We ordinarily assume that we have reliable knowledge of our immediate surroundings, so much so that almost all the time we entrust our lives to the truth of what we take ourselves to know, without a moment’s thought. But if, as Karl Popper and others have maintained, all our knowledge is conjectural, then this habitual assumption that our common sense knowledge of our environment is secure and trustworthy would seem to be an illusion. Popper’s philosophy of science, in particular, fails (...) to do justice to the distinction we ordinarily draw between secure knowledge and mere conjecture. But Popper’s philosophy of science, in particular his attempted solution to the problem of induction, is defective. It fails to take into account that physics, in only accepting unified theories, even though endlessly empirically more successful disunified rivals are always available, makes the persistent metaphysical assumption that all disunified theories are false. Once this point is acknowledged, it becomes clear that a new conception of scientific method is required which sees science as making a hierarchy of metaphysical assumptions concerning the comprehensibility and knowability of the universe. This provides a framework of relatively unproblematic assumptions and associated methods of science within which much more problematic assumptions and associated methods can be critically assessed and improved. This hierarchical view seems at first to intensify the problem of distinguishing certainty from conjecture, in that it emphasizes that scientific knowledge, and even humble common sense knowledge, contain usually unacknowledged cosmological conjectures. But actually it explicates the basis we have for drawing the distinction between trustworthy knowledge and mere conjecture, and even goes some way towards providing a rationale for this distinction, in so far as one exists. (shrink)

The history of western philosophy is split to its core by a long-standing, fundamental dispute. On the one hand there are the so-called empiricists, like Locke, Berkeley, Hume, Mill, Russell, the logical positivists, A. J. Ayer, Karl Popper and most scientists, who hold empirical considerations alone can be appealed to in justifying, or providing a rationale for, claims to factual knowledge, there being no such thing as a priori knowledge – items of factual knowledge that are accepted on grounds other (...) than the empirical. And on the other hand there are the so-called rationalists, like Descartes, Spinoza, Leibniz, Bradley, McTaggart, who hold that a priori knowledge does exist, and even plays a crucial role in science. This long-standing dispute is resolved by the line of thought developed in this essay. The empiricists were right to deny the existence of a priori knowledge where this means factual knowledge of apodictic certainty justified independently of any appeal to experience. They were wrong, however, to deny the existence of a priori knowledge where this means conjectural items of factual knowledge whose acceptance is justified independently of any appeal to experience. Science requires there to be a priori knowledge in this latter sense, and two items of such knowledge will be exhibited. In addition to resolving this empiricist/rationalist dispute, the essay also develops a new conception of science – aim-oriented empiricism – and solves the long-standing problem of what it means to say of a theory that it is unified or explanatory. Furthermore, aim-oriented empiricism does not just change our conception of science; it requires that science itself needs to change. Science needs to become much more like the 17th century conception of natural philosophy, intermingling consideration of testable theories with consideration of untestable metaphysical, epistemological and methodological ideas. The whole relationship between science and the philosophy of science is transformed. The philosophy of science, construed as the exploration and critical assessment of rival ideas about what the aims and methods of science ought to be, ceases to be a meta-discipline, and becomes an integral part of science – or natural philosophy – itself. (shrink)

Mathematicians often speak of conjectures, yet unproved, as probable or well-confirmed by evidence. The Riemann Hypothesis, for example, is widely believed to be almost certainly true. There seems no initial reason to distinguish such probability from the same notion in empirical science. Yet it is hard to see how there could be probabilistic relations between the necessary truths of pure mathematics. The existence of such logical relations, short of certainty, is defended using the theory of logical probability (or (...) objective Bayesianism or non-deductive logic), and some detailed examples of its use in mathematics surveyed. Examples of inductive reasoning in experimental mathematics are given and it is argued that the problem of induction is best appreciated in the mathematical case. (shrink)

