Introduction to Logic

It's incredible to be able to read this logic textbook and appreciate Tarski's intuitively appealing approach to logic. The writing style is clear and the logical syntax is neat and easy to make out. I especially enjoy the fact that, although this is a textbook of sorts, it also reads something like an essay. The text has a philosophical and historical depth not found in some mainstream textbooks e.g. The Logic Book by Bergmann & al.

Ever since ARISTOTLE – mankind has been COMPELLED to live in a state of ‘medius res’ – a Latin phrase which means ‘in the midst of things’; and so for CENTURIES it has NOT been possible for mankind to solve mysteries; eradicate problems; prevent and cure diseases; or make much if ANY advancement.But one cannot sit ‘in the midst of things’ forever – as Michael Faraday proved in the NINETEENTH Century, when he discovered and harnessed the properties of ELECTROMAGNETISM – something that has ALWAYS been here since the dawn of time – and he gave us the solenoid; the transformer; the dynamo; the DC generator; the AC generator; and the electric motor – which paved the way for ‘the national grid’; electrically driven machines; wireless telecommunication; and computers – some brain – some discovery!You are already familiar with the names of five Polish geniuses: Lukabiewice; Rejewski; Zygalski; Rozyki; and the author of this publication – Alfred Tarski. As you know, these five men between them made massive inroads towards certain powerful trends in LOGIC that have created a unified conceptual apparatus as a common basis for the WHOLE of human knowledge (read the paragraph again for better clarification).Prior to people such as Kurt Gödel and Alan Turin - both of whom tore mathematics to shreds on three counts: incompleteness; inconsistency; and (the biggy) DECIDABILITY, mathematics was considered consistent, complete, and RELIABLE – until George Boole; Lewis Carroll; Kurt Gödel and Alan Turin came along and tore it all to shreds.Gödel tackled consistency and reliability while Turin tackled DECIDABILITY – is there a way that mathematics could be pressed into service to make a DECISION about the ‘correctness’ of the result that a line of enquiry yielded? (If this is ‘considered’ true then do that, otherwise do this instead?).The answer is a loud YES – Turin’s thinking changed mathematics irrevocably – and Turin’s wisdom gave the world the ‘thinking machines’ that we enjoy today in every aspect of our daily lives - be it a cardiogram monitor, or an intelligent and extremely ‘intuitive’ mobile phone – with many many more devices to improve mankind’s lot on the horizon in the foreseeable future.Unlike the ‘Organon’ defined in Aristotle’s ‘Prior and posterior analytics’ - which utilises a complex NEGATIVE method of HYPOTHESIS ELIMINATION to search for commonly held truths that shape OPINION – but usually FAILS to sort out truth from fallacy (see my example further down), using simple, easy to grasp principles, THIS powerful masterwork investigates the FUNDAMENTAL LAWS of those operations of the MIND by which REASONING is performed – and in so doing, it shows how to SWIFTLY sort out TRUTH and destroy FALLACY.So – if you are a lawyer or a barrister, or a manager, or in ANY position that requires EFFECTIVE decision taking, or you or your children wish to have a ROBUST method to evaluate the VALIDITY of an argument, then THIS publication is an ESSENTIAL part of your arsenal.A little tip: when you read the book don’t try and ‘dip into it’ – it will be confusing because each construct builds on the ones that precede it. As the king said to the white rabbit in ‘Alice in Wonderland’ “Begin at the beginning and go on till you come to the end: then stop”Before I go on to show the comparisons of Aristotle and Tarski, here are a few everyday postulations that are SHOT TO PIECES using the method.BUY ONE GET ONE FREE is a FALLACY! You CANNOT purchase ONE – you are COMPELLED to purchase TWO! It’s a fallacy that lines the pockets of the supermarkets and causes MILLIONS of TONS of food to be THROWN AWAY on a DAILY basis – food that would feed those in WANT and DESTITUTION.HALF PRICE is a FALLACY. You CANNOT have HALF a price – any more than you can have ‘half a hole’ – a hole is a hole is a hole - a price is a price is a PRICE.In Tarski’s masterwork, to aid persons coming from the CLASSICAL school of ANALYTICAL LOGIC with comprehending his SENTENTIAL CALCULUS, Alfred Tarski refers to the ORGANON – a LOCI developed by mediaeval Muslim scholars in the fourteenth century as an aid to remember the ‘valid moods’ when carrying out a LOGISM (‘analysis’) which leads to SYlogism – analysis of the SOUNDNESS of the logic).Although Alfred Tarski DECIMATES the whole thing at a stroke (as did Lewis Carroll in HIS masterworks ‘Symbolic Logic’ and ‘Game of Logic’ (BOTH parts now available in ‘Mathematical recreations of Lewis Carroll’ – another ‘must read’ publication), by way of explanation, so that you may get your head around it all when it pops up, there are FOUR logical constructs, these being:ALL ‘A’ are ‘B’ – (All new cakes are nice) represented in by the VOWEL ‘A’NO ‘A’ are ‘B’ – (No new cakes are nice) represented by the VOWEL ‘E’SOME ‘A’ are ‘B’ – (Some new cakes are nice) represented by the VOWEL ‘I’SOME ‘A’ are NOT ‘B’ – (Some new cakes are NOT nice) represented by the VOWEL ‘O’This yields 256 LOGICAL SUPPOSITIONS (‘suppose that …?) used in CLASSICAL LOGISM to DEBATE a set of PREMISES – for example AAA; ABA; BEI; BIE; IEB; EIB; IEA - you get the idea.Of the 250 ‘possibilities’, Aristotle (wrongly) considered that only NINETEEN of the 250 permutations were VALID – and that these must be evaluated IN A SET ORDER (again mistaken).These nineteen LOGICAL MOODS use the VOWELS in a series of LOCI