Introduction to Logic: And to the Methodology of Deductive Sciences

by Alfred Tarski

This classic undergraduate treatment examines the deductive method in its first part and explores applications of logic and methodology in constructing mathematical theories in its second part. Exercises appear throughout.

Genres: Philosophy, Logic, Mathematics, Science, Nonfiction, Textbooks, Reference

272 pages, Paperback

First published January 1, 1993

About the author

Alfred Tarski was a Polish logician and mathematician. Educated in the Warsaw School of Mathematics and philosophy, he emigrated to the USA in 1939, and taught and did research in mathematics at the University of California, Berkeley, from 1942 until his death.

A prolific author best known for his work on model theory, metamathematics, and algebraic logic, he also contributed to abstract algebra, topology, geometry, measure theory, mathematical logic, set theory, and analytic philosophy.

He is regarded as perhaps one of the four greatest logicians of all time, matched only by Aristotle, Kurt Gödel, and Gottlob Frege. His biographers Anita and Solomon Feferman state that, "Along with his contemporary, Kurt Gödel, he changed the face of logic in the twentieth century, especially through his work on the concept of truth and the theory of models."

Reviews

[Daniel Solomon · Rating 4 out of 5]

I have mixed feelings about this book, but then I find myself frequently going back to it when I need a more philosophical perspective on logic in a very readable and informal manner.
The book's main strong points: it's a very readable and relatively simple introduction to classical logic, set theory and formal mathematical theory construction, written by one of the top logicians of the 20th century who was heavily involved in logical-empiricism and the development of modern logic, set theory and theoretical computer science. Its perspectives on things like identity, the link to model theory/metamathematics and general perspective of logic as part of the general methodology of science are quite appealing.

At the same time, I somehow wish Tarsky's book was moderately more formal sometimes, mixing in more precise definitions, proofs etc...with the mostly verbal exposition. But then, don't expect this book to replace full blown logic textbook, it's more of a nice complement to studying/revising logic with a more informal and philosophical angle (philosophy in the analytic/logical-empiricist sense of logical analysis of language and science).

[Wired · Rating 3 out of 5]

Admirably clear, but certainly not the book on formal logic I would recommend for philosophy students. The last third of the book is devoted to the application of logic to mathematics (specifically, the derivation of arithmetic from a set of axioms and primitive terms). Were that my area interest, this book would surely get a 4/5.

[Mishehu · Rating 5 out of 5]

December 30:

Just finished this one. Another indication that the non-expert readers of yesteryear were a breed apart: "The reader will easily guess how the concepts of a field and an ordered field are to be extended to arbitrary classes, operations and relations :-)." (Ok, the smiley face was my own addition, but I'm sure Tarski was giggling maniacally or staring Soviet-stone-facedly as he wrote this; either way, a chipper emoticon seemed in order.) Which is to say, Alfred T., not all readers arrive lickety-split at said deduction. The fact that I did manage to get there eventually, and that I understood most everything else in this concise and highly rigorous intro to logic, testifies to the author's great talents as a popularizer. This is a challenging and terrific book.

December 25:

Just beginning this one, but wanted to weigh in with a thought that exceeded the progress update character limit:

From the preface: "In its original form [this book] was intended as a popular scientific book; its aim was to present to the educated layman...a clear idea of that powerful trend of contemporary thought which is concentrated about modern logic. This trend arose originally from the somewhat limited task of stabilizing the foundations of mathematics. In its present phase, however...it seeks to create a unified conceptual apparatus which would supply a common basis for the whole of human knowledge." (1940)

They sure don't make science popularizers (or educated laymen) like they used to...

[T. Tokunaga · Rating 4 out of 5]

【Alfred Tarski / Introduction to Logic / Translated into English by Olaf Helmer】

It would be funny if I sent this to someone online, who says what he says is logically good:

--Therefore, a man using the word "or" in the meaning of contemporary logic will consider the expression given above:

2 • 2 = 5 or New York is a large city

as a meaningful and even a true sentence, since its second part is surely true. (P23, II, 7)

Or even his take on "if 2 • 2 = 5, then New York is a large city" being true (P26, II, 8) because 2 • 2 = 5 is a hypothesis and New York's size is a true conclusion.

--...whenever, in a sentence, we wish to say something about a certain thing, we have to use, in this sentence, not the thing itself but its name or designation. (P58, III, 18)

However, we never should confuse this fallibility of daily logic with science (another mistake of the science person I mentioned).

--Strictly speaking, the terms "sentential function" and "designatory function" do not belong to the domain of logic or mathematics. (P102, V, 32)

And if they uttered the word "model," we can assert that models are not exactly the essence itself, but a realization of certain logic (P126, VI, 38) - which is so often overlooked when we are talking about models in social sciences and humanities - or if they started quoting Gödel, we can ask if they are aware of incompleteness being "two relevant contradictory sentences of which neither can be proved in that discipline" (P135, VI, 41)

However, this book has some deficits: it's not really idealistic as a textbook for "everyone" it calls itself to be: it doesn't have answers for its exercises, its explanations of sufficient verbal explanations about procedures of each proofs (unlike Russell's introductory works). Overall, I'd recommend it if you don't consider it a textbook, but as a test book itself to check on one's own deductive thinking.

[Utsob Roy · Rating 5 out of 5]

An excellent book. Surprisingly, an excellent textbook too! I wish all textbooks were like this!

[Lucille Nguyen · Rating 4 out of 5]

Classic, readable work on logic.

[Dev Null]

I've been reading this off-and-on for a couple of months now, in between other things, but I think its time to give up on it. (It was, among other things, due back at the library...)

I think the book was doing an excellent job on the material... but the material is so basic it was hard to keep any interest. Its possible that the material gets more interesting by the end, but formal definitions of concepts as fundamental as "equals" - while important mathematically - are dull.

One gripe; there's really not much point in putting exercises in a textbook if you're not going to provide the answers, or at least - since some of the exercises are a bit open-ended (which is a good thing!) - some discussion of what the answers might look like and why. I imagine that was left to the role of the teacher using the book, but I didn't have one of those.

[Brian · Rating 2 out of 5]

Not to clear to me. I will reread after a few more semesters of math.