while preserving the extremely compelling truth-theoretic principles at stake, thus bringing out a significant advantage that the theory enjoys over virtually all other (...) non-dialetheic theories. It is finally argued that such advantage is amplified by theoretical considerations made available by the adoption of a correspondentist perspective in the philosophy of truth. (shrink)

I enjoyed reading Max Kölbel's deep and interesting paper. I have learned a lot about points and arguments I am not entirely familiar with, and it has helped me to articulate better my own intuitions about the subject. In particular I share with him the intuition I would now articulate as follows: there are contents p of utterances of declarative sentences like, for instance, 'Licorice is tasty', such that it is not an objective matter whether p. This is the claim (...) that there are non-objective truths and falsehoods, and it is a plain consequence of global truth-evaluability, i.e. the view according to which the content of utterances of all declarative sentences are truth-evaluable. For in this case one, unless radical objectivist, has to accept that for some such contents it is not an objective matter if they are true nor it is an objective matter if they are false. And Kölbel has presented some reasons for such global truth-evaluability: philosophical and linguistic semantics presupposes it, classical logical validity presupposes it, and we do in fact attribute truth to contents of utterances of declarative sentences of any sort. (shrink)

Response to Max Kölbel: "A Criterion for Objectivity", Theoria. Revista de Teoría, Historia y Fundamentos de la Ciencia: Volume > 15 > Issue: 2.

This paper provides a new argument for a position of Crispin Wright's: given that ethical statements can be embedded within all sorts of sentential operators and are subject to definite standards of warrantedness, they must have truth conditions. Allan Gibbard's normative logic' is the only noncognitivist logic that stands a chance of avoiding Geach's Fregean objection. But what, according to Gibbard, is the point of avoiding inconsistency in one's ethical statements? He must say that it is to ensure that (...) one's ethical statements have a property that has certain features. But the only property that has those features is truth. (shrink)

Recently, philosophers have tried to develop a version of truthmaker theory which ties the truthmaking relation closely to the notion of fundamentality. In fact, some of these truthmaker-fundamentalists, as I call them, assume that the notion of fundamentality is intelligible in part by citing, as central examples of fundamentals, truthmakers, which they understand necessarily as constituents of fundamental reality. The aim of this paper is first to bring some order and clarity to this discussion, sketching how far TF is compatible (...) with orthodox truthmaking, and then critically to evaluate the limits of TF. It will be argued that truthmaker theory cannot directly help with articulating the nature of fundamental reality and that T-REL does not necessarily relate truths with anything more fundamental, unless what is fundamental is what the truthbearers in question are about. I shall argue that TF faces a rather thorny dilemma and some general problems. I shall present two exhaustive types of fundamentalism on which a version of TF can be based: deflationary and inflationary. It will be argued that each version of TF runs into significant troubles accounting for all truth, specifically ordinary truths and metaphysical truths about the relations between ordinary facts and fundamental facts. I shall not attempt to solve these problems, but rather, at the end, diagnose the issues with TF as lying in the difficulties with reconciling the manifest image with the scientific and metaphysical images of reality. (shrink)

This paper presents a range of new triviality proofs pertaining to naïve truth theory formulated in paraconsistent relevant logics. It is shown that excluded middle together with various permutation principles such as A → (B → C)⊩B → (A → C) trivialize naïve truth theory. The paper also provides some new triviality proofs which utilize the axioms ((A → B)∧ (B → C)) → (A → C) and (A → ¬A) → ¬A, the fusion connective and the Ackermann (...) constant. An overview over various ways to formulate Leibniz’s law in non-classical logics and two new triviality proofs for naïve set theory are also provided. (shrink)

Argues that there are two distinct senses in which knowledge is incompatible with accidental truth - each of which can be traced to a distinct role played by everyday knowledge attributions.

