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Παράδοξα
Παράδοξα
Θεωρίες που αφορούν τη λογική, το χώρο, το χρόνο, τα μαθηματικά, τη φιλοσοφία
Έχετε αντιμετωπίσει καταστάσεις όπου τα φαινόμενα μάλλον απατούν; Αυτό ισχύει στα παράδοξα, που προκύπτουν με βάση μια συλλογιστική η οποία μας οδηγεί σε ένα προφανώς λογικά απαράδεκτο συμπέρασμα, το οποίο όμως βασίζεται σε προφανώς αποδεκτές υποθέσεις.
Ο καθηγητής φιλοσοφίας Ρ. Μ. Σένσμπουρι μας ξεναγεί στο λαβυρινθώδη, προκλητικό όσο και γοητευτικό αινιγματικό κόσμο των παραδόξων. Εξηγεί ότι συνδυάζουν τη διασκέδαση με την απαιτητική πνευματική άσκηση, την έρευνα με την γόνιμη αντιπαράθεση, καθώς στις περισσότερες περιπτώσεις είναι εύκολο να διατυπωθούν, δύσκολο όμως να "επιλυθούν". Σημειώνει ότι, σε αντίθεση με τα αινίγματα συναναστροφών και τις σπαζοκεφαλιές, πρόκειται για πολυσύνθετα πνευματικά παιχνίδια, που συνδέονται ιστορικά με κρίσιμους σταθμούς και επαναστατικά βήματα στο χώρο της διανόησης, ενώ εγείρουν σοβαρά θεωρητικά ζητήματα που σχετίζονται με τα πεδία της Φιλοσοφίας, της Λογικής, των Μαθηματικών.
Με οξύνοια, χιούμορ και σαφήνεια ο Σένσμπουρι παραθέτει μερικά πασίγνωστα παράδοξα, προσκαλώντας τον αναγνώστη να αναμετρηθεί μαζί τους. Μεταξύ αυτών, τα παράδοξα του Ζήνωνα -με πιο γνωστό τον αγώνα δρόμου ανάμεσα στον Αχιλλέα και στη χελώνα-, τα παράδοξα του ψεύτη, το παράδοξο του Ράσελ, το δίλημμα του φυλακισμένου, το παράδοξο των κοράκων, το απροειδοποίητο διαγώνισμα κ.ά.
Θεωρίες που αφορούν τη λογική, το χώρο, το χρόνο, τα μαθηματικά, τη φιλοσοφία
Έχετε αντιμετωπίσει καταστάσεις όπου τα φαινόμενα μάλλον απατούν; Αυτό ισχύει στα παράδοξα, που προκύπτουν με βάση μια συλλογιστική η οποία μας οδηγεί σε ένα προφανώς λογικά απαράδεκτο συμπέρασμα, το οποίο όμως βασίζεται σε προφανώς αποδεκτές υποθέσεις.
Ο καθηγητής φιλοσοφίας Ρ. Μ. Σένσμπουρι μας ξεναγεί στο λαβυρινθώδη, προκλητικό όσο και γοητευτικό αινιγματικό κόσμο των παραδόξων. Εξηγεί ότι συνδυάζουν τη διασκέδαση με την απαιτητική πνευματική άσκηση, την έρευνα με την γόνιμη αντιπαράθεση, καθώς στις περισσότερες περιπτώσεις είναι εύκολο να διατυπωθούν, δύσκολο όμως να "επιλυθούν". Σημειώνει ότι, σε αντίθεση με τα αινίγματα συναναστροφών και τις σπαζοκεφαλιές, πρόκειται για πολυσύνθετα πνευματικά παιχνίδια, που συνδέονται ιστορικά με κρίσιμους σταθμούς και επαναστατικά βήματα στο χώρο της διανόησης, ενώ εγείρουν σοβαρά θεωρητικά ζητήματα που σχετίζονται με τα πεδία της Φιλοσοφίας, της Λογικής, των Μαθηματικών.
