Logic: A Very Short Introduction
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- Author：Graham Priest
- ISBN：0198811705
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Summary
Logic is often perceived as having little to do with the rest of philosophy， and even less to do with real life。 In this lively and accessible introduction， Graham Priest shows how wrong this conception is。 He explores the philosophical roots of the subject， explaining how modern formal logic deals with issues ranging from the existence of God and the reality of time to paradoxes of probability and decision theory。 Along the way， the basics of formal logic are explained in simple， non-technical terms， showing that logic is a powerful and exciting part of modern philosophy。
In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms， and proofs in mathematics。
ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area。 These pocket-sized books are the perfect way to get ahead in a new subject quickly。 Our expert authors combine facts， analysis， perspective， new ideas， and enthusiasm to make interesting and challenging topics highly readable。
In this new edition Graham Priest expands his discussion to cover the subjects of algorithms and axioms， and proofs in mathematics。
ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area。 These pocket-sized books are the perfect way to get ahead in a new subject quickly。 Our expert authors combine facts， analysis， perspective， new ideas， and enthusiasm to make interesting and challenging topics highly readable。
Reviews
Tejus Vamshi K
，
This book is brilliant because the author delivers the theme of each chapter in strong argumentation， and provides questions for the reader to ponder as well。 However， the title would be more appropriate as "Logic: A Very Short Introduction - for people comfortable with math and puzzles"。 This book is brilliant because the author delivers the theme of each chapter in strong argumentation， and provides questions for the reader to ponder as well。 However， the title would be more appropriate as "Logic: A Very Short Introduction - for people comfortable with math and puzzles"。 。。。more
Andy
，
easily the most complex 'A Very Short Introduction' book that I have read so far。 Priest does a good job dividing areas and theories into chapters。 The maths of logic threw me off a bit but it is such an interesting and tough topic to learn。 easily the most complex 'A Very Short Introduction' book that I have read so far。 Priest does a good job dividing areas and theories into chapters。 The maths of logic threw me off a bit but it is such an interesting and tough topic to learn。 。。。more
Fred Cheyunski
，
Relatively Friendly Update on Logic - I was looking for a friendly and easy to read “history” and update on logic （or dialectic as part of the liberal arts – see my review of Sister Miriam Joseph’s "The Trivium: The Liberal Arts of Logic， Grammar， and Rhetoric "） when I happened on this little book。 Having read a number of sources （see below）， this book presents among the clearest and readily understood descriptions about the topic by comparison。More specifically， this book gives a brief overvi Relatively Friendly Update on Logic - I was looking for a friendly and easy to read “history” and update on logic （or dialectic as part of the liberal arts – see my review of Sister Miriam Joseph’s "The Trivium: The Liberal Arts of Logic， Grammar， and Rhetoric "） when I happened on this little book。 Having read a number of sources （see below）， this book presents among the clearest and readily understood descriptions about the topic by comparison。More specifically， this book gives a brief overview of logic’s current state and treats major questions that concern the field。 That is， modern logic is highly mathematical and is purportedly explained here in a non-mathematical way （see also my review of Rucker's "Mind Tools: The Five Levels of Mathematical Reality"）。According to the author （on pg。 1）， “Logic is the study of what counts as a good reason for what。”The 14 chapters addresses topics that range from “Validity: What Follows From What？” about reasoning and making valid inferences to “Halt！ What Goes There？” about Alan Turing and the use of logic in computing。 The text also shows how logic relates to other parts of philosophy along the way。My favorite and the most valuable part for me comes at the end of book where the author discusses logic’s history and then where the matters in the different chapters were originally addressed。 As author Priest states （on pgs。 119）， “In Western intellectual history， [there are] three great periods in the development of logic。 。 。 The first great period was in ancient Greece between 400 and 200 BCE 。 。 。 Aristotle （384-322） was the major figure 。 。 。 [who] developed a systematic theory of inferences 。 。 。” He goes on to say （on pg。 120）， “The second growth period in Western Logic， starts in the early Middle Ages， with the Arabic philosophers 。 