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, (...) but not jointly, lack the problematic feature. (shrink)

This Element is an introduction to recent work proofs and models in philosophical logic, with a focus on the semantic paradoxes the sorites paradox. It introduces and motivates different proof systems and different kinds of models for a range of logics, including classical logic, intuitionistic logic, a range of three-valued and four-valued logics, and substructural logics. It also compares and contrasts the different approaches to substructural treatments of the paradox, showing how the structural rules of contraction, cut and identity feature (...) in paradoxical derivations. It then introduces model theoretic treatments of the paradoxes, including a simple fixed-point model construction which generates three-valued models for theories of truth, which can provide models for a range of different non-classical logics. The Element closes with a discussion of the relationship between proofs and models, arguing that both have their place in the philosophers' and logicians' toolkits. (shrink)

I offer a new theory of faultless disagreement, according to which truth is absolute (non-relative) but can still be non-objective. What's relative is truth-aptness: a sentence like ‘Vegemite is tasty’ (V) can be truth-accessible and bivalent in one context but not in another. Within a context in which V fails to be bivalent, we can affirm that there is no issue of truth or falsity about V, still disputants, affirming and denying V, were not at fault, (...) since, in their context of assertion V was bivalent. This theory requires a theory of assertion that is a form of cognitive expressivism. (shrink)

In On What Matters, Derek Parfit defends a new metaethical theory, which he calls non-realist cognitivism. It claims that normative judgments are beliefs; that some normative beliefs are true; that the normative concepts that are a part of the propositions that are the contents of normative beliefs are irreducible, unanalysable and of their own unique kind; and that neither the natural features of the reality nor any additional normative features of the reality make the relevant normative beliefs true. The aim (...) of this article is to argue that Parfit’s theory is problematic because its defenders have no resources to make sense of the nature of normative truth, which is an essential element of their view. I do this by showing how the traditional theories of truth are not available for the non-realist cognitivists. (shrink)

As our epistemic ambitions grow, the common and scientific endeavours are becoming increasingly dependent on Machine Learning (ML). The field rests on a single experimental paradigm, which consists of splitting the available data into a training and testing set and using the latter to measure how well the trained ML model generalises to unseen samples. If the model reaches acceptable accuracy, an a posteriori contract comes into effect between humans and the model, supposedly allowing its deployment to target environments. Yet (...) the latter part of the contract depends on human inductive predictions or generalisations, which infer a uniformity between the trained ML model and the targets. The paper asks how we justify the contract between human and machine learning. It is argued that the justification becomes a pressing issue when we use ML to reach ‘elsewheres’ in space and time or deploy ML models in non-benign environments. The paper argues that the only viable version of the contract can be based on optimality (instead of on reliability which cannot be justified without circularity) and aligns this position with Schurz’s optimality justification. It is shown that when dealing with inaccessible/unstable ground-truths (‘elsewheres’ and non-benign targets), the optimality justification undergoes a slight change, which should reflect critically on our epistemic ambitions. Therefore, the study of ML robustness should involve not only heuristics that lead to acceptable accuracies on testing sets. The justification of human inductive predictions or generalisations about the uniformity between ML models and targets should be included as well. Without it, the assumptions about inductive risk minimisation in ML are not addressed in full. (shrink)

A few years ago, believing that human thinking is nonmonotonic, I tried to reconstruct a nonmonotonic reasoning by application of two monotonic procedures. I called them “step forward” and “step backward” . The first procedure is just a consequence operation responsible for an extension of the set of beliefs. The second one, defined on the base of the logic of falsehood reconstructed for the given logic of truthfulness, is responsible for a reduction of the set of beliefs. Both procedures taken (...) together were successfully verified by using so-called AGM , postulates for expansion, contraction and revision formulated by Alchourrón, Gärdenfors and Makinson . Reasoning composed of the mutual application of both procedures seemed to be quite natural for modeling our thinking. At that time, I supposed that it should be nonmonotonic but I was wrong. It turned out impossible to satisfy a definition of the nonmonotonic inference by reasoning composed both steps. To understand why this is impossible, I began to analyze how nonmonotonicity is obtainable in some well-known cases in the literature. I analyzed the problem from two points of view: non-formal examples for nonmonotonicity and formal constructions of nonmonotonic operations/relations. The result of those investigations was astonishing: none of the considered by me cases of nonmonotonicity belonging to point and almost none belonging to satisfies the definition of nonmonotonic inference. Arguments against the nonmonotonic character of well-known examples for nonmonotonicity of human thinking are more precisely presented in [6]. I present them below an abbreviated version of them. (shrink)