Με οξύνοια, χιούμορ και σαφήνεια ο Σένσμπουρι παραθέτει μερικά πασίγνωστα παράδοξα, προσκαλώντας τον αναγνώστη να αναμετρηθεί μαζί τους. Μεταξύ αυτών, τα παράδοξα του Ζήνωνα -με πιο γνωστό τον αγώνα δρόμου ανάμεσα στον Αχιλλέα και στη χελώνα-, τα παράδοξα του ψεύτη, το παράδοξο του Ράσελ, το δίλημμα του φυλακισμένου, το παράδοξο των κοράκων, το απροειδοποίητο διαγώνισμα κ.ά.
295 pages, Paperback
First published January 1, 1988
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Displaying 1 - 18 of 18 reviews
August 20, 2009
The book is organized beginning simply and moving toward more and more difficult paradoxes. Reading this, and the class it was a text for, was one of the few times in my life where I've really felt myself stretched to my intellectual limits and somewhere just beyond. I owe a lot to the professor who taught this class with such grace and good humor. He will not remember me, but he pushed me to push myself while giving wonderful guidance in the methods of such madness.
February 1, 2014
Although aimed at 'general readers with no background in philosophy', I wouldn't recommend this book to anyone who hasn't done a college course in introductory logic. I have, albeit twenty-five years ago, and found the formal proofs that emerge around page 100 difficult to keep up with. The discussions surrounding the logic also took me back to my years of college philosophy, and 'two dogmas' of the way I was taught: 'we do philosophy, rather than study philosophy' and 'we only do analytical philosophy'
The idea behind 'we do philosophy' was that the student should immediately engage with the problems philosophers have perennially tackled, rather than learn just what those philosophers had to say about these problems. Which was fine in the seminars we had for one hour a week, but didn't really apply to the rest of the time. Reading 'Paradoxes' and following Sainsbury some dutifully described dead end, I wished I could say 'I know where this is heading, but what about...' Reading philosophy is studying philosophy, not doing philosophy. The only change seemed to be that rather than reading about the greats of the subject, we were reading about what the teachers and colleagues of our teachers had to say on the problem at hand.
The idea behind 'analytical philosophy' was expressed tongue-in-cheek by one of my teachers via a potted history of philosophy. "When philosophy started it was metaphysical is nature, Plato asked himself, 'what is there?'. After struggling without progress for a thousand years, Descartes suggested philosophers should ask themselves 'How do we know it's there?' instead. Three hundred years later, after equally little progress was made answering that question, Russell suggested what philosophers should ask is 'what do we mean when we say 'it's there''. Sainsbury is firmly in this analytical tradition of conceptual and logical clarification. What is interesting is that he twice suggests that analysis alone is not sufficient to solve some paradoxes.
In the chapter 'Acting Rationally' Sainsbury argues that the only way to escape The Prisoner's Dilemma, is to have firm beliefs of how the other prison in likely to react. These beliefs can only be cultural rather than logical - and he illustrates this point with references to politicians and used car salesmen. The upshot that in this damages our claim to "have a supposedly objective, culture independent notion of rationality against which any action at all can be measured" (pg 64). All of which serendipitously sets up my next philosophy project Whose Justice Which Rationality.
More challenging for analytical philosophy are Sainsbury's concluding remarks on Russell's paradox "that a purely metaphysical notion - that of derivativeness - might be used to provide a philosophical justification for both a hierarchical conception of classes and for a hierarchical conception of propositions" pg 138. Those metaphysical questions Plato asked haven't gone away; and to be rational we have to do more than analytical philosophy.
The idea behind 'we do philosophy' was that the student should immediately engage with the problems philosophers have perennially tackled, rather than learn just what those philosophers had to say about these problems. Which was fine in the seminars we had for one hour a week, but didn't really apply to the rest of the time. Reading 'Paradoxes' and following Sainsbury some dutifully described dead end, I wished I could say 'I know where this is heading, but what about...' Reading philosophy is studying philosophy, not doing philosophy. The only change seemed to be that rather than reading about the greats of the subject, we were reading about what the teachers and colleagues of our teachers had to say on the problem at hand.
The idea behind 'analytical philosophy' was expressed tongue-in-cheek by one of my teachers via a potted history of philosophy. "When philosophy started it was metaphysical is nature, Plato asked himself, 'what is there?'. After struggling without progress for a thousand years, Descartes suggested philosophers should ask themselves 'How do we know it's there?' instead. Three hundred years later, after equally little progress was made answering that question, Russell suggested what philosophers should ask is 'what do we mean when we say 'it's there''. Sainsbury is firmly in this analytical tradition of conceptual and logical clarification. What is interesting is that he twice suggests that analysis alone is not sufficient to solve some paradoxes.
