scholarly journals Numbers, Empiricism and the A Priori

2020 ◽  
Vol 11 (2) ◽  
pp. 149-177
Author(s):  
Olga Ramírez Calle ◽  
Keyword(s):  
Systematic Study ◽  
A Priori ◽  
Logical Thinking ◽  
Ontological Status ◽  
Analytical Philosophy ◽  
Alternative Path ◽  
Synthetic A Priori ◽  
The Difference ◽  
Inferential Thinking ◽  
Logical Rules

The present paper deals with the ontological status of numbers and considers Frege´s proposal in Grundlagen upon the background of the Post-Kantian semantic turn in analytical philosophy. Through a more systematic study of his philosophical premises, it comes to unearth a first level paradox that would unset earlier still than it was exposed by Russell. It then studies an alternative path that, departing from Frege’s initial premises, drives to a conception of numbers as synthetic a priori in a more Kantian sense. On this basis, it tentatively explores a possible derivation of basic logical rules on their behalf, suggesting a more rudimentary basis to inferential thinking, which supports reconsidering the difference between logical thinking and AI. Finally, it reflects upon the contributions of this approach to the problem of the a priori.

Rethinking the Synthetic a priori de re

1998 ◽  
pp. 15-22
Author(s):  
Paul Burger
Keyword(s):  
Ontological Commitment ◽  
Necessary Conditions ◽  
A Priori ◽  
A Posteriori ◽  
Analytical Philosophy ◽  
Radical Empiricism ◽  
De Re ◽  
Direct Awareness ◽  
Synthetic A Priori ◽  
Ontological Turn

Hume and Kant destroyed the belief in the apriori de re, i.e. the rationalist’s doctrine of direct awareness of necessary facts about the nature of being. Later on, analytical philosophy told us that there are only two general classes of statements, synthetics a posteriori and analytics a priori. Quine eventually rejected the a priori in general and advanced a radical empiricism. However, both moderate and radical empiricism has recently been challenged by realistic minded philosophers. They have argued that ontological topics such as the nature of properties, laws or causation remain strongly undetermined by semantic ascent and Quinean ontological commitment, and announced an ontological turn. Are not ontological or metaphysical explanations a priori explanations? Despite his preferred talk in terms of a posteriori realism and inference of the best explanation, Armstrong’s defence of universals looks very much like an apriori one. Others, such as Barry Smith, explicitly defend that there are synthetic propositions a priori de re. I believe in both: Kant was right in claiming that an understanding of what metaphysics can teach us is dependent upon a clear concept of the synthetic a priori, but—against Kant— synthetics a priori de re are legitimate. In this paper I will defend synthetics a priori de re. However, I will reject the rationalist’s appeal to direct awareness of necessary facts as well as undeniableness or infallibility as necessary conditions for a prioris. Instead I will claim that all synthetics a priori express hypothetical truths.

Philosophical Reduction(ism) in Meta-Language Reconstructions of Yhwh as Religious Object

2018 ◽  
Vol 26 (2) ◽  
Author(s):  
Jaco W Gericke
Keyword(s):  
Old Testament ◽  
Hebrew Bible ◽  
A Priori ◽  
Research Problem ◽  
Second Order ◽  
Unified Theory ◽  
Ontological Status ◽  
Introductory Overview ◽  
Theory Of Everything ◽  
Interpretative Approach

In Hebrew Bible/Old Testament scholarship, one encounters a variety of reductive perspectives on what exactly Yahweh as religious object is assumed to be. In this article, a clarification of the research problem is followed by an introductory overview of what is currently available on this topic as is attested in the context of various interpretative methodologies and their associated meta-languages. It is argued that any attempt to describe the actual metaphysical nature and ontological status of the religious object in the jargon of a particular interpretative approach is forever prone to committing the fallacy of reductionism. Even so, given the irreducible methodological perspectivism supervening on heuristic specificity, reductive accounts as such are unavoidable. If this is correct, then it follows a fortiori that a unified theory (of everything Yahweh can be said to be) and an ideal meta-language (with which to perfectly reconstruct the religious object within second-order discourse) are a priori impossible.

Self and Selves

2017 ◽  
Author(s):  
Ralph C.S. Walker
Keyword(s):  
Personal Identity ◽  
Moral Philosophy ◽  
A Priori ◽  
The Status ◽  
The Subject ◽  
Synthetic A Priori

Kant is committed to the reality of a subject self, outside time but active in forming experience. Timeless activity is problematic, but that can be dealt with. But he holds that the subject of experience is not an object of experience, so nothing can be known about it; this raises a problem about the status of his own theory. But he ought to allow that we can know of its existence and activity, as preconditions of experience: the Critique allows that synthetic a priori truths can be known in this way. However, its identity conditions remain unknowable. Kant’s unity of apperception shares much with Locke’s continuity of consciousness, but does not determine the identity of a thing. Personal identity is bodily identity. Only Kant’s moral philosophy justifies recognizing other selves; it could warrant ascribing a similar status to animals.