While working on various medieval philosophers, I have noticed an affinity between their remarks on the reasonableness of accepting propositions that are not matters of proof and strict deduction and St. John Henry Newman’s remarks that we accept unconditionally and rightly everyday ordinary propositions without calibrating them to demonstrable arguments. In particular, Cardinal Matthew of Aquasparta and Blessed John Duns Scotus both claim there is a sense in which assent to everyday propositions is tantamount to knowledge, even though there is (...) no adequate argumentation or demonstrative reasoning compelling us to assent to such propositions. Newman’s distinction between notional and real apprehension of propositions, notional and real assents, and his insistence on the existence of real assents to propositions that are not necessarily proved, or in some cases provable, seem, at first glance, a case parallel to that of the medieval philosophers we have mentioned. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship – (...) the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (shrink)

Various writers point out that accepting the terms of a contract does not imply consent to the background conditions of this contract. This is an important critical insight allowing for a critical perspective on the principle of free contract, according to which the state should not interfere with what adult agents contractually agree upon. In this paper I argue that the practical relevance of this critical insight depends on the availability of answers to three questions: (1) Which are the core (...) features of baseline background conditions supporting a well-ordered labor market enhancing economic welfare? (2) In which cases and for which reasons are non-market institutions needed in order to support these features? (3) Under which conditions and at which levels can collective mechanisms be expected to support adequate non-market institutions ‘curing market failure’? Some of the core properties of labor markets and labor contracts are discussed which need to be taken into account in attempts to answer these questions, most notably problems of contract enforcement, market failure and collective action. (shrink)

We argue that Recanati burdens his otherwise salutary “Mental File” account of singular thought with an “Actualist” assumption that he has inherited from the discussion of singular thought since at least Evans, according to which singular thoughts can only be about actual objects: apparent singular thoughts involving “empty” terms lack truth-valuable content. This assumption flies in the face of manifestly singular thoughts involving not only fictional and mistakenly postulated entities, such as Zeus and the planet Vulcan, but also “perceptual (...) inexistents,” e.g., Kanizsa figures, rainbows, words and phonemes, as well as hosts of at best metaphysically problematic “objects,” such as properties, numbers, ceremonies, contracts, symphonies, “the sky,” “the rain.” Indeed, reflection on what seems to be the boundless diversity of “things” about which we seem to be able to have singular thoughts strongly suggests that there may be no general metaphysics of objects, much less “acquaintance” and “epistemically rewarding” relations that would distinguish singular from non-singular thought. We recommend that Recanati and other mental file theorists confine the theory to a metaphysically neutral account of singular thought as specific kind of internally “focused” computational state, and not seek any general account of the relation of thought to reality. (shrink)

Sometimes a belief that p promotes having true beliefs, whether or not p is true. This gives reasons to believe that p, but most epistemologists would deny that it gives epistemic reasons, or that these reasons can epistemically justify the belief that p. Call these reasons to believe “truth promoting non-evidential reasons for belief.” This paper argues that three common views in epistemology, taken together, entail that reasons of this sort can epistemically justify beliefs. These three claims are: epistemic (...) oughts are normative, epistemic oughts have a source, and the source of epistemic oughts is an end that has true belief as a necessary component. These claims would be hard for many epistemologists to deny, but accepting them, and thus accepting that truth promoting non-evidential reasons can justify beliefs, has significant consequences for epistemology. The paper considers accounts of epistemic oughts that endorse these claims but might seem to avoid the consequence that truth promoting non-evidential reasons generate real epistemic oughts, and shows that none do. (shrink)

In recent work, J. Adam Carter argues that truth-relativism should be compatible with the so-called conformist response to peer disagreement about taste to the effect that subjects should revise their opinions. However, Carter claims that truth-relativism cannot make sense of this response since it cannot make sense of the idea that when two subjects are recognised as epistemic peers, they should acknowledge that they are equally likely to be right about the targeted issue. The main aim of this (...) paper is a modest one: to argue that truth-relativists should not be worried about their alleged incompatibility with conformism for they should be non-conformists. (shrink)