In recent years, there has been increasing interest in investigating science communication. Some studies that address this issue attempt to develop a model to determine the level of confidence that an author or a scientific community has at a given time towards a theory or a group of theories. A well-established approach suggests that, in order to determine the level of certainty authors have with regard to the statements they make, one can identify specific lexical and morphosyntactical markers which (...) indicate their epistemic attitudes. This method is considered particularly appealing because it permits the development of an algorithmic model based on the quantitative analysis of the occurrence of these markers to assess automatically and objectively the opinion of an author or the predominant opinion of a scientific community on a topic at a given time. In this contribution we show that this line of research presents many kinds of problems especially when it is applied to research articles. To this aim, we propose two main lines of reasoning. The first one relies generally on the argumentative structure of scientific articles and shows that certainty/uncertainty markers are used differently in different argument forms and that therefore their number/frequency of use does not offer reliable indications for determining whether the topic at issue is considered by the authors to be more or less factual/speculative. The second one is based on the analysis of a sample of psychiatric research articles on homosexuality written over a long time span and taken from The British Journal of Psychiatry. Since the psychiatric perspective on homosexuality changed radically during the decades in which these articles were published, they offer an inventory of various kinds of argumentative strategies directed both at defending and confuting dominant as well as marginal positions. We focus especially on uncertainty markers and show that frequently the positions stated using expressions indicating uncertainty are actually not considered as conjectural or speculative by their authors, but that the use of uncertainty markers is motivated by a number of different and often incongruent rhetorical strategies. (shrink)

The doxastic zoo contains many animals: belief, acceptance, belief in, belief that, certainty, conjecture, guess, conviction, denial, disbelief in, disbelief that, judgment, commitment, etc. It also contains belief’s “strange bedfellows”: credences, partial beliefs, tacit beliefs, subdoxastic states, creedal feelings, feelings of knowing, in-between believings, pathological beliefs, phobias, aliefs, delusions, biases, besires. How to order the zoo? I propose to distinguish doxastic attitudes from non-doxastic epistemic attitudes. The criterion is the existence of correctness conditions. Most bedfellows do not have such (...) normative conditions. So they should not be allowed in the Doxastic Club. (shrink)

When we engage in practical deliberation, we sometimes engage in careful probabilistic reasoning. At other times, we simply make flat out assumptions about how the world is or will be. A question thus arises: when, if ever, is it rationally permissible to engage in the latter, less sophisticated kind of practical deliberation? Recently, a number of authors have argued that the answer concerns whether one knows that p. Others have argued that the answer concerns whether one is justified in believing (...) that one knows that p. Against both of these, this paper argues that the answer concerns whether p is ‘practically certain’—that is, whether the actual epistemic probability that p differs from epistemic certainty that p only in ways that are irrelevant to the decision one currently faces. (shrink)

When is it permissible to rely on a proposition in practical reasoning? Standard answers to this question face serious challenges. This paper uses these challenges to motivate a certainty norm of practical reasoning. This norm holds that one is permitted to rely on p in practical reasoning if and only if p is epistemically certain. After developing and defending this norm, I consider its broader implications. Taking a certainty norm seriously calls into question traditional assumptions about the importance (...) of belief and knowledge. In particular, it raises the possibility that many epistemological jobs that are usually assigned to belief and knowledge should be reallocated to two related but importantly different states: psychological and epistemic certainty. (shrink)

In this paper, a modified form of Collatz conjecture for neutrosophic numbers n ∈ (Z U I) is defined. We see for any n ∈ (Z U I) the related sequence using the formula (3a + 1) + (3b + 1)I converges to any one of the 55 elements mentioned in this paper. Using the akin formula of Collatz conjecture viz. (3a- 1) + (3b -1)I the neutrosophic numbers converges to any one of the 55 elements mentioned with appropriate modifications. (...) Thus, it is conjectured that every n ∈ (Z U I) has a finite sequence which converges to any one of the 55 elements. (shrink)

Delusions are unhinged hinge certainties. Delusions are defined as strongly anchored beliefs that do not change in the face of adverse evidence. The same goes for Wittgensteinian certainties. My paper refines the so-called framework views of delusion, presenting an argument that epistemically speaking, considering them to be certainties best accounts for delusions’ doxastic profile. Until now there has been little argument in favour of this position and the original proposals made too extreme predictions about the belief systems of delusional patients. (...) I show that my account fares better with the diverse objections that have been raised against older framework views of delusion (Campbell 2001, Gipps and Rhodes 2008). Finally, I examine what makes a harmless hinge into a pathological delusion. (shrink)

