The concept of certainty may be approached contextually through the use of dialogue. Drawing on sources from anthropology, archaeology, socio-linguistics and critical philosophy, and using both conversation and academic exposition, Three Apodeictic Dialogues offers a unique perspective on some of the disconcerting questions that animate belief, desire, and communication.

One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

Essentialist theories are based on notions of necessity and essentiality. Kinds and Quasi-Kinds can be defined in terms of these notions. Aristotle's essentialism asserts that Kinds are unions of Quasi-Kinds, Kinds that can overlap are necessarily included in a common Kind, and Kinds partition into sub-Kinds. Truth-conditions for the apodeictic propositions of Aristotle's modal syllogistic are stated in terms of necessity and essentiality, but independent of theses -. While the basic insights motivating Patterson's and Nortmann's interpretations of modal syllogistic (...) are sound, nonetheless there are significant mistakes in the detail. Given -, truth-conditions for apodeictic propositions can be stated in terms of essentiality, but independently of the notion of necessity, thus confirming Johnson's interpretation. (shrink)

VIRTUALLY ALL MODAL LOGICIANS after Aristotle have been troubled by his insistence that, given a valid first figure categorical syllogism.

We give a simple definition of validity for syllogisms involving necessary and assertoric premises which validates all and only the Aristotelian apodeictic syllogisms.

What is a problem? What is problematic about any problem whatsoever, philosophical or otherwise? As the origin of assertion and apodeiction, the problematic suspends the categories of necessity and contingency, possibility and impossibility. And it is this suspension that is the essence of the problem, which is why it is so suspenseful. But then, how is the problem problematic? Only if what is suspended neither comes to presence, nor simply goes out into absence, that is, if the suspension continues, which (...) continues the problem. But what is problematic about suspension? As a consideration of language shows, the problem of suspension is the problem of implication. If being, for example, is merely implied, neither present nor absent, then it is the suspension of both, at least insofar as it is problematic. And this not only says something about language; rather, it has ontological implications as well — it speaks of being, and the being of anything whatsoever. For if being is implied, if that is the problem of being, it is because being is an implication. Then the being of things like problems is implied as well; or being is in things by implication. But what does it mean for being to be neither presence nor absence, but an implication? It means that being is implied in a way that is problematic — before it is necessary, or even possible. For being’s way of being is characterized by suspension — which has implications for thinking and speaking about being, and about things like problems, even about anything whatsoever. And this has implications for what being implies, namely, unity and time and aspect. (shrink)

In 1928, Friedrich Solmsen argued that Aristotle'sPosterior Analyticswas largely composed before thePrior Analytics. Ross rejected Solmsen's position in 1939, and a rather lengthy series of rebuttals and counter-attacks between the two scholars followed. Quite recently, Jonathan Barnes has revived this issue with arguments in favour of something very close to Solmsen's thesis: that Aristotle first developed a theory of demonstration (‘apodeictic’) before he had worked out the syllogistic, and that thePosterior Analyticswas originally conceived against this background. Subsequently, when Aristotle (...) formulated a syllogistic, he is supposed by Barnes to have revised or added to the contents of thePosterior Analyticsso as to make syllogistic the logic of Aristotelian science. Thus, Barnes says: ‘the syllogism is in fact an incidental adjunct to the theory of demonstration: the theory can be formulated without reference, explicit or implicit, to Syllogistic, and itcould havebeen discovered by someone who knew nothing whatever about the Syllogism’ (pp. 33–4). (shrink)

Abstract: This paper proposes a way to understand Kant's modalities of judgment—problematic, assertoric, and apodeictic—in terms of the location of a judgment in an inference. Other interpretations have tended to understand these modalities of judgment in terms of one or other conventional notion of modality. For example, Mattey (1986) argues that we should take them to be connected to notions of epistemic or doxastic modality. I shall argue that this is wrong, and that these kinds of interpretation of the (...) modality of judgments cannot be reconciled with a key claim made by Kant, namely, that the modality of a judgment does not contribute to its content, and has nothing to do with the matter that is judged. I offer an alternative interpretation based upon Kant's explicating these modalities in terms of the location of a judgment in an inference, whereby the modality of a judgment is determined by the role a judgment plays in a given course of reasoning. If I am right, then Kant in fact presents an intriguing thesis pertaining to the inferential status and potential of all our judgments. (shrink)

Aristotle's modal syllogistic has been described as "incoherent," "a failure," "a realm of darkness." Even the gentler critics claim that it is inconsistent. I offer an interpretation according to which validity in the modal syllogistic is always obtained by substituting modal terms in the nonmodal syllogistic, and restricting the principles of modal conversion. In this paper I discuss the apodeictic syllogistic, showing that the restrictions I propose are powerful enough to do all the work Aristotle requires and, in fact, (...) are supported by a close analysis of Aristotle's text. The upshot of this is that there is for Aristotle no separate modal syllogistic. (shrink)

Reasoning that compares two objects or situations to draw conclusions about previously unknown properties of one of them has traditionally been taken to be ampliative and probabilistic. I propose that it is apodeictic reasoning from a premise about isomorphic structures that is often uncertain, but which we may have good reasons to believe. I characterize the structures and their isomorphism, describe patterns of reasoning appropriate to them, and discuss some complications not immediately obvious.