。 。but blossoms in the medieval European Universities， such as Paris and Oxford， in the twelfth to fourteenth centuries 。 。 。 where those such as Duns Scotus （1266 -1308） 。 。 。 and William of Ockham （1285-1349） 。 。 。 systematized and developed the logic they inherited from ancient Greece 。 。 。” The author continues that “The development of abstract algebra in the 19th century 。 。 。 triggered the start of a the third 。 。 。 of the three periods。 Radical new logical ideas were developed by thinkers such as Frege （1848-1925） and Russell （1872-1970） 。 。 。 logical theories developing from this work are referred to as ‘modern logic’ as opposed to ‘traditional logic’ that preceded it。” He closes this section （on pg。 121） indicating that “Developments in logic continued apace throughout the 20th century， and show no signs of slowing down yet。”While Priest’s account and framework are quite useful， it is helpful to consult other sources to fill in areas that his narrative does not deal with as well or at all。 For instance， Robert Adamson’s “A Short History of Logic”（see mention of Jevon also cited in Joseph's work alluded to above）， William and Martha Kneale’s “Development of Logic” devote considerable attention to Peter Ramus （see Ong's "Ramus， Method， and the Decay of Dialogue: From the Art of Discourse to the Art of Reason"）， Descartes and Francis Bacon and the rise of the scientific method （see my review of Bauer's "The Story of Western Science: From the Writings of Aristotle to the Big Bang Theory"）。 Then， there are Alex Malpass and Marianna Marfori’s “The History of Philosophical and Formal Logic: From Aristotle to Tarski” and Barry Gower’s “Scientific Method: A Historical and Philosophical Introduction” which are have chapters devoted to those such as Charles S。 Peirce---e。g。 “abduction，” and John Venn---e。g。 Venn diagrams， and allude to their influence on logical approaches along with their applications （e。g。 see my review of Minto's "The Pyramid Principle 3rd Edition"）。Even with my comments， I was glad to find Priest’s “Logic: A Very Short Introduction” as a helpful outline and aid for getting up to date on the logic’s history and present status。 。。。more
T Vignesh Nayak
，
Nice into for logicThis book is really good， if you are interested in logic。 Otherwise you have to read it slowly or some chapters even twice。 All chapters are very short， sometime you feel it could have been explained in detail。 I enjoyed it。 Author provides examples which are easy to understand for beginners。
Isaac Samuel Miller
，
Great intro to logicThis book is jam packed with insightful ideologies and theories。 I found some of the concepts to be contradictory whilst many of them are still great and logical concepts though。A lot of math is in this book—which is awesome。 I recommend this book for true logicians or philosophy lovers。
Rahul Shah
，
It's a good way of formally describing a lot of the logic I was taught in school through my math classes。 Definitely a topic to explore more of in the future。 It's a good way of formally describing a lot of the logic I was taught in school through my math classes。 Definitely a topic to explore more of in the future。 。。。more
Alastair
，
Before saying anything else if you are going to get a basic book on Logic don't get this one， get Logic by Wilfred Hodges （Pelican - Out of Print）。 You can find it easily online for less than this book and it is way better。It took me a long time to get through this book。 Not because it was long， but because it was too short。。。。 Sadly， I always finish books I start so I made it out the other side。I will start with the positives of the book which are:1。 It has problems and solutions in the back2。 Before saying anything else if you are going to get a basic book on Logic don't get this one， get Logic by Wilfred Hodges （Pelican - Out of Print）。 You can find it easily online for less than this book and it is way better。It took me a long time to get through this book。 Not because it was long， but because it was too short。。。。 Sadly， I always finish books I start so I made it out the other side。I will start with the positives of the book which are:1。 It has problems and solutions in the back2。 It has a glossary page of terms at the back incase you forget what something meansThose are probably the best bits。I've read quite a few "Very Short Introduction" books now and I've come to the conclusion that they're not very good。 Most of them seem to be written by people who can't figure out what kind of book they're writing。 They tend to be too short to give the reader any depth in the topic， but also too short for the author to actually explain the basics of the topic。 Basically， a book for someone who doesn't need to read it。With that said， this is definitely the worst one I have read。Throughout the book the author seems to have a hard time staying on topic， which， given the brevity of the chapters makes most of them fairly pointless， reminding me more of one of those 10 minute explanatory Youtube videos where they spend 9 minutes rambling about the weather and then copy a load of text on screen at the end and think they're the bees-knees 。 If the chapters have to be short （or even "Very Short"） then they ought to be focused on the topic at hand。This book is only easy to read finishable if you already know enough logic to begin with to not need a "Very Short Introduction" and that point， why waste your time with this。 。。。more