Most philosophers, including all materialists I know of, believe that I am a complex thing?a thing with parts?and that my mental life is (or is a result of) the interaction of these parts. These philosophers often believe that I am a body or a brain, and my mental life is (or is a product of) brain activity. In this paper, I develop and defend a novel argument against this view. The argument turns on certainty, that highest epistemic status that (...) a precious few of our beliefs enjoy. For example, on the basis of introspection, I am certain that I am not in fierce pain right now. But if I am a complex thing like a body or a brain, then introspection might be a causal series of events extended in time. And any such process could go awry. So, if introspection is such a process, then I could gain good evidence that the introspective process has gone awry and that I am, contrary to appearances, feeling fierce pain right now. Therefore, the view that I am a complex thing like a body or a brain forces open the possibility that I cannot be certain that I am not feeling fierce pain right now. Since that is clearly not an open possibility, it follows that I am not a complex thing. I conclude by responding to three objections. (shrink)

This overview of the philosophy of certainty will distinguish two types of certainty, specify controversial theses about certainty from recent literature, and explain some of the arguments for and against those theses.

In [R. Vaught, Denumerable models of complete theories, in: Infinitistic Methods, Pregamon, London, 1961, pp. 303–321] Vaught conjectured that a countable first order theory has countably many or 20 many countable models. Here, the following special case is proved.

We show the Borel Conjecture is consistent with the continuum large.

This radical reading of Wittgenstein's third and last masterpiece, On Certainty, has major implications for philosophy. It elucidates Wittgenstein's ultimate thoughts on the nature of our basic beliefs and his demystification of scepticism. Our basic certainties are shown to be nonepistemic, nonpropositional attitudes that, as such, have no verbal occurrence but manifest themselves exclusively in our actions. This fundamental certainty is a belief-in, a primitive confidence or ur-trust whose practical nature bridges the hitherto unresolved categorial gap between belief (...) and action. (shrink)

This paper argues that we should assign certainty a central place in epistemology. While epistemic certainty played an important role in the history of epistemology, recent epistemology has tended to dismiss certainty as an unattainable ideal, focusing its attention on knowledge instead. I argue that this is a mistake. Attending to certainty attributions in the wild suggests that much of our everyday knowledge qualifies, in appropriate contexts, as certain. After developing a semantics for certainty ascriptions, (...) I put certainty to explanatory work. Specifically, I argue that by taking certainty as our central epistemic notion, we can shed light on a variety of important topics, including evidence and evidential probability, epistemic modals, and the normative constraints on credence and assertion. (shrink)

This paper publishes for the first time 132 conjectures by Nicolaus Heinsius on Ovid’s Metamorphoses 1‒4. The value and possible motivations of each proposal are briefly assessed.

Michael G. Titelbaum presents a new Bayesian framework for modeling rational degrees of belief—the first of its kind to represent rational requirements on agents who undergo certainty loss.

We survey the history of Shelah’s conjecture on strongly dependent fields, give an equivalent formulation in terms of a classification of strongly dependent fields and prove that the conjecture implies that every strongly dependent field has finite dp-rank.

Rich with historical and cultural value, these works are published unaltered from the original University of Minnesota Press editions.

Now in paperback, Jean-Luc Marion's groundbreaking philosophy of human uncertainty. In Negative Certainties, renowned philosopher Jean-Luc Marion challenges some of the most fundamental assumptions we have developed about knowledge: that it is categorical, predicative, and positive. Following Descartes, Kant, and Heidegger, he looks toward our finitude and the limits of our reason. He asks an astonishingly simple—but profoundly provocative—question in order to open up an entirely new way of thinking about knowledge: Isn’t our uncertainty, our finitude, and rational limitations, one (...) of the few things we can be certain about? Marion shows how the assumption of knowledge as positive demands a reductive epistemology that disregards immeasurable or disorderly phenomena. He shows that we have experiences every day that have no identifiable causes or predictable reasons and that these constitute a very real knowledge—a knowledge of the limits of what can be known. Establishing this “negative certainty,” Marion applies it to four aporias, or issues of certain uncertainty: the definition of man; the nature of God; the unconditionality of the gift; and the unpredictability of events. Translated for the first time into English, Negative Certainties is an invigorating work of epistemological inquiry that will take a central place in Marion’s oeuvre. (shrink)

This paper seeks to widen the dialogue between the “epistemology of peer disagreement” and the epistemology informed by Wittgenstein’s last notebooks, later edited as On Certainty. The paper defends the following theses: not all certainties are groundless; many of them are beliefs; and they do not have a common essence. An epistemic peer need not share all of my certainties. Which response to a disagreement over a certainty is called for, depends on the type of certainty in (...) question. Sometimes a form of relativism is the right response. Reasonable, mutually recognized peer disagreement over a certainty is possible.—The paper thus addresses both interpretative and systematic issues. It uses Wittgenstein as a resource for thinking about peer disagreement over certainties. (shrink)

According to epistemic fallibilism, we cannot be certain of anything. According to the Christian tradition, faith comes with certainty. I develop this dilemma from recent accounts of fallibilism and various representatives of the Christian tradition. I then argue that on John Henry Newman's account of faith the dilemma is merely apparent. Finally, I develop Newman's account of the certainty that accompanies faith and is compatible with fallibilism.