A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.

Anaximander, the sixth-century BCE philosopher of Miletus, is often credited as being the instigator of both science and philosophy. The first recorded philosopher to posit the idea of the boundless cosmos, he was also the first to attempt to explain the origins of the world and humankind in rational terms. Anaximander's philosophy encompasses theories of justice, cosmogony, geometry, cosmology, zoology and meteorology. Anaximander: A Re-assessment draws together these wide-ranging threads into a single, coherent picture of the man, his worldview and (...) his legacy to the history of thought. Arguing that Anaximander's statements are both apodeictic and based on observation of the world around him, Andrew Gregory examines how Anaximander's theories can all be construed in such a way that they are consistent with and supportive of each other. This includes the tenet that the philosophical elements of Anaximander's thought (his account of the apeiron, the extant fragment) can be harmonised to support his views on the natural world. The work further explores how these theories relate to early Greek thought and in particular conceptions of theogony and meterology in Hesiod and Homer. (shrink)

Non-reductive physicalism is the view that mental events cause other events in virtue of their mental properties and that mental properties supervene on, without being identical to, physical properties. Jaegwon Kim has presented several much-discussed arguments against this view. But the much simpler causal closure argument, which purports to establish that every mental property is identical to a physical property, has received less attention than Kim’s arguments. This paper aims to show how a non-reductive physicalist should rebut the causal closure (...) argument. A crucial premise in the argument is a principle stating that the physical world is causally closed. It states, roughly, that every physical event has a physical sufficient cause. I argue that when the principle is formulated in this way, the causal closure argument is invalid. Less frequently, the causal closure principle is formulated in terms of a difference-making conception of causation so that it states that every physical effect has a physical difference-making cause. I argue that the principle, so formulated, is false and the causal closure argument unsound. Either way the argument lacks the apodeictic force to compel acceptance of its conclusion. (shrink)

In his works on argumentation, Aristotle develops three main forms: apodeictical, dialectical, and rhetorical argumentation; dialectic is subdivided into several subspecies. The purpose of this paper is to discuss all of the forms described by Aristotle, to examine their differences and to point out their interrelations. This leads to an examination of the differentiating criteria and their applicability in the case of each argumentation form—and in particular to the question regarding the number of criteria that are necessary to describe each (...) form clearly and unambiguously. It is argued that Aristotle’s works on argumentation contain an implicit system of argumentation forms that is based on no more than three criteria. (shrink)

We are once again back to the faculty of arts and to Siger of Brabant, and we are concerned to set forth his attitude toward the problem of the soul in Aristotle, not paraphrasing it, as was done earlier, but giving it in terms of the analytical discussion of the preceding two sections. A vitally important point must be made at the outset: Siger is not consciously attempting to accommodate Aristotle to the Faith. He is interested only in reconstructing the (...) Stagirite's own argument in a systematic and coherent manner, regardless of whether the conclusions come into conflict with Christian doctrine or not. Admittedly, he recognizes that these conclusions are sometimes at variance with Christian teachings, and he makes no attempt to blink these variations, but there is not in Siger any of the Thomist conviction that reason, properly exercised, cannot do otherwise than confirm the truths of faith. No--Siger reluctantly finds that properly employed reasoning can sometimes produce conclusions in conflict with truths of faith. His analysis of the Aristotelian doctrine of the soul, as presented in his De anima intellectiva, leads him to conclude that the rigorous application of systematic reasoning to the given premisses could have led to no other answers than the ones that Aristotle seems to reach. Bonaventure, faced with this dilemma, assumed that Aristotle's reasoning was proper and therefore concluded that his premisses must have been wrong; Aquinas agrees with Siger that the premisses were correct and therefore decides that the reasoning was faulty or perhaps merely inadequate, since the conclusions reached fail to confirm the truths of the Christian Revelation. Siger, however, finds both the premisses and the reasoning proper, and thus he is ultimately forced to the device of calling the resulting conclusions only "philosophical" and saying that they are always replaceable by the apodeictic certainties of the Faith. The recent research on Siger--Gilson, Van Steenberghen, and Nardi--has recognized that he was by no means insincere, or deliberately controverting the Faith; these commentators well understand that he is trying carefully and dispassionately to set forth the Aristotelian argument in all its consistency. When the conclusions reached appear to be contrary to Christian doctrine, he can do no more than say, as he does. (shrink)