Daniel Goodman
，
I have a vague background in formal logic and this book did not much serve as a refresher。 The syntax and symbols used by the author were unlike anything I have encountered （perhaps that is my fault！） and made his explanations more confusing rather than clarifying。 As such， the book read more like an extremely compressed technical textbook for an advanced user rather than an introduction。 At least it was short！ I did appreciate him talking about other aspects of formal logic which were more new I have a vague background in formal logic and this book did not much serve as a refresher。 The syntax and symbols used by the author were unlike anything I have encountered （perhaps that is my fault！） and made his explanations more confusing rather than clarifying。 As such， the book read more like an extremely compressed technical textbook for an advanced user rather than an introduction。 At least it was short！ I did appreciate him talking about other aspects of formal logic which were more new to me--the application of tenses， probability， decision theory， etc。 More annoying was the author's incessant need to use the contents of nearly every chapter as an excuse to air his specific grievances with Christian apologetics。 。。。more
Janheart Nazarene Layoso
，
It made me confused that's why I didn't read it thoroughly， i just skimmed through the pages。。 I'll read this again if i become an expert in mathematics ;-; because that's when I'll get to understand this ;-; it was good though （the parts that i understood） I'll change my rating if i get back this book It made me confused that's why I didn't read it thoroughly， i just skimmed through the pages。。 I'll read this again if i become an expert in mathematics ;-; because that's when I'll get to understand this ;-; it was good though （the parts that i understood） I'll change my rating if i get back this book 。。。more
Till
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Holds what it promises。 Short and concise introductions to logic， from my understanding well explained， even though it gets more complex at the end。
D
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Good book。 Easy to read because of the nice writing and the short chapters。 Gives a nice introduction to global points of logic and surface level of logic。 It also does well to show to current issues that this basic logic faces。 Would recommend this book。
Sean Richardson
，
An enjoyable introduction to logic， exploring not only classical logic， but also the non-classical forms on which Professor Priest is an expert。
Martin Omedo
，
Have you ever heard assertions like “you are being illogical” during the informal debates are commonplace in these streets of social media and the same being conflated to you being wrong？Well。 To say someone ‘isn’t being logical’ is almost the same as saying they are wrong。 But this isn’t quite right。Logic is concerned with the relations between statements， and what a correct inference is。 If I say that， ‘all men are made of ice-cream。 I am a man。 Therefore， I am made of ice-cream’， baloney as t Have you ever heard assertions like “you are being illogical” during the informal debates are commonplace in these streets of social media and the same being conflated to you being wrong？Well。 To say someone ‘isn’t being logical’ is almost the same as saying they are wrong。 But this isn’t quite right。Logic is concerned with the relations between statements， and what a correct inference is。 If I say that， ‘all men are made of ice-cream。 I am a man。 Therefore， I am made of ice-cream’， baloney as the statement sounds， but the logic is correct。Logic takes statements and abstracts to the general form of their deduction。 Logic treats propositions such as ‘… is made of ice-cream’， like a black box， and merely studies the relationship between these propositions supposing they were true or false。So， logic isn’t concerned with truth in the world， instead it studies the basis of correct inference。 Someone who is illogical thus makes incorrect inferences given facts about propositions and objects。That said。If you want to want to understand the logic framework on steroids， I would recommend the book， Logic: A Very Short Introduction by Graham Priest。 The book does a great job to introduce you to the concept of logic， validity， premises， conclusion and how the same applies to various logical theories that have been debated for aeons。 