Anti-realistic conceptions of truth and falsity are usually epistemic or inferentialist. Truth is regarded as knowability, or provability, or warranted assertability, and the falsity of a statement or formula is identified with the truth of its negation. In this paper, a non-inferentialist but nevertheless anti-realistic conception of logical truth and falsity is developed. According to this conception, a formula (or a declarative sentence) A is logically true if and only if no matter what is told about (...) what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain partial order on non-ontic semantic values as its value. The ordering in question is a told-true order. Analogously, a formula A is logically false just in case no matter what is told about what is told about the truth or falsity of atomic sentences, A always receives the top-element of a certain told-false order as its value. Here, truth and falsity are pari passu , and it is the treatment of truth and falsity as independent of each other that leads to an informational interpretation of these notions in terms of a certain kind of higher-level information. (shrink)

Theories where truth is a naive concept fall under the following dilemma: either the theory is subject to Curry’s Paradox, which engenders triviality, or the theory is not trivial but the resulting conditional is too weak. In this paper we explore a number of theories which arguably do not fall under this dilemma. In these theories the conditional is characterized in terms of non-deterministic matrices. These non-deterministic theories are similar to infinitely-valued Łukasiewicz logic in that they are consistent and (...) their conditionals are quite strong. The difference is the following: while Łukasiewicz logic is \-inconsistent, the non-deterministic theories might turn out to be \-consistent. (shrink)

On October 5th, 2017, the New York Times published an article that would establish the #MeToo movement and help millions of women across the globe to raise their voice and share their stories of sexual harassment, aggression and/or violence. If Harvey Weinstein was the main accused, he was, actually, the epitome of a systemic, as well as an endemic, issue that didn’t stop at the studios’ doors and was made possible thanks to a rather surprising and quite unexpected accomplice. In (...) fact, “Hollywood’s open secret” has been well-guarded by, among other things, the contract and its law. In the eyes of a contract law specialist, whether it be a man or a woman, the major highlight of Jodi Kantor and Megan Twohey’s article rests in their ability to have brought to light contracts—the, now, infamous and highly criticised “NDAs” (non-disclosure agreements)—that ensured Weinstein the freedom to buy his victims’ silence. The first goal of this essay is trying to understand, on the one hand, how could that be possible and, on the other hand, explain to a larger audience how a tool usually used for economic and commercial purposes could have been diverted from its traditional use. It also aims to present measures that have been adopted in the United States to fight these agreements, and imagine what could they be in a country such as France. Although these types of “NDAs” don’t seem to find their equivalent in the French public sphere, it is still helpful to ponder over remedies offered by the new French law of contract shall these contracts ever come to exist… or arise. (shrink)