words to jog the MEMORY of the person evaluating a proposition of the ORDER OF EVALUATION.For example, the word ‘Barbara’ stimulates for the order ‘b A rb A r A’; ‘calarent’ yields ‘c A l A r E nt; Darrii yields ‘d A rr I I; ‘Ferioque’ yields f E r I O qu E; Siri yields s I r I – and so on (snore) – ALL of which is REDUNDANT and NONE of which is required to master DEDUCTIVE LOGIC.Lewis Carroll was the first person to realise this – as you will discover for yourself should you purchase the book ‘Mathematical recreations of Lewis Carroll’ (available from Amazon) and play his ‘Game of logic’ (which is just fabulous); whilst George Boole was the first person to express logic MATHEMATICALLY.I have intentionally explained all of this to you because Alfred Tarski refers to the Organon when he explains WHY it is NOT needed when using his SENTENTIAL CALCULUS method to determine truth (Mr Carroll you were SO close to making this HUGE leap in logical assessment – a leap that led to the invention of the machine that changed the world forever – the COMPUTER)In Lewis Carroll’s masterworks ‘Alice in Wonderland’ and ‘Alice through the looking glass (and what she found there)’, Alice encounters many trials and tribulations to quickly teach children many valuable lessons about life in a humorous and memorable way.In ‘Alice in Wonderland’ Alice finds herself trapped in a room surrounded by LARGE locked doors - doors that she is BARRED from entering – some for her own good - such as the Duchesses house (pig and pepper) – which teaches Alice to ‘look before you leap’ – and some because she is not PERMITTED to open them (because she is a woman) so Alice cannot make any progress (glass ceilings) – which include the ‘gentlemen’s club’ where resides the ‘mad hatter’ and his crony the March Hare who teach Alice to realise the importance of speaking LOGICALLY.Alice learns not to ‘wallow in self-pity’ or she will drown in her own sorrows (The pool of tears); before being CONNED out of her wealth (sweeties) by a bunch of VERY strange creatures which include a ROPER (someone who ‘ropes you in’); a SHILL (someone who allegedly ‘wins’ the ‘con’); and a BOUNCER (someone who will beat the living daylights out of you if you reveal the con for what it is) – all of whom ‘walk away’ after they have ‘pulled the con’ – leaving Alice bewildered and ALONE.In ‘Alice’s evidence’ (chapter 12), Alice finds herself in a COURTROOM where a knave (The knave of Hearts) is accused of stealing some tarts.The knave is being FRAMED for a crime he did NOT commit, and Carroll uses the SOCRATIC TECHNIQUE in a very humorous way to show how USELESS it is, so as to explain to children why ‘criminals’ often escape justice (the Socratic method of ‘cross-examination’ is taught to Barristers to REFUTE EVIDENCE so as to ‘win’ cases) and to be on their guard for statements which are FALLACY.To set the scene: Alice is the size of a ‘playing card’ but as Alice gains more and more confidence she begins to ‘grow’ (in confidence and stature).KING: Rule Forty-two - ALL PERSONS MORE THAN A MILE HIGH TO LEAVE THE COURT.Everybody looks at Alice.ALICE: I'M not a mile high!KING: Yes you are!QUEEN: Nearly two miles high!ALICE: That's not a regular rule: you invented it just now.KING: It's the oldest rule in the book.ALICE: Then it ought to be Number One.WHITE RABBIT: There's more evidence to come yet, please your Majesty - it seems to be a letter written by the prisoner.JURYMAN: Is it in the prisoner’s handwriting?WHITE RABBIT: No!KING: He must have imitated somebody else's hand!KNAVE: Please your Majesty, I didn't write it, and they can't prove that I did: there's no name signed at the end.KING: If you didn't SIGN it that only makes the matter worse. You MUST have meant some mischief, or else you'd have signed your name like an honest man.QUEEN: That PROVES his guilt!ALICE: IT PROVES NOTHING OF THE SORT!KING: Read it out!WHITE RABBIT: Where shall I begin, please your Majesty?KING: Begin at the beginning and go on till you come to the end: then stop.AND SO dear reader – since you are showing keen interest, here are a couple of ‘teasers’ for YOU to deduce.Q1 You are a barrister and your client is suing a third party for alleged battery (harmfully striking someone without provocation).When testifying, you ask the defendant if she struck your client.The defendant responds “I may have – but only after he came at me first!”Choose what YOU consider is the STRONGEST basis for an objection?Is it:A The question requires a conclusionB The response is argumentativeC The response is speculativeD The response is non-responsiveQ2 You are a barrister and you are examining a witness. Are leading questions allowed?A Yes when the presiding judge asks a question of the witness.B No – leading questions are not allowed because the questioner, not the witness is testifying when a leading question is asked.C Yes but only during cross-examination of a witness.D Yes unless the question is unfair.Q3 You are a barrister, your client is on trial for the murder of a drug dealer, and your client testifies that he never met the victim. Which of the following convictions can the prosecutor ask your client about on cross-examination?A A conviction for shoplifting the year before.B A conviction for forging a credit card application the year before.C A conviction for the possession of crack cocaine the year before.D A murder conviction 20 years ago.So how did you do?If you DIDN’T answer ‘D’ to question one (non-responsive waffle); OR you DIDN’T answer ‘C’ to question two (I put it to you that … IS allowed when cross-questioning) OR you DIDN’T answer ‘B’ to question three (admissible evidence to establish that the person is UNTRUSTWORTHY) then YOU might benefit from this book!Have fun reading it - and come away enlightened!