The text is ideal for giving students of logic a quick introduction to formal logic or for adding pizzaz to an otherwise dry logic course。The last chapter of the book does a great job of situating various concepts of logic in their historical context which helps the readers understand what motivated the various logicians being discussed come up with the different logic theories as they did。In principle， logicians and philosophers wrote to each other， making most of their work esoteric， Graham， nonetheless makes logic in this book very accessible even for the novice。 Be that as it may， logic is undoubtedly a technical subject; but the roots of its forest of technical ideas and result sink deep into philosophical soil。 The great logicians of the past， of course， have been concerned with the forest; however， most have done so because of an engagement with the philosophical grounds。 Be deceived not by the size of the book， it is too saturated to be read like any other book。 。。。more
Nicolò Musmeci
，
Overall interesting， especially when it confutes/debunks common philosophical fallacies that have lasted for millennia （e。g。 the Ontological argument） or solves paradoxes。 Also the final 2 chapters on Turing and Godel's works are a great addition to the new edition。 However the author sometimes spends an excessive number of pages discussing technical subtleties that I am not sure are of interest to non-technical readers （e。g。 a whole chapter is dedicated to explain how we can consistently talk a Overall interesting， especially when it confutes/debunks common philosophical fallacies that have lasted for millennia （e。g。 the Ontological argument） or solves paradoxes。 Also the final 2 chapters on Turing and Godel's works are a great addition to the new edition。 However the author sometimes spends an excessive number of pages discussing technical subtleties that I am not sure are of interest to non-technical readers （e。g。 a whole chapter is dedicated to explain how we can consistently talk about past and future events with logical operators） 。。。more
Gerard Kornacki
，
A very good introduction to logic， recommend to anyone interested in gaining a fundamental background in the subject。
Jacob Norman
，
Philosophy， to me， is something of a “necessary evil。” Necessary， because it’s not a choice; we are all philosophers because we all think， and we’re all heirs of philosophical debates reaching back through the generations。 And evil， obviously， because。。。 well， let me explain—I often hear the phrase “necessary evil” used in reference to politics。 I think its use in that way is analogous to my use of it in regard to philosophy。 In politics—at least US politics—there is no ultimate winner， just bri Philosophy， to me， is something of a “necessary evil。” Necessary， because it’s not a choice; we are all philosophers because we all think， and we’re all heirs of philosophical debates reaching back through the generations。 And evil， obviously， because。。。 well， let me explain—I often hear the phrase “necessary evil” used in reference to politics。 I think its use in that way is analogous to my use of it in regard to philosophy。 In politics—at least US politics—there is no ultimate winner， just brief intervals of rest for a party or candidate， with nothing but unpredictable flux promised in the future。 There is no final outcome immune to change because there’s always the next political cycle。 The good is freedom of conscience and a responsible vote from informed citizenry; The ultimate good is the political process and it’s continuation， by any means necessary。 This allows for a political climate of hostility， sometimes to the point of war， as long as the process continues and the principles giving it life are observed—those principles always being subject to change。 Conflict is built right in to the political process。 Paradoxically， the price is conflict; The reward， stability。 It’s evil because conflict and hostility are inherent in it and unavoidable; yet necessary because what’s the present alternative？Philosophy is much more serious than politics， and actually subsumes it as just one of it’s many concerns。 More necessary， and potentially， far more wicked。 Philosophy has laid claim to thought and reason and logic。 Which brings me to this book: Logic: A Very Short Introduction。 I should be clear here， however， and retract my statement about philosophy being evil; I’ll settle for it being frustrating， instead。 Frustrating because of the discovery of radical skepticism in the Enlightenment period and years following。Radical skepticism essentially means that everything can be doubted。 It does not mean that there are no ultimate metaphysical truths， or say， that all truth is relative， but just simply that it is possible to doubt everything。 Nothing is incontestable， not even that statement。 