"It is an interesting and largely unexplored question whether Aristotle is in practice faithful to the general idea of science, and to the rules of method, sketched in his Analytics".It is this issue, "the Problem of Demonstration," which this study is concerned to explore. The objective of this study is not so much to render a detailed and definitive solution to the problem, but rather to suggest a context within which such a solution may be reached. Further, this study is (...) intended not as an historical critique of an historical question in a classical author but as a philosophical enquiry into the roots, in Aristotle, of a perennial philosophical question. The structure of the study is as follows: In the first chapter the problem is stated, and the possible modes of response to the problem are briefly canvassed, in order to set the framework of the response to be offered here. The second chapter attempts, through an examination of certain texts from the Posterior Analytics and elsewhere, to specify and to raise objections to the particular elements in the traditional inter¬ pretation of Aristotle's methodological intentions which have generated the problem of demonstration. Aristotle's teachings concerning the nature of knowledge include reference both to the distinctive object of knowledge and to the psychology of knowing. At one time Aristotle gives a more subjective and psychological, at other times a more object-based account of what is essential to knowledge. In the third chapter it is suggested that we must examine the manner in which Aristotle accommodates these two aspects when he comes to design a methodology of science. Aristotle's views on the aim of science are, therefore, examined as a source of insight into the balance struck between these two aspects in his writings. It is here argued that when we attempt to understand Aristotle's methodological intentions concerning the apodeictic syllogism we must not underestimate the importance in Aristotle's thought of the doctrine. It is this doctrine which, chiefly, enables Aristotle to produce a methodological doctrine which is consistent with his accounts of the nature of knowledge. Chapter four considers the evidence for understanding the Analytics as a training in critical technique, and why Aristotle feels that the apodeictic syllogism is unsuited to the task of communicating findings. The principal theme of this chapter is an examination of the Aristotelian doctrine which holds that the logical training as provided by the Analytics constitutes a and, as such, is unsuited to the task of publication. Chapter five draws together the results of the discussion, and attempts to reconstruct the specific Aristotelian context which renders Aristotle's theory and practice coherent, and which may make it possible to determine the degree of consistency operative throughout his works. A model is presented which, it is suggested, reflects the position intended by Aristotle for those bodies of demonstrated judg¬ ments prefigured in the Posterior Analytics within the economy of Aristotle's methodological theory and practice in science and philosophy. (shrink)

Aristotle's modal syllogistic has been an object of study ever since the time of Theophrastus; but these studies have been somewhat desultory. Remarkably, in the 1990s several new lines of research have appeared, with series of original publications by Fred Johnson, Richard Patterson and Ulrich Nortmann. Johnson presented for the first time a formal semantics adequate to a de re reading of the apodeictic syllogistic; this was based on a simple intuition linking the modal syllogistic to Aristotelian metaphysics. Nortmann (...) developed an ingenious de dicto analysis. Patterson articulated the links between the modal syllogistic and the metaphysics, using an analysis which strictly speaking is neither de re nor de dicto. My own studies in this field date from 1976, when my colleague Peter Roeper and I jointly wrote a paper "Aristotle's apodeictic syllogisms" for the XXIInd History of Logic Conference in Krakow. This paper contained the disjunctive reading of particular affirmative apodeictic propositions, which I still favour. Nonetheless, I did not consider that paper's results decisive or comprehensive enough to publish, and my 1981 book The Syllogism contained no treatment of the modal syllogism. The paper's ideas lay dormant till 1989, when I read Johnson's and Patterson's initial articles. I began publishing on the topic in 1991. Gradually my thoughts acquired a certain comprehensiveness and systematicity, till in 1993 I was able to take a semester's sabbatical to write up a draft of this book. (shrink)

This chapter begins with a discussion of Kant's theory of judgment-forms. It argues that it is not true in Kant's logic that assertoric or apodeictic judgments imply problematic ones, in the manner in which necessity and truth imply possibility in even the weakest systems of modern modal logic. The chapter then discusses theories of judgment-form after Kant, the theory of quantification, Frege's Begriffsschrift, C. I. Lewis and the beginnings of modern modal logic, the proof-theoretic approach to modal logic, possible (...) world semantics, correspondence theory, and modality and quantification. (shrink)