I am an engineer by profession and my background is that of circuit design and signal processing. I have a PhD in analog circuit design. I read math purely out of interest and I am extremely passionate about it. Unfortunately, I do not have a professor to guide me so I look for good books online and teach myself.Not to refute what other reviewers have said but I feel that the negative points that are usually mentioned about this book are actually the most positive aspects about the book. It is amazing that the same aspect can be very useful for one person while for others, it might not be that suitable.1. People say that it is verbose: For me, I would like to rephrase that as 'the book carefully walks the student through the basic notion and structure of logic the way it must be in an introductory course'. For someone like me who is new to pure math, his presentation is extremely useful. Logic is very abstract and unless taught well, it will not sink in.Example: Why the hell did they formulate the 'if....then....' statement in such a weird manner? More precisely, the sentence 'if 2+2=5, then santa clara is a small town' is considered true. Why? For someone who is being introduced to logic for the first time, this sentence will sound really weird. What the hell is the relationship between 2+2=5 and the size of santa clara? On top of that, how can this statement be true when the two sentences are not related in any possible way?The answer lies in the difference between material logic which is used in mathematical logic and formal logic which we are all familiar with. MATH LOGIC is not same as the logic we are used to. I realized this when I read this book and has been explained extremely well in the second chapter. Please do make sure that you read the paragraphs which are marked with '*' sign. Those are supposed to be difficult concepts but whether you understand it or not, the quality of the experience of the learning process increases by a h_uge factor if you read those sections. The difference between material logic and formal logic is discussed in a section marked with '*'.2. People say that the first half of the book is well known and is redundant: It is not. For me, it is a boon that he wrote those initial sections explaining very carefully what a sentence is and what a sentential function is. If you are doing a course in a school, the prof helps the student with these subtle but extremely important concepts. For someone like me who is doing self study of pure math, these sections are extremely useful.I would like to stress that it is an INTRODUCTORY course and it lives very well to the title. If you are really familiar with this matter, then I suggest you move on to Schoenfeld's or Rautenberg's books.All in all, this has been a great book to read so far and I am quite positive that it will prove crucial in me being able to read the more advanced books on mathematical logic.

very useful book; fast shipping

This is a pure jewel and it definitely surpasses Quine's and Hodges's books on the same subject : in fact, I enjoyed reading the three of them.This book now stands in my list of outstanding books on logic :1. A. Tarski's "Introduction to Logic", a jewel, followed by P. Smith's superb entry-point "An introduction to Formal logic" and the lovely "Logic, a very short introduction" by Graham Priest2. D. Goldrei's "Propositional and Predicate calculus"3. Wilfrid Hodges' "Logic", followed by Smullyan's "First-order logic".4. P. Smith's "An introduction to Gödel's theorems".5. Kleene's "Introduction to metamathematics" & "Mathematical Logic".6. G. Priest's " Introduction to non-classical logic".Hence forgetting altogether Van Dalen's indigestible "Logic & Stucture" as well as the even more indigestible Enderton, Mendelson & al...