Lexicon of Arguments


Philosophical and Scientific Issues in Dispute
 
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The author or concept searched is found in the following 4 entries.
Disputed term/author/ism Author
Entry
Reference
Motion Russell
 
Books on Amazon:
Bertrand Russell
Kursbuch 8 IV 15
Motion/change/Russell: old/Zenon: "state of change" - today/VsZenon: at one time in one place, at another time in another place - wrong, to say that it is in the next moment located in the "adjacent place" - wrong: jump within a moment (Zenon has correctly identified) ---
Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967

15
Time: The banishment of the infinitely small quantity has peculiar consequences: e.g. there is no longer something like a next moment. (> Time). If there are to be no infinitely small quantities, no two moments follow one another directly, but there are always more moments inbetween. Consequently, there must be an infinite number of additional moments between two arbitrary moments. If the number were finite, then one would be closer to the first of the two moments and it would be the next! This is precisely where the philosophy of the infinite begins.
Space: the same applies to the space. However small a space is, it can be further subdivided. In this way we never reach the infinitely small quantity. No finite number of divisions leads to the > point.
Nevertheless, there are points, but they are not achieved by successive divisions. Points are not infinitely small distances.
Motion, change: strange results: earlier, it was thought that when something changes, it must be in a state of change when it moves, in a state of motion.
This is wrong from today's point of view: If a body moves, one can only say that it is at one time at the place and at another time at a different place.
We must not say that it will be at the next place in the next moment because there is no next moment.

R I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

R II
B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

R IV
B. Russell
Probleme der Philosophie Frankfurt 1967

R VI
B. Russell
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996

Paradoxes Logic Texts
 
Books on Amazon
Re III 187f
Paradoxes: Hierarchy (Tarski)-problem: Kreter does not know which level his own statement assumes - it is only meaningful if truth attribution takes place at a lower level - it requires knowledge! (> Knowledge/understanding). Self-reference: is not always bad or faulty.
---
Re III 192f
Curry paradox: If A and if A. then B, then B - If this conditional sentence is true, then snow is black - ponendo ponens - solution: contraction: two applications are replaced by one - change of logic. Example: If this (conditional) theorem is true, then snow is black.
Consequentia mirabilis: If A, then ~ A, thus ~ A - contraction: If A, then if A, then 0 = 1; So if A, then 0 = 1 - contraction leads to triviality: it makes every statement from the curry paradox true.
---
Re III 196
Semantically completed: language contains its own truth predicates - avoidance of paradox: is done by separation of the truth conditions from fallacy conditions. ---
Sai V 17
Zenon/Sainsbury: Zenon's thesis: no area of space is infinitely divisible, so that it has an infinite number of parts, if each part has a certain extent, for then the sum is infinitly large - Zenon tried to show with this, that not really many things exist - overall, no object can have parts, for then it must be infinitely large. ---
V 19
Sainsbury: infinite division goes only mentally. - Problem: then no composition to space - in the composition, however, the space does not have to grow indefinitely. - e.g. sequences with limit. ---
Sai V 38f
Arrow/Paradox/Zenon: at any time, the flying arrow takes a space that is identical to it. The arrow cannot move in a moment because movement requires a period of time and a moment is seen as a point - this also applies to everything else: nothing moves. Time/AristotelesVsZenon: Time does not consist of points - SainsburyVsAristoteles: today: we are constantly trying to allow points of time: E.g. acceleration at a point, etc. ---
V 39
The question of whether the arrow is moving or resting in a moment is also related to other moments - Defininition rest/Sainsbury: an object rests under the condition that it is also at the same point in all nearby moments - no information about the individual moment can determine whether the arrow is moving - the premise is acceptable: no movement at the moment - but the conclusion is unacceptable. ---
Sai V 184
Sentence/Statement: is only circular at a certain occasion - paradox is therefore not in the meaning, but in the occasion - ((s)> usage theory)
Logic Texts
Me I Albert Menne Folgerichtig Denken Darmstadt 1988
HH II Hoyningen-Huene Formale Logik, Stuttgart 1998
Re III Stephen Read Philosophie der Logik Hamburg 1997
Sal IV Wesley C. Salmon Logik Stuttgart 1983
Sai V R.M.Sainsbury Paradoxien Stuttgart 2001
Space Russell
 