The Logicism of Frege, Dedekind, and Russell

2009 ◽  
Author(s):  
William Demopoulos ◽  
Peter Clark
Keyword(s):  
A Priori ◽  
The Core ◽  
Common Thread ◽  
Synthetic A Priori ◽  
The Common

This article is organized around logicism's answers to the following questions: What is the basis for our knowledge of the infinity of the numbers? How is arithmetic applicable to reality? Why is reasoning by induction justified? Although there are, as is seen in this article, important differences, the common thread that runs through all three of the authors discussed in this article their opposition to the Kantian thesis that reflection on reasoning with mere concepts (i.e., without attention to intuitions formed a priori) can never succeed in providing satisfactory answers to these three questions. This description of the core of the view differs from more usual formulations which represent the opposition to Kant as an opposition to the contention that mathematics in general, and arithmetic in particular, are synthetic a priori rather than analytic.

On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems

2003 ◽  
Vol 10 (3) ◽  
pp. 401-410
Author(s):  
M. S. Agranovich ◽  
B. A. Amosov
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Fourier Coefficients ◽  
Elliptic Boundary ◽  
A Priori ◽  
Adjoint Problem ◽  
Elliptic Boundary Value ◽  
Right Hand ◽  
The Difference ◽  
The Right

Abstract We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.

Magnetotelluric static shift: Estimation and removal using the cokriging method

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. F25-F34 ◽  
Author(s):  
Benoit Tournerie ◽  
Michel Chouteau ◽  
Denis Marcotte
Keyword(s):  
Apparent Resistivity ◽  
A Priori ◽  
Shift Factor ◽  
Static Shift ◽  
Geostatistical Model ◽  
Data Set ◽  
Resistivity Sounding ◽  
The Difference ◽  
Cross Variogram

We present and test a new method to correct for the static shift affecting magnetotelluric (MT) apparent resistivity sounding curves. We use geostatistical analysis of apparent resistivity and phase data for selected periods. For each period, we first estimate and model the experimental variograms and cross variogram between phase and apparent resistivity. We then use the geostatistical model to estimate, by cokriging, the corrected apparent resistivities using the measured phases and apparent resistivities. The static shift factor is obtained as the difference between the logarithm of the corrected and measured apparent resistivities. We retain as final static shift estimates the ones for the period displaying the best correlation with the estimates at all periods. We present a 3D synthetic case study showing that the static shift is retrieved quite precisely when the static shift factors are uniformly distributed around zero. If the static shift distribution has a nonzero mean, we obtained best results when an apparent resistivity data subset can be identified a priori as unaffected by static shift and cokriging is done using only this subset. The method has been successfully tested on the synthetic COPROD-2S2 2D MT data set and on a 3D-survey data set from Las Cañadas Caldera (Tenerife, Canary Islands) severely affected by static shift.

scholarly journals Another Name for Liberty: Revelation, ‘Objectivity,’ and Intellectual Freedom in Barth and Marion

Open Theology ◽  
2019 ◽  
Vol 5 (1) ◽  
pp. 430-450
Author(s):  
Kristóf Oltvai
Keyword(s):  
A Priori ◽  
The Other ◽  
Christian Theology ◽  
Intellectual Freedom ◽  
Specific Kind ◽  
Absolute Truth ◽  
Saturated Phenomenon ◽  
Other Hand ◽  
The Difference ◽  
The Relationship

Abstract Karl Barth’s and Jean-Luc Marion’s theories of revelation, though prominent and popular, are often criticized by both theologians and philosophers for effacing the human subject’s epistemic integrity. I argue here that, in fact, both Barth and Marion appeal to revelation in an attempt to respond to a tendency within philosophy to coerce thought. Philosophy, when it claims to be able to access a universal, absolute truth within history, degenerates into ideology. By making conceptually possible some ‚evental’ phenomena that always evade a priori epistemic conditions, Barth’s and Marion’s theories of revelation relativize all philosophical knowledge, rendering any ideological claim to absolute truth impossible. The difference between their two theories, then, lies in how they understand the relationship between philosophy and theology. For Barth, philosophy’s attempts to make itself absolute is a produce of sinful human vanity; its corrective is thus an authentic revealed theology, which Barth articulates in Christian, dogmatic terms. Marion, on the other hand, equipped with Heidegger’s critique of ontotheology, highlights one specific kind of philosophizing—metaphysics—as generative of ideology. To counter metaphysics, Marion draws heavily on Barth’s account of revelation but secularizes it, reinterpreting the ‚event’ as the saturated phenomenon. Revelation’s unpredictability is thus preserved within Marion’s philosophy, but is no longer restricted to the appearing of God. Both understandings of revelation achieve the same epistemological result, however. Reality can never be rendered transparent to thought; within history, all truth is provisional. A concept of revelation drawn originally from Christian theology thus, counterintuitively, is what secures philosophy’s right to challenge and critique the pre-given, a hermeneutic freedom I suggest is the meaning of sola scriptura.