That discovery is gloomy and not what we want to hear， but this came out of a search in the seventeenth and eighteenth century for indubitable truths—a secure foundation of certain facts on which to build a structure of knowledge， deductively。 Whether one agrees with these views， frankly， is irrelevant。 The important thing is that it's possible to doubt everything， to question everything。 Why can everything be questioned， you ask？ Because the attempt to find a fact， immune to doubt， failed。 Every chain of reasoning can be traced back to an initial assumption， large or small， that makes the conclusion of said argument less than certain。 Notice that certainty is very high bar， evoking the stuff of mathematics。 And really， is it so surprising that there's this paradox， this tension， between object and subject， fact and opinion， the neural processes and external world of 'truth。' The human condition has been talked about since humans have been talking: finite， limited， and contingent—that's who we are， and there's no escaping it。 There is an infinite gulf between subjective and the objective。 Philosophy fails to deliver on its grand aim—objective truth—making this review and all other knowledge， unfortunately， less than certain。We’re stuck here， having to use philosophy， its concepts and categories， its tools and its legacy。 But the certainty to which we aspire， that ground of uninterested objectivity that our minds dream of， is only a dream。 That’s just my opinion though。 。。。more
Timothy Wilson
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The author takes too many semantic liberties in arguments that wrench at denying the existence of God。 Again， shoddy examples of Modern Logic trying to circumvent the Law of Non-Contradiction， and the exclusivity of truth。He is a good writer， and I enjoyed his sense of humor; however， this platform was ill-used in airing out his religious bias。
Gaurav Singh
，
Accessible content for an amateur logician （like me）
Iva Khavtasi
，
გრემ პრისტი საინტერესოდ ახერხებს თანამედროვე “გაკალკულუსებული” ლოგიკა თავის ფილოსოფიურ ფესვებს დაუბრუნოს。 მცირე რაოდენობის ფურცლებით მკითხველს უღვივებს ინტერესს ფორმალური ლოგიკისადმი。 თუმცა სიმბოლოების ენა， წიგნის ზომის გათვალისწინებით， ზოგჯერ თითქოს ზედმეტია。 4/5ქართულ გამოცემაში დაშვებულია არა მარტო უამრავი ტექნიკური შეცდომა， არამედ რამდენიმე შინაარსობრივიც。 ეს უკანასკნელი ალბათ იმის ბრალიცაა， რომ სპეციალიზებული ენა ჯერ კიდევ განუვითარებელია， მაგრამ ტექნიკური შეცდომების პატიება უბრალოდ არ შეიძ გრემ პრისტი საინტერესოდ ახერხებს თანამედროვე “გაკალკულუსებული” ლოგიკა თავის ფილოსოფიურ ფესვებს დაუბრუნოს。 მცირე რაოდენობის ფურცლებით მკითხველს უღვივებს ინტერესს ფორმალური ლოგიკისადმი。 თუმცა სიმბოლოების ენა， წიგნის ზომის გათვალისწინებით， ზოგჯერ თითქოს ზედმეტია。 4/5ქართულ გამოცემაში დაშვებულია არა მარტო უამრავი ტექნიკური შეცდომა， არამედ რამდენიმე შინაარსობრივიც。 ეს უკანასკნელი ალბათ იმის ბრალიცაა， რომ სპეციალიზებული ენა ჯერ კიდევ განუვითარებელია， მაგრამ ტექნიკური შეცდომების პატიება უბრალოდ არ შეიძლება და ზოგიერთ ნაწილს ფორმალური ლოგიკიდან არაფორმალურ “fuzzy logic”-ად აქცევს。 ნაჩქარევი。 2/5 。。。more
Dana Robinson
，
This is an excellent introduction to logic from the point of view of philosophy。 If your exposure to logic was via high school math or computer science classes， you consider giving this book a read to get a feel for the depth of modern logic。 You're missing out on quite a bit。 This is an excellent introduction to logic from the point of view of philosophy。 If your exposure to logic was via high school math or computer science classes， you consider giving this book a read to get a feel for the depth of modern logic。 You're missing out on quite a bit。 。。。more
Rene Stein
，
Knížka není pro začátečníky ani pro pokročilé。 Základní a jednoduché termíny jsou špatně vysvětleny （modus ponens）， naprosto zmršený je výklad materiální implikace a finitních deskripcí。 Složitější témata jsou jen načrtnuta （modální logika， temporálni logika）， v kapitole o bayesovské pravděpodobností jsou zbytečná odvození， do kterých se autor zamotá natolik， že mu na jednom místě máme "věřit"， že dosadil správná čísla。 A opět chyby v knize - už na straně 24 je zcela špatně tabulka pro triviální Knížka není pro začátečníky ani pro pokročilé。 Základní a jednoduché termíny jsou špatně vysvětleny （modus ponens）， naprosto zmršený je výklad materiální implikace a finitních deskripcí。 Složitější témata jsou jen načrtnuta （modální logika， temporálni logika）， v kapitole o bayesovské pravděpodobností jsou zbytečná odvození， do kterých se autor zamotá natolik， že mu na jednom místě máme "věřit"， že dosadil správná čísla。 A opět chyby v knize - už na straně 24 je zcela špatně tabulka pro triviální úsudek q | q or p。 。。。more
Jay Aldous
，
A good yet consice introduction to the topic （despite being a little longer than most others in the series）。 I felt a little lost at times and felt the need to go over a few chapters more than once but I would attribute that more to the nature of the subject than the author himself。