My dissertation challenges much of the last 1700 years of interpretation on important parts of Aristotle's philosophy. In this work I examine in depth each of the four viable answers Aristotle provides to the question "what is knowledge?" I begin with the answer that "knowledge is an 'apodeictic hexis'" . An understanding of this statement requires a prior consideration of many aspects of Aristotle's ontology and psychology, as well as epistemology. This consideration provides not only an analysis of this (...) answer, but also a philosophical foundation for the subsequent chapters. The second chapter examines Aristotle's claim that knowledge is a "hupolepsis" . This answer is a brief way of indicating the place of knowledge in our psychology. Although there is not much direct, explicit evidence surviving which makes clear what "hupolepsis" is, Aristotle's surviving uses of this notion are adequate for revealing its salient features. The third answer comes from Posterior Analytics I.2.71b9--16 , and is connected to the fourth, which comes from Nicomachean Ethics VII. I show that the logos knowledge has, or is with, is either an immediate, necessary and true statement or a proof . The former is anapodeictic knowledge, and the latter apodeictic knowledge. These two kinds of knowledge have both semantic and psychological aspects, and I examine both kinds in detail. The fourth chapter examines the question that logically follows, namely "given this account of knowledge, is knowledge possible?" In conclusion I provide a summary and address some of issues which follow from my work, providing a segue to a sequel. (shrink)

Fred's semantics for McCall's syntactic presentation of Aristotle's assertoric and apodeictic syllogistic is altered to free it from Thom's objections that it is unAristotelian. The altered semantics rejects Baroco-XLL and Bocardo-LXL, which Thom says Aristotle should have accepted. Aristotle's proofs that use ecthesis are formalized by using singular sentences. With one exception the (acceptance) axioms for McCall's system L-X-M are derivable. Formal proofs are shown to be sound.

_Physics_ VIII 1 presents a multi-stage argument concluding that there was not, nor ever will be, a time when there was not nor will not be motion (_Phys_. VIII 1.252b5-6). In this paper I shall argue that chapter’s argument is dialectical in a precise way. My claim will be that _Physics_ VIII 1 is apodeictically conditioned – its structure must be understood in terms of the theory of science in the _Posterior Analytics_ and the methods for establishing principles in the (...) _Topics. Physics_ VIII 1 is not demonstrative in a straightforward deductive way, but is structured with the nature of a scientific _genos_ and requirements for scientific knowledge always in mind. Aristotle begins by asking about the eternality of motion, posing a pair of conceptual opposites that form a mutually exclusive and logically exhaustive dichotomy. But the initial statement of the dichotomy turns out to require substantial unpacking, leading eventually to a single remaining option, that motion in the cosmos is eternal. But the status of this conclusion itself turns out to be problematic. Put in terms of Aristotle’s theory of science, all _phusiologoi_ made motion a posit or hypothesis, whether they regarded motion as eternal or not. Though Aristotle has rejected one option, at a deeper level, he finds all previous accounts lacking. Because motion is fundamental to all coming-to-beand-passing-away, what is at stake is the status and adequacy of a principle governing the whole science of nature (_tên theôrian pasan_; 250b17). In this way, the chapter prepares for the subsequent investigation into the principles of cosmic motion. (shrink)

The Babylonian Talmud, compiled from the 2nd to 7th centuries C.E., is the primary source for all subsequent Jewish laws. It is not written in apodeictic style, but rather as a discursive record of (real or imagined) legal (and other) arguments crossing a wide range of technical topics. Thus, it is not a simple matter to infer general methodological principles underlying the Talmudic approach to legal reasoning. Nevertheless, in this article, we propose a general principle that we believe helps (...) to explain the variety of methods used by the Rabbis of the Talmud for resolving uncertainty in matters of Jewish Law (henceforth: Halakhah). Such uncertainty might arise either if the facts of a case are clear but the relevant law is debatable or if the facts themselves are unclear. (shrink)

One of the permanent factors driving philosophy is the puzzle presented by our embodiment. Our consciousness is embodied. We are its embodiment; we are that curious amalgam that we try to describe in terms of mind and body. Philosophy has sought again and again to describe their relation. Yet each time it attempts this from one of these aspects, the other hides itself. From the perspective of mind, everything appears as a content of consciousness. Yet, from the perspective of the (...) body, there are no conscious contents. There are only neural pathways and chemical processes. As thinkers as early as Locke and Leibniz realized, we may search the brain as thoroughly as we wish; within its material structure, we will never find a conscious content.[i] Both perspectives are obviously one-sided. We are both mind and body; we are determined by our conscious contents and our physical makeup. Husserl’s Logical Investigations takes account of this fact in speaking of the real and ideal determination of the subject. As embodied beings, we are subject to real causal laws. Such laws, insofar as the relate to our mental contents, take these as determined by the contents temporally proceeding them.[ii] As engaged in mind, we are also subject to the ideal laws of “authentic thought.” These are nontemporal, logical laws governing “the compatibility or incompatibility of mentally realizable contents.” In the Investigations, the problem of the mind’s relation to the body comes to a head in these two determinations. How can the same set of mental acts be subject to both causal and logical laws? How can a causally determined subject grasp an apodictically certain set of logical relations? As Theodor DeBoer puts this question: “on the one hand, these acts are empirically necessary and determined; on the other hand, an idea realizes itself in them through which they claim apodeictic validity. How can both these views be combined?”[iii]. (shrink)