Kurt Gödel’s Incompleteness theorem is well known in Mathematics/Logic/Philosophy circles. Gödel was able to find a way for any given P (UTM), (read as, “P of UTM” for “Program of Universal Truth Machine”), actually to write down a complicated polynomial that has a solution iff (=if and only if), G is true, where G stands for a Gödel-sentence. So, if G’s truth is a necessary condition for the truth of a given polynomial, then P (UTM) has to (...) answer first that G is true in order to secure the truth of the said polynomial. But, interestingly, P (UTM) could never answer that G was true. This necessarily implies that there is at least one truth a P (UTM), however large it may be, cannot speak out. Daya Krishna and Karl Potter’s controversy regarding the construal of India’s Philosophies dates back to the time of Potter’s publication of “Presuppositions of India’s Philosophies” (1963, Englewood Cliffs Prentice-Hall Inc.) In attacking many of India’s philosophies, Daya Krishna appears to have unwittingly touched a crucial point: how can there be the knowledge of a ‘non-cognitive’ mokṣa? [‘mokṣa’ is the final state of existence of an individual away from Social Contract]—See this author’s Indian Social Contract and its Dissolution (2008) mokṣa does not permit the knowledge of one’s own self in the ordinary way with threefold distinction, i.e., subject–knowledge-object or knower–knowledge–known. But what is important is to demonstrate whether such ‘knowledge’ of non-cognitive mokṣa state can be logically shown, in a language, to be possible to attain, and that there is no contradiction involved in such demonstration, because, no one can possibly express the ‘experience-itself’ in language. Hence, if such ‘knowledge’ can be shown to be logically not impossible in language, then, not only Daya Krishna’s arguments against ‘non-cognitive mokṣa’ get refuted but also it would show the possibility of achieving ‘completeness’ in its truest sense, as opposed to Gödel’s ‘Incompleteness’. In such circumstances, man would himself become a Universal Truth Machine. This is because the final state of mokṣa is construed as the state of complete knowledge in Advaita. This possibility of ‘completeness’ is set in this paper in the backdrop of Śrī Śaṅkarācārya’s Advaitic (Non-dualistic) claim involved in the mahāvākyas (extra-ordinary propositions). (Mahāvākyas that Śaṅkara refers to are basically taken from different Upaniṣads. For example, “Aham Brahmāsmi” is from Bṛhadāraṇyaka Upanisad, and “Tattvamasi” is from Chāndogya Upaniṣad. Śrī Śaṅkarācārya has written extensively. His main works include his Commentary on Brahma-Sūtras, on major Upaniṣads, and on ŚrīmadBhagavadGītā, called Bhāṣyas of them, respectively. Almost all these works are available in English translation published by Advaita Ashrama, 5 Dehi Entally Road, Calcutta, 700014.) On the other hand, the ‘Incompleteness’ of Gödel is due to the intervening G-sentence, which has an adverse self-referential element. Gödel’s incompleteness theorem in its mathematical form with an elaborate introduction by R.W. Braithwaite can be found in Meltzer (Kurt Gödel: on formally undecidable propositions of principia mathematica and related systems. Oliver & Boyd, Edinburgh, 1962). The present author believes first that semantic content cannot be substituted by any amount of arithmoquining, (Arithmoquining or arithmatization means, as Braithwaite says,—“Gödel’s novel metamathematical method is that of attaching numbers to the signs, to the series of signs (formulae) and to the series of series of signs (“proof-schemata”) which occur in his formal system…Gödel invented what might be called co-ordinate metamathematics…”) Meltzer (1962 p. 7). In Antone (2006) it is said “The problem is that he (Gödel) tries to replace an abstract version of the number (which can exist) with the concept of a real number version of that abstract notion. We can state the abstraction of what the number needs to be, [the arithmoquining of a number cannot be a proof-pair and an arithmoquine] but that is a concept that cannot be turned into a specific number, because by definition no such number can exist.”.), especially so where first-hand personal experience is called for. Therefore, what ultimately rules is the semanticity as in a first-hand experience. Similar points are voiced, albeit implicitly, in Antone (Who understands Gödel’s incompleteness theorem, 2006). (“…it is so important to understand that Gödel’s theorem only is true with respect to formal systems—which is the exact opposite of the analogous UTM (Antone (2006) webpage 2. And galatomic says in the same discussion chain that “saying” that it ((is)) only true for formal systems is more significant… We only know the world through “formal” categories of understanding… If the world as it is in itself has no incompleteness problem, which I am sure is true, it does not mean much, because that is not the world of time and space that we experience. So it is more significant that formal systems are incomplete than the inexperiencable ‘World in Itself’ has no such problem.—galatomic”) Antone (2006) webpage 2. Nevertheless galatomic certainly, but unwittingly succeeds in highlighting the possibility of experiencing the ‘completeness’ Second, even if any formal system including the system of Advaita of Śaṅkara is to be subsumed or interpreted under Gödel’s theorem, or Tarski’s semantic unprovability theses, the ultimate appeal would lie to the point of human involvement in realizing completeness since any formal system is ‘Incomplete’ always by its very nature as ‘objectual’, and fails to comprehend the ‘subject’ within its fold. (shrink)

Kirkham’s book is not a plain attempt of asking the questions like ‘What is truth?’ since it would, according to him, be one more mistake followed by confusion. The components of this four-dimensional confusion (vagueness, ambiguity, several ways of describing the same project, and one answer for two distinctly different questions about truth) find its original explanation in Kirkham’s book. Having stated that all of the previous theories of truth were just irrelevant to the question of “What (...) is truth” because when asking different questions about truth, he draws his non-trivial approach of assigning each theorist to the particular question (or ‘project’) he or she was trying to answer with his or her theory of truth. So, the main merit of Kirkham’s work is the clarification of this most urgent philosophical problem of truth on the way of metaphysics. (shrink)