In a recent number of Philosophy of Science, Mr. C. D. Hardie offers some interesting suggestions concerning the problem of other minds. In his view the fact that we feel certain of their existence constitutes a problem; and he wishes to find a rational justification for this certainty. “What grounds have I for believing in the existence of other minds?” he asks. He is attracted by the traditional argument from analogy, but finds it incomplete; for “any conclusion arrived at (...) by analogy and induction is at best only probable,” and “I am certain that other minds exist.” Again we find him remarking that “there is room for an account which makes our knowledge of them depend in some way on analogy... but which is such that we can be certain that other minds exist....”. (shrink)

Demands for absolute or near certainty are a common way for those with a political agenda to undermine science and to delay action. Through our combined experience in science, philosophy and cultural theory, we are acquainted with these attempts to undermine science. We want to help readers figure out how to evaluate their merits or lack thereof.

This is a conjecture about the conditions and operating structures that are required for the phenomenality of certain mental states. Specifically, full-blown phenomenality is assumed, as contrasted with constrained examples of phenomenal experience such as sensations of color and pain. Propositional attitudes and content, while not phenomenal per se, are standardly concurrent and may condition phenomenal states (e.g., when tied to false beliefs). It is conjectured that full phenomenality natively arises in coherent processes of situated sensory synthesis and representation (with (...) conceptual content) that are looped, mereologically whole and multi-dimensional. And that phenomenal states are typically phase-states within a parameterized conjoint structure of world and experiencer processes that are causally modulated across Markov blankets (which are conditionally independent and may be nested: cf. M. Kirchoff, et. al., 2017, 2018; and T. Burge, 2010, re: anti-individualism). Though they may, it is not accepted that phenomenally conscious states must be targets of higher-order representations (cf. A. Byrne, 2004). (shrink)

The present paper explores three interrelated topics in Popper's theory of science: (1) his view of conjecture, (2) the aim of science, and (3) his (never fully articulated) theory of meaning. Central to Popper's theory of science is the notion of conjecture. Popper writes as if scientists faced with a problem proceed to tackle it by conjecture, that is, by guesses uninformed by inferential considerations. This paper develops a contrast between guesses and educated guesses in an attempt to show that (...) there is more to scientific conjecture than conjecture. The suggestion is made that some inductive considerations enter into the process of educated guessing or scientific conjecture in such a way that the ‘context of discovery’ cannot be sharply separated from the ‘context of justification’. This discussion leads to a tension between Popper's negative method of conjecture and his realism. Given Popper's (implicit) theory of meaning it seems Popper's epistemology (the conjecture and refutation method) is incompatible with his metaphysical realism. (shrink)

This paper investigates the historical origin and ancestors of typicality, which is now a central concept in Boltzmannian Statistical Mechanics and Bohmian Mechanics. Although Ludwig Boltzmann did not use the word typicality, its main idea, namely, that something happens almost always or is valid for almost all cases, plays a crucial role for his explanation of how thermodynamic systems approach equilibrium. At the beginning of the 20th century, the focus on almost always or almost everywhere was fruitful for developing measure (...) theory and probability theory. It was apparently Hugh Everett III who first mentioned typicality in physics in 1957 while searching for a justification of the Born rule in his interpretation of quantum mechanics. The historically closest concept before these developments is moral certainty, which was invented by the medieval French theologian Jean Gerson, and it became a standard concept at least until the Age of Enlightenment, when Jakob Bernoulli proved the Law of Large numbers. (shrink)

In an article published in 1974, Menas conjectured that any stationary subset of can be split in many pairwise disjoint stationary subsets. Even though the conjecture was shown long ago by Baumgartner and Taylor to be consistently false, it is still haunting papers on. In which situations does it hold? How much of it can be proven in ZFC? We start with an abridged history of the conjecture, then we formulate a new version of it, and finally we keep weakening (...) this new assertion until, building on the work of Usuba, we hit something we can prove. (shrink)