This paper examines three recent discussions of Aristotle's system of syllogisms with apodeictic and assertoric premisses. Though they contain no cross-references, and though they arrive at disparate interpretations, all three pieces share a common aim. That aim is to construct an intuitively graspable interpretation of Aristotle's modal syllogistic which is based on metaphysical considerations. I argue that none of these authors has succeeded in this; nevertheless, I share their broad aim, and attempt to show that a more satisfactory interpretation (...) can be formulated by combining and developing elements drawn from all three. (shrink)

Aristotle assesses as valid three first figure syllogisms, each of which contains at least one premiss expressing a de re contingency. In fact, all three of these moods (namely, Barbara-QQQ, Barbara-XQM, and Barbara-LQM) are invalid. Utilizing the concept of ampliation, this paper shows how the mood Barbara-QQQ must be refined if it is to be deemed valid. It can then become clear as to how Barbara-XQM and Barbara-LQM can be disambiguated and ultimately validated. In treating all three moods, some theses (...) from S4 will be exploited in the context of distinguishing de dicto and de re modes of attributing possibility and necessity. Various Aristotelian propositional forms and rules of inference, including argumentation by ecthesis, will shape the presentation. The viability of Aristotle’s views on the convertibility of universal negative apodeictic propositions will emerge as decisive in evaluating the success of his modal syllogistic. (shrink)

Aristotle assesses as valid three first figure syllogisms, each of which contains at least one premiss expressing a de re contingency. In fact, all three of these moods (namely, Barbara-QQQ, Barbara-XQM, and Barbara-LQM) are invalid. Utilizing the concept of ampliation, this paper shows how the mood Barbara-QQQ must be refined if it is to be deemed valid. It can then become clear as to how Barbara-XQM and Barbara-LQM can be disambiguated and ultimately validated. In treating all three moods, some theses (...) from S4 will be exploited in the context of distinguishing de dicto and de re modes of attributing possibility and necessity. Various Aristotelian propositional forms and rules of inference, including argumentation by ecthesis, will shape the presentation. The viability of Aristotle’s views on the convertibility of universal negative apodeictic propositions will emerge as decisive in evaluating the success of his modal syllogistic. (shrink)

