Reply to Boghossian on the Distinction between the A Priori and the A Posteriori1

2020 ◽  
pp. 156-167
Author(s):  
Paul Boghossian ◽  
Timothy Williamson
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
A Posteriori

This chapter replies to Boghossian’s defence of the epistemological depth of the a priori–a posteriori distinction in Chapter 9 against the author’s critique in Chapter 8. It shows that nothing essential to the argument depends on the distinction between inner and outer experience. It then explains how Boghossian provides no workable alternative to the account in Chapter 8 of the role of imagination in generating knowledge in the key examples, and why the absence of such an alternative leaves Boghossian in danger of drifting into very extensive scepticism about mathematical knowledge. It is also noted that epistemological externalism does not figure as a premise in the key arguments of Chapter 8, although they may offer support for such externalism.

scholarly journals The Concept of Theoretical-Empirical Dualism in Teaching Math

2020 ◽  
Vol 29 (4) ◽  
pp. 85-95
Author(s):  
G. D. Gefan
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Research Work ◽  
Cognitive Activity ◽  
Teaching Mathematics ◽  
Mathematical Education ◽  
A Posteriori ◽  
Research Activities ◽  
New Knowledge

Among the problems of mathematical education, the article highlights: (1) insufficient attention paid to the fundamental, structure-forming role of mathematics; (2) speculative learning, its isolation from practice. The concept of theoretical-empirical dualism in teaching is formulated as the unity of the abstract-theoretical and experimental-empirical cognitive activity of students. According to the author, a priori and a posteriori mathematical knowledge should be distinguished. A priori knowledge either seems to an individual to be completely obvious, indisputable, or he assimilates it uncritically, “on faith”. A posteriori mathematical knowledge subjectively arises in the process of student’s intense theoretical and practical activity, and is being actively and comprehensively verified experimentally – either using mathematical applications, or through mathematical experiments. The empirical component of teaching mathematics implies a variety of forms and methods of active (including computer) and professionally oriented learning, giving experience in independent formulation of problems, joint search for ways to solve them, interaction and teamwork. Particular attention is paid to the use of mathematical experiments in those frequent cases when it is necessary to replace or supplement complex evidence, illustrate new knowledge, and give research skills. Monte Carlo mathematical experiments are demonstrated, which serve, in particular, as a bright, figurative, and convincing form of reinforcing theoretical knowledge in the field of stochastic branches of mathematics. The research work of students is considered as the highest stage of the students’ theoretical-empirical activity. The article proposes subjects of research activities of students in the process or upon completion of the study of probabilistic and statistical disciplines.

How Deep is the Distinction between A Priori and A Posteriori Knowledge?1

2020 ◽  
pp. 117-136
Author(s):  
Paul Boghossian ◽  
Timothy Williamson
Keyword(s):  
Mathematical Knowledge ◽  
A Priori ◽  
Ways Of Knowing ◽  
A Posteriori ◽  
Theoretical Terms ◽  
Clear Cases

This chapter argues that although a distinction can be drawn between a priori and a posteriori ways of knowing or forms of justification, by contrasting paradigm cases on each side, the result is epistemologically shallow: it does not cut at the joints, because some clear cases of the a priori differ from some clear cases of the a posteriori only in epistemologically superficial ways. By contrast, attempts to draw the distinction in more theoretical terms, for instance by distinguishing evidential from enabling roles for experience in knowledge, end up by classifying paradigm cases on unwanted sides of the line. Although the role of the imagination in the chapter’s key examples may seem abnormal, it is argued that it generalizes much more widely than one might expect to logical and mathematical knowledge.

Necessity, Certainty, and the A Priori

1988 ◽  
Vol 18 (1) ◽  
pp. 43-66 ◽  
Author(s):  
Albert Casullo
Keyword(s):  
Cognitive Processes ◽  
Mathematical Knowledge ◽  
A Priori ◽  
Theory Of Knowledge ◽  
A Posteriori ◽  
Unitary Theory ◽  
Knowledge Based

Empiricist theories of knowledge are attractive for they offer the prospect of a unitary theory of knowledge based on relatively well understood physiological and cognitive processes. Mathematical knowledge, however, has been a traditional stumbling block for such theories. There are three primary features of mathematical knowledge which have led epistemologists to the conclusion that it cannot be accommodated within an empiricist framework: 1) mathematical propositions appear to be immune from empirical disconfirmation; 2) mathematical propositions appear to be known with certainty; and 3) mathematical propositions are necessary. Epistemologists who believe that some nonmathematical propositions, such as logical or ethical propositions, cannot be known a posteriori also typically appeal to the three factors cited above in defending their position. The primary purpose of this paper is to examine whether any of these alleged features of mathematical propositions establishes that knowledge of such propositions cannot be a posteriori.

A priori and a posteriori derived dietary patterns in infancy and cardiometabolic health in childhood: The role of body composition

2018 ◽  
Vol 37 (5) ◽  
pp. 1589-1595 ◽  
Author(s):  
Elisabeth T.M. Leermakers ◽  
Edith H. van den Hooven ◽  
Oscar H. Franco ◽  
Vincent W.V. Jaddoe ◽  
Henriëtte A. Moll ◽  
...  
Keyword(s):  
Body Composition ◽  
Dietary Patterns ◽  
A Priori ◽  
Cardiometabolic Health ◽  
A Posteriori

Inference, Agency, and Responsibility

Reasoning ◽  
2019 ◽  
pp. 101-124 ◽  
Author(s):  
Paul Boghossian
Keyword(s):  
Philosophy Of Mind ◽  
A Priori ◽  
A Posteriori