The aim of this paper is to vindicate the Cartesian quest for certainty by arguing that to aim at certainty is a constitutive feature of cognition. My argument hinges on three observations concerning the nature of doubt and judgment: first, it is always possible to have a doubt as to whether p in so far as one takes the truth of p to be uncertain; second, in so far as one takes the truth of p to be certain, (...) one is no longer able to genuinely wonder whether p is true; third, to ask the question whether p is to desire to receive a true answer. On this ground I clarify in what sense certainty is the aim of cognition. I then argue that in judging that p we commit ourselves to p’s being certain and that certainty is the constitutive norm of judgment. The paper as a whole provides a picture of the interplay between doubt and judgment that aims at vindicating the traditional insight that our ability to doubt testifies our aspiration to know with absolute certainty. (shrink)

The text of Fronto is in a very corrupt state, and the startling discrepancies which exist between different collations, as well as the unintelligibility of many of the readings deciphered, seem to justify a good deal of conjectural emendation. I append some attempts to complete or restore the sense in some passages of the Greek letters which seem hitherto to have been left in an unsatisfactory state. Not having had access to the MS, I have relied on the collations of (...) Naber and others for a statement of what is to be found in the palimpsest. (shrink)

A numeral system is an infinite sequence of different closed normal -terms intended to code the integers in -calculus. Barendregt has shown that if we can represent, for a numeral system, the functions Successor, Predecessor, and Zero Test, then all total recursive functions can be represented. In this paper we prove the independancy of these three particular functions. We give at the end a conjecture on the number of unary functions necessary to represent all total recursive functions.

Written over the last 18 months of his life and inspired by his interest in G. E. Moore's defence of common sense, this much discussed volume collects Wittgenstein's reflections on knowledge and certainty, on what it is to know a proposition for sure.

In this discussion note, I put forth an argument from the factivity of knowledge for the conclusion that knowledge is epistemic certainty. If this argument is sound, then epistemologists who think that knowledge is factive are thereby also committed to the view that knowledge is epistemic certainty.

To what extent can we doubt certainties? How are certainties expressed in words? Which language games convey certainty? To answer these questions we have to recall the method Wittgenstein used in his investigations. When we look at language games and forms of life as inseparable phenomena, do forms of life then provide any certainty? On the other hand, do we automatically relapse into relativism once we doubt certainties? Which formal structures underlie certainty and doubt? The book is (...) intended to answer these questions. (shrink)

At Aeschylus Agamemnon 985 the manuscript reading ψαμμίας ἀκάτα is corrupt, giving neither meter nor sense. Wilamowitz’ conjecture ψάμμος ἄμπτα has met with some editorial approval, but its sense is dubious and should be rejected. I propose instead ψάλλον ἀκταῖς, “they were plucking on the shore”, referring to the performance of a paean on the lyre by the Greek fleet departing for, or, less likely, arriving at, Troy. The fleet’s departure would be an appropriate time for the soldiers to perform (...) a paean, for which the lyre was a common accompaniment. Plucking a lyre without strumming, however, as ψάλλον implies, seems to have been a less common performance technique, sometimes culturally marked as ‘Asian’. While there is evidence that a paean with plucked accompaniment might have seemed unexceptional to a Greek audience, if Aeschylus did intend an Asian connotation, I suggest that the Chorus, having just witnessed Agamemnon tread on the purple cloths, would thereby portray the Greek army as already tainted by tryphe on their departure for Troy. Whether ‘Greek’ or ‘Trojan’, the conjectured army’s paean would form an effective counterpoint to the lyre-less threnos in the Chorus’ heart that dominates the ode. (shrink)

In this paper Peter Klein's criticism of Wittgenstein in "Certainty: A Refutation of Scepticism" is addressed. Klein claims that, according to Wittgenstein, we attribute knowledge of a proposition p to a person only if that person is not certain of p. I argue that a careful reading of Wittgenstein's On Certainty reveals that there are two kinds of objective certainty that Wittgenstein had in mind; propositional objective certainty and normative objective certainty. Klein fails to distinguish (...) between the two and uses what I call propositional objective certainty to make his point against Wittgenstein. I claim that when Wittgenstein said that knowledge and certainty belong to different categories he was talking of normative objective certainty and, therefore, that Klein's criticism is misplaced and attributes to Wittgenstein a position that is not his. (shrink)