This article investigates the prospect of giving de dicto- and de re-necessity a uniform treatment. The historical starting point is a puzzle raised by Aristotle's claim, advanced in one of the modal chapters of his Prior Analytics, that universally privative apodeictic premises simply convert. As regards the Prior and the Posterior Analytics, the data suggest a representation of propositions of the type in question by doubly modally qualified formulae of modal predicate logic that display a necessity operator in two (...) distinct positions. Can the N-operator occurring in these positions be given a unified semantical treatment (which would justify dispensing with a notational differentiation)? A positive answer, based on a suitably shaped truth condition for N-formulae, is given, and is supported in the final section with an alternative proof theoretically based conception of a property's essential belonging to an individual. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:61. HUME'S GEOMETRIC "OBJECTS" Arithmetic and algebra allow of precision and certainty. The science of geometry is not likewise a perfect and infallible science. At any rate, this is Hume's teaching in the Treatise. When two numbers are so combin ' d, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and 'tis for want of such a standard (...) of equality in extension, that geometry can scarce be esteem'd a perfect and infallible science. 1 The ideas of, say, equality and right line shade into· inequality and curve. It must not be supposed, however, that the vagueness of these ideas renders all judgments uncertain and fallible. 'Tie evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies....Such judgments are not only common, but in many cases certain and infallible. (T47) Nevertheless, geometry is a fallible science because its essential ideas are vague. Vagueness, due to lack of boundaries between ideas, is in the ideas themselves. For this reason, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. (T49) (Yet, some forty pages earlier Hume argued at length that the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each [T18]) As far as the Treatise goes, geometry is the science of measurement and as such it must allow for error. Even if precise geometric standards could be had, they would not make the propositions of geometry certain. Thus, we might precisely define a right line by a rule of order of indivisible points. But geometry, construed as the science of measurement, would not be perfected. Nor, if it were (the standard), is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserv ' d. The original standard of a right line is in reality nothing but a certain general appearance. (T52) 62. In the Enquiries, Hume continues to hold that notions essential to geometry, for example, equality, right line, and so on, are sensibles. But they are no longer generic appearances. They are determinate. The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate... even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. 2 In addition, geometry is no longer merely the science of measurement. The truths of Euclid, Hume holds, would remain truths even if there were no figures in nature. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. (EHU25) Professor Zabeeh, in his commentary on Hume, holds that Hume did not mean to imply that Euclid could dispense with the observation of figures. However, whenever possible Hume should be taken at his word: observation of figures is not a truth condition for propositions of geometry. A distinction must be drawn between discovery conditions and what Hume calls the "truth or evidence" of a geometric proposition. We may suppose that observation of figures is a discovery condition. But it is hardly a truth condition. The certainty, as opposed to the discovery, of geometric propositions does not depend on the existence in nature of any figure. I am mainly concerned, however, with Professor Zabeeh' s account of how, according to Hume, geometric propositions retain their certainty and evidence in the face of recalcitrant experience. Noting that Hume does not "fully explain," he gives the real reason for Hume's belief in the apodeictic certainty of mathematical truths. He appears to assume we never allow such truths to be controverted by empirical evidence. That is to say, if perchance we find, by measurement, that the sum of the angles of a Euclidean triangle 63. does not equal 180 degrees, either we say that we measured wrongly or we say that the triangle we have been measuring is not Euclidean.4 This formulation of Hume's reason avoids... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:61. HUME'S GEOMETRIC "OBJECTS" Arithmetic and algebra allow of precision and certainty. The science of geometry is not likewise a perfect and infallible science. At any rate, this is Hume's teaching in the Treatise. When two numbers are so combin ' d, as that the one has always an unite answering to every unite of the other, we pronounce them equal; and 'tis for want of such a standard (...) of equality in extension, that geometry can scarce be esteem'd a perfect and infallible science. 1 The ideas of, say, equality and right line shade into· inequality and curve. It must not be supposed, however, that the vagueness of these ideas renders all judgments uncertain and fallible. 'Tie evident, that the eye, or rather the mind is often able at one view to determine the proportions of bodies....Such judgments are not only common, but in many cases certain and infallible. (T47) Nevertheless, geometry is a fallible science because its essential ideas are vague. Vagueness, due to lack of boundaries between ideas, is in the ideas themselves. For this reason, 'tis impossible to produce any definition of them, which will fix the precise boundaries betwixt them. (T49) (Yet, some forty pages earlier Hume argued at length that the mind cannot form any notion of quantity or quality without forming a precise notion of the degrees of each [T18]) As far as the Treatise goes, geometry is the science of measurement and as such it must allow for error. Even if precise geometric standards could be had, they would not make the propositions of geometry certain. Thus, we might precisely define a right line by a rule of order of indivisible points. But geometry, construed as the science of measurement, would not be perfected. Nor, if it were (the standard), is there any such firmness in our senses or imagination, as to determine when such an order is violated or preserv ' d. The original standard of a right line is in reality nothing but a certain general appearance. (T52) 62. In the Enquiries, Hume continues to hold that notions essential to geometry, for example, equality, right line, and so on, are sensibles. But they are no longer generic appearances. They are determinate. The great advantage of the mathematical sciences above the moral consists in this, that the ideas of the former, being sensible, are always clear and determinate... even when no definition is employed, the object itself may be presented to the senses, and by that means be steadily and clearly apprehended. 2 In addition, geometry is no longer merely the science of measurement. The truths of Euclid, Hume holds, would remain truths even if there were no figures in nature. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence. (EHU25) Professor Zabeeh, in his commentary on Hume, holds that Hume did not mean to imply that Euclid could dispense with the observation of figures. However, whenever possible Hume should be taken at his word: observation of figures is not a truth condition for propositions of geometry. A distinction must be drawn between discovery conditions and what Hume calls the "truth or evidence" of a geometric proposition. We may suppose that observation of figures is a discovery condition. But it is hardly a truth condition. The certainty, as opposed to the discovery, of geometric propositions does not depend on the existence in nature of any figure. I am mainly concerned, however, with Professor Zabeeh' s account of how, according to Hume, geometric propositions retain their certainty and evidence in the face of recalcitrant experience. Noting that Hume does not "fully explain," he gives the real reason for Hume's belief in the apodeictic certainty of mathematical truths. He appears to assume we never allow such truths to be controverted by empirical evidence. That is to say, if perchance we find, by measurement, that the sum of the angles of a Euclidean triangle 63. does not equal 180 degrees, either we say that we measured wrongly or we say that the triangle we have been measuring is not Euclidean.4 This formulation of Hume's reason avoids... (shrink)