N
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Quick， efficient， to the point and clear。 Like a good text book it presents interesting ideas through short examples that encourage and invite brainwork before reading on。 Like a good work of non-fiction， it starts multiple parallel threads， establishes a connection or a progression line of complexity， and leaves you with a list of further reading materials that are clearly placed on different nodes getting deeper。 This is what I'm disappointed to not get from other VSIs。 Bottom line: came here Quick， efficient， to the point and clear。 Like a good text book it presents interesting ideas through short examples that encourage and invite brainwork before reading on。 Like a good work of non-fiction， it starts multiple parallel threads， establishes a connection or a progression line of complexity， and leaves you with a list of further reading materials that are clearly placed on different nodes getting deeper。 This is what I'm disappointed to not get from other VSIs。 Bottom line: came here for a fast primer on syllogism language/symbols/topics， got it。 No furths。 Actually， one furth: 5th book this year with logic in the title。 Neat。NotesLogic not interested in validity of premisses， but in validity of relationship that if premisses are true， then the conclusion is true。{backwards E}x， an element of x。 {Inverted A}y， for all y。 Cosmological argument for God: there exists a thing x， that is the cause of everything。 That is god。 Confuses ‘everything has a cause’ with ‘there is one thing that caused everything’ixCx， there is an x such that x meets conditions C。 Ontological argument for God: Define set of properties like omnipotence， omniscience， existence。 There exists an x that meets all these conditions ie God。 Since existence is one condition， God exists。 Self-referential statements needn’t be T/F， they can be both/neither。 This statement is true， can be both T/F valid。 This statement is false is neither T/F valid。 These T+F values have implications when used as premisses to draw other conclusions。 -p （not p） being true， does not mean p is false。 Square （must）， Diamond （might） are modal operators。 Sq（p） = -Di（-p）。 False statement p （I will sleep in 2hrs） can still have truth value for Di（p）。 Leibniz truth of fact？ Di， truth in one of Leibniz’s possible worlds。 Sq， truth in all possible worlds。 If a， then b: a->b。 a->sq（b） and sq（a->b） are different。 1） is if a， then definitely b。 2） is if b， then definitely a （if divorce b， then definitely had been married a）。 2） does not imply 1）， because while all divorces are marriages， all marriages are not divorces。 This is the problem with Aristotle’s fatalism （whatever is， must be）。 But speaking of past。 p->sq（p）。 What was， must be。 But if someone predicted p before it happened， then p->sq（p） is true value for them。 Reverse C，actually more of a left-fallen U， approx ）， is material conditional ie -（a & -b）。 If a， cannot not be b。 But a）b is not the same as a->b。 How？ It just says there is no T+F， does not rule out FT and FF。 Since FT， a not ->b。 If a， then c。 If a&b？ Then c？ Not necessarily。 I fall from roof。 I die。 I fall from roof and I have a parachute。 I live。 s=sun is shining。 Ps， was the case that sun is shining。 Fs， will be the case that sun is shining。 FPs， will have been shining。 PFs， was the case that it will be shining。 FPFs？ FFP？ Compound tenses。 McTaggart: Something cannot be both past and future as it is happening， so not P and F。 But an event is both future and past from different viewpoints。 But that’s actually saying it is both PF （at some point it was future） and PP （at some point it was past）。 It cannot be PP and FF？ But that’s actually saying it is both PPP and PFF！ Infinite regress and contradiction。 Verb is has 2 forms， property， John is red， jR; and identity， John is the person who won the race j=w。 Leibniz law states， if jR and j=w， then wR。 Conditional probability P（a/b）>P（-a/b） then inductive inference is valid。 This is what Holmes does （not deduction） noticing things like clothing of person p。 Reference class is denominator for probability， what to use， population of London？ Europe？ Males？ Truest reference class is just person p， in which case P=50%， either he is or isn’t a writer。Argument from design is ordered cosmos is more likely with god than without god （if god， then likely to create order）， ie P（o/g） > P（o/-g）。 This is true， but for inductive validity， we need P（g/o）>P（-g/o）。 High o/g not equal to high g/o。 These are inverse probabilities。 P（g/o） = P（o/g）*Pg/Po。If we accept that P（o/g）>P（o/-g）， ie P（g/o）*Po/Pg > P（-g/o）*Po/P-g， simplify to P（g/o）/P（-g/o）>Pg/P-g。 So for this to be >1， Pg > P-g。 So order has nothing to do with it， tautology， probability of god is higher because probability of god was higher。 Put another way， P（og） is high， but P（g/o） is P（og）/Po and P（o/g） is P（og）/Pg。 