What happens when we reason our way from one proposition to another? This process is usually called “inference” and this chapter examines its nature. It revisits the author’s earlier attempts to explain the nature of the process of inference, and tries to further clarify why we need the type of “intellectualist” account of that process that he has been pursuing. In the course of doing so, the chapter traces some unexpected connections between our topic and the distinction between a priori and a posteriori justification, and tries to draw some general methodological morals about the role of phenomenology in the philosophy of mind.

scholarly journals Epistemología de los profesores sobre el conocimiento matemático escolar: un estudio de caso

2021 ◽  
Vol 24 (2) ◽  
pp. 177-206
Author(s):  
Karla Sepúlveda Obreque ◽  
◽  
Javier Lezama Andalón ◽  
Keyword(s):  
Qualitative Study ◽  
Human Activity ◽  
Mathematical Knowledge ◽  
A Priori ◽  
Microscopic Analysis ◽  
Human Action ◽  
A Priori Knowledge ◽  
Epistemic Relativism ◽  
Estudio De Caso

It was sought to know the epistemology of the teachers on school mathematical knowledge. The study was framed in the Socioepistemological Theory, understanding mathematics as a human activity from epistemic relativism. This qualitative study used microscopic analysis to form categories and then dialectically analyzed those categories. The investigative interest arose when observing the influence of Eurocentrism, the mono epistemisism of the school and the absence of some knowledge in teaching. The epistemology of the teacher influences his teaching and affects the school model as a tool for change or social continuity. The results showed that teachers mostly understand mathematics as a priori knowledge, assigning to human action the role of discovering, interpreting or formalizing it.

Philosophical Naturalism

2016 ◽  
Author(s):  
Hilary Kornblith
Keyword(s):  
Experimental Philosophy ◽  
Methodological Approach ◽  
A Priori ◽  
Empirical Work ◽  
Philosophical Methodology ◽  
A Posteriori ◽  
Cognitive Sciences ◽  
Philosophical Naturalism ◽  
Philosophical Questions

This article focuses on naturalistic approaches to philosophical methodology. It begins with an overview of naturalism, its relationship with views about the a priori, and the implications of a philosopher’s commitment to naturalism for proper method in philosophy. It then considers the disagreement among naturalists about the tenability of the a priori/a posteriori distinction with respect to naturalism, before turning to a discussion of the use of science to address philosophical questions. It also looks at work in epistemology which draws on results in the cognitive sciences as a way of understanding the nature of knowledge, with particular emphasis on the role of Alvin Goldman in getting epistemologists to pay attention to the import of empirical work for understanding epistemological issues. Finally, it explores experimental philosophy as a methodological approach to philosophical questions and comments on the debate over the legitimacy of armchair methods in philosophy.

The role of fossils in the phylogenetic reconstruction of Echinodermata

1997 ◽  
Vol 3 ◽  
pp. 267-288 ◽  
Author(s):  
Colin D. Sumrall
Keyword(s):  
Phylogenetic Analyses ◽  
A Priori ◽  
Phylogenetic Reconstruction ◽  
Morphological Data ◽  
Character State ◽  
A Posteriori ◽  
State Transformation ◽  
Single Character ◽  
Fossil Data

Morphological data can be used effectively in phylogenetic analyses to determine relationships among echinoderm clades. These data in the form of characters are simply hypotheses that any observed morphological state among taxa results from a single character state transformation and is therefore, homologous. All such character states must be scored as potentially homologous unless the hypothesis of homology can be rejected by the tests of similarity, conjunction (a priori), or character congruence (a posteriori). Fossils are not always more incomplete than extant forms and incompleteness originates from non-preservation and long phylogenetic branches. The greatest strength of fossil data lies in its ability to effectively shorten long phylogenetic branches by occurring on the tree nearer to the nodes than extant terminal taxa and thus circumventing positively misleading results encountered in parsimony analysis under long branch conditions.

Hume’s History of England

2014 ◽  
Author(s):  
Donald T. Siebert
Keyword(s):  
Cultural History ◽  
A Priori ◽  
A Posteriori ◽  
Historical Evidence ◽  
Literal Sense ◽  
Political Events ◽  
History Of ◽  
William Robertson

This chapter argues for the History of England’s importance in Hume’s overall achievement. The chapter describes the History’s genesis, reception, methods, and aims. In the role of historian, Hume shared with the ancients the assumption that history is an elevated genre functioning as the “Mistress of Wisdom.” Yet this long work is more notable for historiographical innovation. Like William Robertson and Edward Gibbon, Hume wrote conjectural or philosophical history. Like Machiavelli, Voltaire, and Montesquieu, Hume wrote civil or cultural history, including detailed information on political events, law, commerce, and manners. In a larger sense, the History demonstrates a great philosopher leaving his study (or “closet”) to deal with that practical, sometimes intractable world outside the study. A priori reasoning is tested against that a posteriori reality provided by historical evidence. Thus, in writing the History, Hume became an empiricist in an almost literal sense.

On the Idea of and Necessity for a Metaphysics of Morals

2021 ◽  
pp. 21-37
Author(s):  
Mark Timmons
Keyword(s):  
A Priori ◽  
A Posteriori ◽  
General Introduction ◽  
Synthetic A Priori ◽  
Metaphysics Of Morals

This chapter focuses on Section I of the general introduction to The Metaphysics of Morals in which Kant explains what a metaphysics of morals is, and why there must be one. To properly understand Kant’s views on these matters requires explaining Kant’s conception of philosophy and the place of metaphysics as a branch of philosophy. In spelling this out, the chapter discusses key distinctions between theoretical and practical cognition, empirical (a posteriori) versus rational (a priori) sources of cognition, and the analytic/synthetic distinction as Kant understood it. For Kant, a metaphysics of morals is that branch of philosophy concerned with those synthetic a priori propositions and principles fundamental to morality. The chapter also explains the role of anthropology in a metaphysics of morals.

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