Three Kantian Routes to the Synthetic A Priori

2021 ◽  
pp. 1-28
Author(s):  
Robert Audi
Keyword(s):  
A Priori ◽  
Pure Reason ◽  
Critique Of Pure Reason ◽  
Insufficient Attention ◽  
Synthetic A Priori ◽  
The One ◽  
Philosophical Importance

Abstract Kant influentially distinguished analytic from synthetic a priori propositions, and he took certain propositions in the latter category to be of immense philosophical importance. His distinction between the analytic and the synthetic has been accepted by many and attacked by others; but despite its importance, a number of discussions of it since at least W. V. Quine’s have paid insufficient attention to some of the passages in which Kant draws the distinction. This paper seeks to clarify what appear to be three distinct conceptions of the analytic (and implicitly of the synthetic) that are presented in Kant’s Critique of Pure Reason and in some other Kantian texts. The conceptions are important in themselves, and their differences are significant even if they are extensionally equivalent. The paper is also aimed at showing how the proposed understanding of these conceptions—and especially the one that has received insufficient attention from philosophers—may bear on how we should conceive the synthetic a priori, in and beyond Kant’s own writings.

NUMERICAL SOLUTION OF TWO-DIMENSIONAL PROBLEMS OF THERMOVISCOELASTICITY

2021 ◽  
Vol 335 (1) ◽  
pp. 60-64
Author(s):  
M. Bukenov ◽  
Ye. Mukhametov
Keyword(s):  
A Priori ◽  
Elastic Collision ◽  
Qualitative Behavior ◽  
Stress Profile ◽  
Two Dimensional ◽  
A Priori Information ◽  
Deformable Solids ◽  
Methods Of Calculation ◽  
The Difference ◽  
Priori Information

This paper considers the numerical implementation of two-dimensional thermoviscoelastic waves. The elastic collision of an aluminum cylinder with a two-layer plate of aluminum and iron is considered. In work [1] the difference schemes and algorithm of their realization are given. The most complete reviews of the main methods of calculation of transients in deformable solids can be found in [2, 3, 4], which also indicates the need and importance of generalized studies on the comparative evaluation of different methods and identification of the areas of their most rational application. In the analysis and physical interpretation of numerical results in this work it is also useful to use a priori information about the qualitative behavior of the solution and all kinds of information about the physics of the phenomena under study. Here is the stage of evolution of contact resistance of collision – plate, stress profile.

XXV. Note on the tides in the port of London

1832 ◽  
Vol 122 ◽  
pp. 595-599 ◽  
Keyword(s):  
Great Britain ◽  
A Priori ◽  
High Water ◽  
Eastern Coast ◽  
The Moon ◽  
Cape Of Good Hope ◽  
The Difference

Mr. Stratford has favoured me with a comparison of the predicted times of high water deduced from Mr. Bulpit’s Tables, White’s Ephemeris, and the British Almanac, with the observations at the London Docks. These observations are, unfortunately, so imperfect, that the differences must not be entirely attributed to the errors of the Tables, which, however, seem susceptible of much improvement. I subjoin this comparison; and in order to convey an idea of the confidence which may be placed in the observations, I also subjoin a comparison, by Mr. Deacon, of the observations at the London and St. Katherine’s Docks, which are made according to the same plan, and of which the merit is the same. The differences in the determinations at these two places, which are only about a quarter of a mile distant from each other, may serve to indicate the reliance which can be placed in either. In my paper on the Tides at Brest, I remarked that the retard or the constant λ — λ, is considerably greater as deduced from observation here than at Brest. That this must be the case is also evident from the following very simple à priori considerations.—The highest high water takes place when the moon passes the meridian at a time equal to the retard. The tide is propagated from Brest to London, round Scotland, in about twenty-two hours, that is, supposing the tide which takes place in our river to be principally due to that branch of the tide which descends along the eastern coast of Great Britain, which I believe to be the case. The highest tide therefore is propagated from Brest to London in about twenty-two hours, and the difference in the retard or in the constant λ — λ, will be nearly the moon’s motion in twenty-two hours, or about 11°; I made the difference in the retard from observation 10°. The tide takes about fifteen hours to reach Brest from the Cape of Good Hope; no doubt the retard there is considerably less.

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