P-o/g is low， so wherever there is god， likely order。 But there are many more other ways to be ordered。 So Po much higher than Pg， making P（g/o） much lower than P（o/g）。 Principle of indifference， in some cases you start with prior probabilities equal 1/n for n things， like n different jars with balls and picking the right one。 Others you can’t， like prob（Monday） vs prob（not Monday） is not symmetric。 Prob（god） vs Prob（not god） is not symmetric。 Pascal’s wager expected value believe （b） vs exist （e） is simple。 E（b/e+-e） >> E（-b/e+-e）。 But not so simple， because exist is not binary， many states， god， allah， vishnu etc， and payoff for belief in g/allah is highly -ve。 Aristotle’s Lyceum in Athens， syllogisms。 Eubilides etc in Megara doing conditionals， paradoxes。 Buddhist logic。 Then long gap to 13/14th century Duns Scotus， Ockham。 Then long gap， Leibniz lone bright spot but math not advanced enough until abstract algebra in 18/19th。 Frege， Russell - modern logic。Big Names: Peirce （existential modifier reverse E）。 Saul Kripke （possible worlds）。 C。I。Lewis （modal operators）。 Diodorus Cronus （Megarian）。 Paul Grice （conversational implicature）。 Arthur Prior （temporal reasoning）。 Hobbes （Ship of Theseus）。 Lukasiewisz （wookazyevitz） （vagueness）。 Laplace， Bernoulli， Carnap （probability and induction）。 Bayes。 Aquinas， Anselm， Descartes （God）。 。。。more
Henrique Iwao
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Uma introdução muito pequenina sobre lógica， mas com uma sacada a mais: em um livro introdutório， com os tópicos esperados， resuminhos e exercícios， ainda assim já aponta para literatura divertida sobre o assunto， colocando alguns problemas históricos interessantes （como a aposta de pascal， a irrealidade do tempo etc， paradoxo de sorites）， e introduz conteúdos diversos como lógica fuzzy， teoria da decisão， lógica modal。
W
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The difference between ◻（a→b） and a→◻b is going to be the mystery that tortures me on my deathbed。 This is a very tough but fairly fair book。 Logic is an interesting mathematical alternative to literary philosophy， but apparently just as ultimately fruitless。I think this would be a great asset for someone participating in an academic course on logic。 As a resource for comprehending the nature of the wider topic of philosophy， it was slightly disappointing。 But it's nice to be reassured that ther The difference between ◻（a→b） and a→◻b is going to be the mystery that tortures me on my deathbed。 This is a very tough but fairly fair book。 Logic is an interesting mathematical alternative to literary philosophy， but apparently just as ultimately fruitless。I think this would be a great asset for someone participating in an academic course on logic。 As a resource for comprehending the nature of the wider topic of philosophy， it was slightly disappointing。 But it's nice to be reassured that there isn't a numerical world out there of shining and sturdy formulae in which the reliable truth resides。 。。。more
Animesh Mitra
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Not bad。 Easy read。
Christopher
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Great accessible book on a subject that gets into very technical detail。 Graham Priest， who is known for his work on non-classical systems of logic， provides a fair， even-handed introduction to the subject of logic。 Highly recommended！
Klaire Hoang
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It would be perfect if Charles Wheelan and Yuvah Noah Harari can rewrite this book。 Honestly， a book about logic but the writing is too subpar and illogical。------On second thought， maybe this is the type of book that provides you with desirable difficulties。 The struggle is so real that I literally throw a small party whenever I can fully understand a chapter （and successfully solve its problem）。 Overall， if you allow your mind to be shaped by the author's stream of thoughts， it is getting easi It would be perfect if Charles Wheelan and Yuvah Noah Harari can rewrite this book。 Honestly， a book about logic but the writing is too subpar and illogical。------On second thought， maybe this is the type of book that provides you with desirable difficulties。 The struggle is so real that I literally throw a small party whenever I can fully understand a chapter （and successfully solve its problem）。 Overall， if you allow your mind to be shaped by the author's stream of thoughts， it is getting easier to grasp all the concepts because admittedly he is bad at explaining， but his bad way of explaining is repetitive。 Get used to the struggle and you will look at this book under a new light。 。。。more
Eric
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A very good introduction。 Discussions of aspects of logic are well motivated and interesting。 It covers a lot of ground in a very concise and accessible way。
Eghlima
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