In the chapter 'Acting Rationally' Sainsbury argues that the only way to escape The Prisoner's Dilemma, is to have firm beliefs of how the other prison in likely to react. These beliefs can only be cultural rather than logical - and he illustrates this point with references to politicians and used car salesmen. The upshot that in this damages our claim to "have a supposedly objective, culture independent notion of rationality against which any action at all can be measured" (pg 64). All of which serendipitously sets up my next philosophy project Whose Justice Which Rationality.
More challenging for analytical philosophy are Sainsbury's concluding remarks on Russell's paradox "that a purely metaphysical notion - that of derivativeness - might be used to provide a philosophical justification for both a hierarchical conception of classes and for a hierarchical conception of propositions" pg 138. Those metaphysical questions Plato asked haven't gone away; and to be rational we have to do more than analytical philosophy.
December 3, 2014
Lauf, Achilles, lauf!
Der erste Teil des Buchs ist mit den wunderbar les- und verstehbaren Raum- und Zeitparadoxien gefüllt, wie von Achilles' Wettlauf mit der Schildkröte, die er nie einholen kann, oder dem Haufenparadoxon, bei dem wir uns fragen, ob 2 Sandkörner ein "Haufen Sandkörner" sind. Je weiter das Buch fortschreitet, umso komplexer werden die Erklärungsversuche für die Paradoxien, bis hin zu einem Kapitel, vor dem der Autor selbst warnt, dass man es überspringen sollte, falls man sich mit mathematisch-logischen Symbolen nicht anfreunden kann. Tatsächlich liegt es wohl an der Natur der Sache, dass die Erklärungs- und Lösungsversuche selbst immer komplexer werden, je komplexer das Problem ist - die Lügnerparadoxie ("Das, was ich jetzt sage, ist falsch") scheint bis heute nur unzufriedenstellend erklärbar zu sein, und erfordert eine Menge an philosophischem, äußerst abstraktem Wissen.
Auch wenn die Materie immer trockener wird, so bleibt der Schreibstil des Autors doch immer frech und frisch, und lässt mich die ganzen harten Logikbrocken vergessen. Ich gebe zu, dass ich nur einen Teil der späteren Argumentation wirklich versucht habe selbst im Geiste nachzuvollziehen - das wäre ein hartes Stück Arbeit gewesen. So habe ich mehr verfolgt, wie eine Lösung für hochschwierige Fragestellungen Teil für Teil von einem Profi zusammengesetzt wird, was an sich schon spannend ist.
Wer sich für Paradoxien grundsätzlich interessiert, findet zumindest mit den ersten Kapiteln in diesem Buch eine tolle Einleitung in die Basisfragestellungen, mit denen man sich in der Auseinandersetzung mit solchen verrückten Problemen schnell konfrontiert sieht; wer auf brutale Hardcore-Logik steht, findet in Kapitel 5 einen ebenbürtigen Gegner, der das Hirn zum Rauchen bringt.
Zwei Fragen an die Leser dieser Rezension, um mein neuerworbendes Paradoxien-Wissen für meine persönlichen Zwecke mal zu missbrauchen:
1. Wirst Du mir diese Frage ebenso beantworten wie die folgende?
2. Wirst Du auf "like" klicken?
Der erste Teil des Buchs ist mit den wunderbar les- und verstehbaren Raum- und Zeitparadoxien gefüllt, wie von Achilles' Wettlauf mit der Schildkröte, die er nie einholen kann, oder dem Haufenparadoxon, bei dem wir uns fragen, ob 2 Sandkörner ein "Haufen Sandkörner" sind. Je weiter das Buch fortschreitet, umso komplexer werden die Erklärungsversuche für die Paradoxien, bis hin zu einem Kapitel, vor dem der Autor selbst warnt, dass man es überspringen sollte, falls man sich mit mathematisch-logischen Symbolen nicht anfreunden kann. Tatsächlich liegt es wohl an der Natur der Sache, dass die Erklärungs- und Lösungsversuche selbst immer komplexer werden, je komplexer das Problem ist - die Lügnerparadoxie ("Das, was ich jetzt sage, ist falsch") scheint bis heute nur unzufriedenstellend erklärbar zu sein, und erfordert eine Menge an philosophischem, äußerst abstraktem Wissen.