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This (...) completeness transfer result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

I will argue that the standard formulation of non-factualism in terms of a denial of truth-aptness is consistent with a version of deflationsim. My line of argument assumes the use conception of meaning. This brings out an interesting consequence since mostly the philosophers who endorse the use conception of meaning, e.g. Paul Horwich, hold that deflationism is inconsistent with the strategy of implementing non-factualism in terms of a denial of truth-aptness and thereby urge a reformulation of non-factualism.

This is an essay at the intersection of metaethics and the history of contemporary analytic philosophy. It explores the relationships between Allan Gibbard’s mature quasi-realist expressivism and (i) three non-naturalistic varieties of what I call “non-inflationary realism” and (ii) moral fictionalism. Moral or normative realism is frequently (if mistakenly) taken to involve certain existence-affirming external assumptions about the metaphysical status of substantive normative thought and discourse. The non-inflationary realists seek to embrace moral or normative objectivity and truth without any (...) distinctly—as they see it, “inflated”—moral or normative ontology. This position, along with a shared emphasis on the primacy of substantive moral or normative thought and discourse, brings them very close to Gibbard, and so to what it is tempting to treat as a strikingly different metaethical account. Focusing on the non-inflationary realists Ronald Dworkin, T.M. Scanlon, and Derek Parfit, I examine similarities among their views, and between each of these views and Gibbard’s. I argue that the non-inflationary realist project should be understood as including the work not only of these figures, characteristically seen as among its paradigmatic representatives, but also, crucially, that of Gibbard. They all agree that our moral or normative claims purport to state normative truths and that such claims are capable of being true or false and that when true they do not depend on the particular standpoint anyone happens to take. Our moral or normative thoughts can be characterized as beliefs. We can have moral knowledge. There are substantive moral and normative facts. These facts are not reducible to non-normative facts. Normative concepts cannot be analyzed in purely naturalistic terms; and normative facts do not depend on any robustly existent truth-makers. Focusing on these shared commitments enables me to home in on the apparent differences that nonetheless remain. They differ in significant respects, for instance, about whether—and, if so, to what extent—we can make any meaningful external (non-substantive) judgments about the moral or normative and about whether there is a role for property-based explanations that minimalism about the normative fails to capture. By investigating these and other differences, I shed light on what is at stake in giving an adequate account of our moral and normative thought and talk. I pursue this aim further by considering why it might seem that quasi-realist expressivism was a form of normative fictionalism or error theory—though it is not. I attempt here to clear up confusions stemming from common assumptions associated with terms like “realism,” “cognitivism,” or “fictionalism” with respect to morality or normativity. I distinguish some differences in the ways in which normative properties can be understood by non-inflationary realists and the roles they can play in explaining normativity. I underscore the implausibility of treating the moral domain as completely autonomous. And I attempt to offer suggestions regarding some conceptual options that remain to be further explored. I maintain that Gibbard makes explicit otherwise unacknowledged implications of Scanlon’s or Dworkin’s accounts, implications regarding deep differences between normative or moral and other domains, implications which might help explain the uneasiness that prompts Scanlon and Dworkin to resist Gibbard’s account and that pushes Parfit toward what seems to be a sort of intermediate position between non-inflationary and more ontologically committed realism. Non-inflationary realism forces us to rethink metaethics in interesting and promising ways. (shrink)

Any "classical" theory of truth will satisfy tarski's criterion ("p" is true if and only if p), And the principle of bivalence (every proposition is either true or false). A non-Classical theory may be obtained by rejecting these principles: - in fact it is shown that rejection of the second entails rejection of the first. If the resulting non-Classical theory is formalized, A system structurally isomorphic to either s4 or s5 is obtained. An attempt is made to show that (...) the essential insights of intuitionist logic may be preserved if we replace their complex and in many respects "unintuitive" propositional logic by a theory of truth which is non-Classical in the sense described above. (shrink)