Friedrich Albert Lange (1828-1875) author of a famous History of Materialism and Critique of Its Present Significance (1866, English transI. 1877-79, repr. 1925 with introduction by Bertrand Russell), was also interested in the epistemological foundations of formal logic. Part I of his intended two-volume Logische Studien was published posthumously in 1877 by Hermann Cohen, head of the Marburg school of neo-Kantianism. Lange, departing from Kant, claims that spatial intuition is the source of the apodeictic character not only of the (...) truths of mathematics, but also of the truths of logic. He aims at showing this by basing validity and invalidity of syllogistic inferences on an interpretation of the standard forms (of proposition in assertoric syllogistic) with the help of the five kinds of possible relations (in fact what is known today as the Gergonne-Euler relations) between extensions of concepts given to us as areas in a plane, i.e.in space. Generality is achieved by considering all possible variations within each type of spatial relation, exhibiting a connection between concept and intuition reminding Lange of the Kantian "schema". Lange is well aware of the contemporary English "algebraic" logic, but he considers its approach as the appropriate one for a logic of content (Inhaltslogik) and not for a logic of extension (Umfangslogik). Lange did not live to enjoy the recognition by some leading logicians (amongst them John Venn, to whose reference in 1881 to Lange's "admirable Logische Studien" the present paper owes it title), nor could he respond to the many critics of his proposed foundation of logic. Its radicality as well as its broad reception (and discussion up to at least 1959) seem to entitle Lange's Logische Studien to an, if modest, place in the history of logic in the 19th century. (shrink)

Friedrich Albert Lange author of a famous History of Materialism and Critique of Its Present Significance, was also interested in the epistemological foundations of formal logic.Part I of his intended two‐volume Logische Studienwas published posthumously in 1877 by Hermann Cohen“head”of the Marburg school of neo‐Kantianism.Lange, departing from Kant, claims that spatial intuition is the source of the apodeictic character not only of the truths of mathematics, but also of the truths of logic.He aims at showing this by basing validity (...) and invalidity of syllogistic inferences on an interpretation of the standard forms with the help of the five kinds of possible relations between extensions of concepts given to us as areas in a plane, i.e.in space.Generality is achieved by considering all possible variations within each type of spatial relation, exhibiting a connection between concept and intuition reminding Lange of the Kantian “schema”. Lange is well aware of the contemporary English “algebraic” logic, but he considers its approach as the appropriate one for a logic of content and not for a logic of extension Lange did not live to enjoy the recognition by some leading logicians, nor could he respond to the many critics of his proposed foundation of logic.Its radicality as well as its broad reception seem to entitle Lange’s Logische Studiento an, if modest, place in the history of logic in the 19th century. (shrink)

Richard Rorty and Edmund Husserl would appear to be poles apart, facing each other from opposite corners of the philosophical ring. Husserl is a rationalist searching for an absolute foundation for science which will guarantee its apodeictic truth. Rorty is a post-modernist for whom science is but one discourse among many, none of which corresponds with reality.