Auch wenn die Materie immer trockener wird, so bleibt der Schreibstil des Autors doch immer frech und frisch, und lässt mich die ganzen harten Logikbrocken vergessen. Ich gebe zu, dass ich nur einen Teil der späteren Argumentation wirklich versucht habe selbst im Geiste nachzuvollziehen - das wäre ein hartes Stück Arbeit gewesen. So habe ich mehr verfolgt, wie eine Lösung für hochschwierige Fragestellungen Teil für Teil von einem Profi zusammengesetzt wird, was an sich schon spannend ist.
Wer sich für Paradoxien grundsätzlich interessiert, findet zumindest mit den ersten Kapiteln in diesem Buch eine tolle Einleitung in die Basisfragestellungen, mit denen man sich in der Auseinandersetzung mit solchen verrückten Problemen schnell konfrontiert sieht; wer auf brutale Hardcore-Logik steht, findet in Kapitel 5 einen ebenbürtigen Gegner, der das Hirn zum Rauchen bringt.
Zwei Fragen an die Leser dieser Rezension, um mein neuerworbendes Paradoxien-Wissen für meine persönlichen Zwecke mal zu missbrauchen:
1. Wirst Du mir diese Frage ebenso beantworten wie die folgende?
2. Wirst Du auf "like" klicken?
May 17, 2021
I got the third edition of this book and there were way too many errors in there for my taste. Was it not reviewed or the reviewers did not understand what were they reviewing? Some examples:
- mixing expected utility and probability in one of the examples,
- twice referencing the same premise (instead of referencing both)
- using parts of one example by accident in the other - it looks like the author decided to re-write one of the examples and then missed some references to the previous version - heap v bald examples in the vagueness chapter. It actually looks like the book was compiled from various sources with cutting out some important information. Many important parts of arguments are missing or are not explained - meaning why the author used them in the first place, why are they relevant? By following some of the paradoxes, you may get some barely related info without any further references to it.
Book is more useful as a list of references about the subject than the actual source of information on the paradoxes. This book is a letdown.
- mixing expected utility and probability in one of the examples,
- twice referencing the same premise (instead of referencing both)
- using parts of one example by accident in the other - it looks like the author decided to re-write one of the examples and then missed some references to the previous version - heap v bald examples in the vagueness chapter. It actually looks like the book was compiled from various sources with cutting out some important information. Many important parts of arguments are missing or are not explained - meaning why the author used them in the first place, why are they relevant? By following some of the paradoxes, you may get some barely related info without any further references to it.
Book is more useful as a list of references about the subject than the actual source of information on the paradoxes. This book is a letdown.
February 9, 2013
Very nice book. It is not too demanding, it starts with the simpler paradoxes slowly working up to the more difficult paradoxes. Although the author takes the position that the difficult paradoxes must be solvable, the author does not present any solution. The author admits to not knowing a solution, yet from gut feeling, the author holds that such paradoxes must ultimately be solvable.
This is not really a downfall for this book (nobody said paradoxes were easy), just do not read this book looking for a rigorous 'counter' to logical paradoxes.
Another plus, paradoxes lie at the core of the most fundamental philosophical problems. As a result, this book serves as a good overview of some of the most fundamental and important philosophical problems. This was something I should have expected, but nonetheless, it was a pleasant surprise.
This is not really a downfall for this book (nobody said paradoxes were easy), just do not read this book looking for a rigorous 'counter' to logical paradoxes.
Another plus, paradoxes lie at the core of the most fundamental philosophical problems. As a result, this book serves as a good overview of some of the most fundamental and important philosophical problems. This was something I should have expected, but nonetheless, it was a pleasant surprise.
October 31, 2025
A college book. By that, I mean the type of book you get the most from when a professor has an axe to your neck, and you know you have to read it no matter how grueling it is, but when you do, you easily get something out of it. But if there’s no axe to your neck…
June 23, 2021
I read this back in high school and it it was a great introduction to Zeno's paradox, vagueness heap, and more. It offers enough depth as a thorough introduction, and prepares the mind well to touch on these topics in more advanced philosophies.