Books on Amazon:
Bertrand Russell
Kursbuch 8 Mathematik, Frankfurt/M. März 1967
12
Weierstraß/Russell: banished the infinitesimal variable from mathematics - VsZenon: error: to think that the world must always be the same because there is no state of change. - Without infinitesimal variables: time: no more "next moment". - No immediate result of two moments - in between there are ever more moments. - Space: dito: always further divisible.
B. Russell, ABC of Relativity Theory Frankfurt 1989
II 46
Def "space-like"/Russell: Two events are space-like if it is impossible for a body to move fast enoug to be present at both events - but he can be "halfway" and perceive both as happening at the same time. Def "time-like"/Russell: Two events are time-like if it is possible for a physical body to be present at both events. Borderline case: E.g. two events as part of a light beam or - E.g. an event. perception of the other event: then distance 0.
Def distance/Russell: is a physical fact which is part of the events and does not depend on the circumstances of observer.
Neglecting gravitation, one can apply the Secial Theory of Relativity. Then the distance between two events can be calculated if one knows the spatial and temporal distance, measured by an arbitrary observer.

R I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

R II
B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

R IV
B. Russell
Probleme der Philosophie Frankfurt 1967

R VI
B. Russell
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996

Zeno Russell
 
Books on Amazon:
Bertrand Russell
Bertrand Russell Die Mathematik und die Metaphysiker 1901 in: Kursbuch 8 Mathematik 1967

13
RussellVsZenon: Zenon only made the mistake of drawing the conclusion (if he drew any conclusions at all) that because there is no state of change, the world would be in the same state at any given time. But this conclusion cannot be drawn according to Weierstrass.
---
15
Time: The banishment of the infinitely small quantities has peculiar consequences: e.g. there is no longer anything like a next moment. (> Time). If there are to be no infinitely small quantities, no two moments follow one another directly, but there are always other moments inbetween. Consequently there must be an infinite number of additional moments between two arbitrary moments. If the number were finite, then one would be closer to the first of the two moments and so would be the next! This is precisely where the philosophy of the infinite begins.
---
19
Zenon/Russell: Everyone who attacked Zenon was not right about it, because they allowed his premisses. Zenon probably invoked the assumption that the whole has more elements than a part. ---
20
Then Achilles must have been in more places than the turtle. And it followed that he could never catch up with them.
If we allow the axiom that the whole thing has more elements than a part, Zeno's conclusion fits perfectly.
The retention of the axiom leads to other paradoxes of which I call one the paradox of Tristram Shandy. It is the reversal of the Zenonian paradox and says that the turtle can get everywhere if you give it only enough time. Tristram Shandy needed two years to list the course of the first two days of his life and complained that the material accumulated faster than he could capture it.
Russell: I assert now that if he had lived his life that way further on, he would not have missed any part of his biography. For the hundredth part is written in the thousandth year, and so on.

R I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

R II
B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

R IV
B. Russell
Probleme der Philosophie Frankfurt 1967

R VI
B. Russell
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996


The author or concept searched is found in the following controversies.
Disputed term/author/ism Author Vs Author
Entry
Reference
Zeno Russell Vs Zeno
 
Books on Amazon:
Bertrand Russell
B. Russell Die Mathematik und die Metaphysiker in Kursbuch IV S. 12 Frankfurt 1967

Weierstrass (who probably did not think of Zenon) has banished the infinitely small quantities from mathematics and thus has finally proved that we live in an unchanging world, and that the arrow is actually in an idle state during flight.
RussellVsZenon: Zenon only committed the error to conclude (if he ever drew conclusions) that, because there is not a state of change, the world is at any time in the same state.
This conclusion is not to draw according to Weierstrass.


R I
B. Russell/A.N. Whitehead
Principia Mathematica Frankfurt 1986

R II
B. Russell
Das ABC der Relativitätstheorie Frankfurt 1989

R IV
B. Russell
Probleme der Philosophie Frankfurt 1967

R VI
B. Russell
Die Philosophie des logischen Atomismus
In
Eigennamen, U. Wolf (Hg), Frankfurt 1993

R VII
B. Russell
Wahrheit und Falschheit
In
Wahrheitstheorien, G. Skirbekk (Hg), Frankfurt 1996