In the introductory first chapter the author states his conviction that Aristotle’s theory of learning, at the center of which stands the apodeictic syllogism, is inadequate because partial. Chapter 2 is a balanced survey of Aristotle’s syllogistic, which does not serve the purpose of discovery, but is intended to turn into science knowledge already acquired. All learning proceeds from preexisting knowledge which is structured by demonstration. Next Bauman turns to Plato’s theory of learning as present in the Meno: learning (...) is remembering. His account of the Socratic method of making a disciple see the truth by pertinent questions is excellent. He warns us to avoid extreme interpretations of ἀνάμνησις. According to Aristotle, Plato confounded the process of remembering with induction. The process of learning consists in the passing from opinion to knowledge. Aristotle’s theory as explained in the Posterior Analytics widely differs from Plato’s. In chapter 5, Bauman examines whether the syllogism based on a universal major is a petitio principii, a charge laid against it ever since antiquity and repeated by John Stuart Mill. For Mill, induction is the only form of real inference, but Bauman shows that Mill’s position is not correct. Aristotle sets up a method which allows us to understand why things are the way they are and to pass on knowledge. In chapter 6, Bauman compares Aristotle’s method with what teachers usually do and with how textbook authors conceive the passing on of knowledge. Some previous knowledge is necessary for all teaching. Aristotle focused on how the sciences should be taught, showing how conclusions are implicitly contained in principles or can be deduced from them. Bauman thinks that this is restricting learning far too much and remains unsatisfactory. He disagrees with Aristotle’s statement that all scientific knowledge is expressible in propositions in the indicative mood. The syllogism cannot be the only mode for all teaching. This difficulty, however, can be solved when one keeps in mind what strictly scientific knowledge in the Aristotelian sense is, and that there are other forms of knowledge such as opinion, factual knowledge, and dialectic. Furthermore one should also consider that the syllogism is basic to all forms of reasoning, even if there are syllogisms of different types. A printing mistake on page 191, line 13 should be corrected.—Leo J. Elders, Institute for Philosophy, “Rolduc,” Kerkrade, The Netherlands. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Descartes and Husserl. The Philosophical Project of Radical BeginningsMichael K. ShimPaul S. MacDonald. Descartes and Husserl. The Philosophical Project of Radical Beginnings. Albany: State University of New York Press, 2000. Pp. 285. Paper, $21.95.The enormous influence exerted by Descartes on Husserl's phenomenological philosophy cannot be underestimated. Not only is Husserl quite open and explicit about his philosophical debt to Descartes, but the fundamental motivation of the phenomenological [End (...) Page 593] method (directed towards apodeicticity and the purification of consciousness) would most likely be meaningless without reference to the Cartesian precedent. Consequently, almost every exegetical approach to Husserlian phenomenology has at least mentioned the relevance of the Cartesian tradition. Unfortunately, rare has been the phenomenological treatment of Descartes current with the latest scholarship. As an exception to this general shortcoming, MacDonald's book is a most welcome entry into Husserl scholarship.One of MacDonald's main theses is that Descartes and Husserl shared similarities in historical circumstances and, thus, shared similar motives for their "radical beginnings" in philosophy. With regards to Descartes' historical circumstances, by providing a breathtaking overview of sixteenth-century skepticism, MacDonald gives a cogent account of what led to Descartes' attempted construction of an absolute epistemological foundation for philosophy. However, the "conceptual confusions and collapses" of neo-skepticism will "survive the Cartesian overthrow and, like a persistent contagion" (31) reappear in the form of nineteenth-century psychologism. MacDonald does a convincing job of highlighting the skeptical profile of psychologism by providing systematic parallels between the mainstays of neo-skepticism and nineteenth-century psychologism: namely, distrust of objective knowledge, subjective reductionism and epistemological relativism. Accordingly, what motivates Husserl's epoché has both historical and systematic resources in the Cartesian reduction. The point itself is nothing new, and Husserl himself stresses the skepticism of nineteenth-century psychologism, but the scholarship and erudition that inform MacDonald's detailed historical account is to be commended.The truly ambitious aspect of the book, however, is the painstakingly worked out systematic comparison between the respective philosophical projects. In this respect, MacDonald takes two correlated approaches. The first approach takes up the metaphors of discovery and "voyage of exploration" (5) common to both thinkers' writings in order to explicate the meaning of philosophical transformation or "conversion," a "cognitive-affective reorientation of the whole self" (227). However, these metaphors are to be understood as symptomatic of deeper formal parallels between the two thinkers.The second approach begins with the daring claim that "Descartes' and Husserl's formal ontologies are... functionally equivalent" (95), a claim MacDonald proposes to reinforce by examining the structural parallels between Descartes' simple-complex dyad on the one hand and Husserl's part-whole theory as introduced in the Third Logical Investigations. This claim is brought into relief by a reformation of Descartes' conception of "ideas." Rather than restrict the Cartesian conception of ideas to "objective content," MacDonald emphasizes the act-quality of Cartesian ideas (125-7). Thereby an intentional conception of Cartesian ideas is made possible. Anyone familiar with Husserl should not find this surprising: what MacDonald is trying to suggest is a division of Cartesian ideas into noesis and noema, with the "material" aspect of act-ideas finding phenomenological restoration in Husserl's "hyletic data." With these elements in place, MacDonald largely succeeds in constructing a fuller and richer than usual comparison between methodical doubt and the phenomenological reduction (151ff), centered on a non-mystical eidetic intuitionism. MacDonald's ultimate conclusion is [End Page 594] that Husserlian phenomenology, as "first philosophy," is thoroughly consistent with Cartesian metaphysics, now understood as "second philosophy" (243).MacDonald's systematic conclusions are much bolder than one might think, since they are adduced by running against the letter of Husserl's own interpretation of Descartes. The background claim is that Husserl himself did not fully appreciate his debt to Descartes, and it is this exegetical failure that has led to his eventual abandonment of the "Cartesian Way." However, in order to make such an assertion, MacDonald would be obligated to demonstrate the Cartesian influences on the phenomenological pillars of the later Husserl: i.e., temporalization, genetic analysis and the theory of intersubjectivity—as programmatically outlined in the Fourth and... (shrink)