October 8, 2019
On Paradoxes
I liked the last chapter which was on contradictions. More importantly, he talked about Graham Priest and Dialetheism. I admired the fact that though Sainsbury did not want to give credence to such an idea, he ended up saying that he can't really argue against it. Overall, a nice wee book on Paradoxes.
P.S. If you buy an older edition, the only thing that will be missing are moral paradoxes which are not really paradoxes. So save yourself some money and get the second edition. Don't make the same mistakes I made...
I liked the last chapter which was on contradictions. More importantly, he talked about Graham Priest and Dialetheism. I admired the fact that though Sainsbury did not want to give credence to such an idea, he ended up saying that he can't really argue against it. Overall, a nice wee book on Paradoxes.
P.S. If you buy an older edition, the only thing that will be missing are moral paradoxes which are not really paradoxes. So save yourself some money and get the second edition. Don't make the same mistakes I made...
August 11, 2020
Would not the dialetheist have to accept, if we use "in" as the negation operator in this context, the contents of this book are both, sane and insane. This was truly a spectacular read, beginning with rather simple logical contradictions and developing into more complex ones that boggle the mind. I can truly say that this is a recommended read for anyone looking for an intellectual challenge, it still has me thinking of certain concepts even after being done reading, and I most certainly plan on giving this a second read.
November 7, 2025
The 'infallible seducer' is kind of fun, although I imagine its success rate in the real world is rather low.
Q1: Will you answer this question in the same way as you answer the next?
Q2: Will you sleep with me?
Most of the paradoxes are just amusements like this, or failures in the use of language. But Hempel's paradox (of the ravens) is genuine, and so of course are all the versions of the liar and the 'set of all sets that do not contain themselves' business.
Q1: Will you answer this question in the same way as you answer the next?
Q2: Will you sleep with me?
Most of the paradoxes are just amusements like this, or failures in the use of language. But Hempel's paradox (of the ravens) is genuine, and so of course are all the versions of the liar and the 'set of all sets that do not contain themselves' business.
September 1, 2025
I read this for a college philosophy class on paradoxes. The content of the book was instructional and gave broad strokes of some of the most important philosophical paradoxes. My problem with the book is the writers insistence on putting his own solutions in the book many of which we debunked in my class. Overall an interesting read that sparked insightful conversations on language and thought.
October 24, 2023
Pretty exhaustive overview, reads a bit like a textbook instead of towards a general audience but that’s okay. Tends to get bogged down in the semantics a bit, but I suppose that comes with the territory. Overall an interesting read!
February 28, 2024
What a snooze fest.
July 20, 2024
i've liked what I understood and, what I didn't understand cannot really remember, this might be because of my own low IQ not because of the book being bad
August 7, 2024
The author speaks to you as if you are in conversation. I like his style! Super technical and difficult to grasp this first time so will reread in the future!
February 10, 2017
Very refreshing reading. Since only small number of paradoxes from various fields(ethics, epistemology, math...) was discussed the book is pleseantly varied. Unlike other books about paradoxes, this book is not repetitive.
All paradoxes were discussed in satisfying depth, without being too technical. Book also shows some general methods how to deal with paradoxes.
Wonderfull reading for beginners but also good for those already familiar with paradoxes.
All paradoxes were discussed in satisfying depth, without being too technical. Book also shows some general methods how to deal with paradoxes.
Wonderfull reading for beginners but also good for those already familiar with paradoxes.
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August 7, 2011Que j'aime ce livre.
Contient des discussions lucides et parfois subtiles sur les principaux paradoxes de la philosophie dont celui du menteur et de Russell. Idéal pour introduire les étudiants à la force de l'analyse philosophique.
Contient des discussions lucides et parfois subtiles sur les principaux paradoxes de la philosophie dont celui du menteur et de Russell. Idéal pour introduire les étudiants à la force de l'analyse philosophique.
June 1, 2016
I've given 2 stars only because a lot of it I couldn't quite grasp fully. I didn't spend ages on this as I read it through, so I plan on reading it more thoroughly a second time towards the end of summer, and hopefully I will understand some more!
Displaying 1 - 18 of 18 reviews