# Why aren't the values true and false part of logic, which is concerned only with the preservation of truth in arguments?

I quoted from the author's "Introduction for Instructors" on p. 15 where he's trying to distinguish his book from standard logic books that "did not address significant problems and confusions—those that were common among the students in those classes and those that appeared among students in other philosophy courses, even when such students had taken more than one class in logic and critical thinking."

I'm trying to decide if this book will introduce me comfortably to logic. But I don't understand the emboldened sentences. Can someone explain them so that a 16 year old high schooler can understand?

How can logic be "concerned only with the preservation of truth in arguments", if the values true and false aren't part of logic? Then again, I don't understand what the authors means by "minimalist account of the values true and false" or "preservation of truth".

Critical thinking, as understood in this book, includes logic—formal and informal—but in addition all rigorous methods for reliably arriving at true propositions. Hence the book contains a minimalist account of the values true and false. Such an account is not part of logic, which is concerned only with the preservation of truth in arguments. The account of truth and falsity given here is minimal in the sense that it includes all schemas of the form "It is true that P if and only if P," where that P is a proposition which may be expressed in some language and P picks out the state of affairs which the proposition purports to describe. This account is stated less formally in the text by distinguishing the state of affairs picked out by the proposition "P" from the proposition "P." While this account is close to deflationary accounts such as those given by Horwich$$^1$$, it is not meant to be a philosophically adequate account of truth and falsity, but rather, in keeping with the pedagogical purposes of the book, is meant to help students avoid common confusions by distinguishing the language with which we talk about the world from the world about which we talk. Moreover, this account of truth and falsity is not intended to rise to the level of a correspondence theory of truth, since it proposes no detailed articulation of states of affairs in accord with the articulation of propositions.

The Elements of Arguments: An Introduction to Critical Thinking and Logic by Philip Turetzky. I screen shot the whole p. 16 if you like more context.

• "contains a minimalist account of the values true and false" means that the machinery of logic presupposes the existence of truth values: True and False in the standard framework (so-called Classical logic). "minimal" because the said approach does not try to explicate what truth values are: this is considered out of scope and is a philosophical problem. Commented Jan 4, 2021 at 7:01
• Having said that, there are more advanced logical researches dealing with the basic properties of Truth and with the Theory of Truth Commented Jan 4, 2021 at 7:03

What is meant is that logic isn't concerned with the actual truth value of statements in the real world, or what exactly it means for a statement to be true. Logic is only concerned with how the truth value of a complex expression is determined by the assumed truth values of its component expressions, and how truth is preserved when reasoning from premises to a conclusion. Logic is about the structure of sentences and arguments, whereas assumptions about which primitive statements are true to begin with have to be made from the outside.

Logic will tell you that if you accept the premises that all humans are mortal and that Sokrataes is a human, then you have to accept the conclusion that Sokrates is mortal.

Logic will not tell you whether to accept the premise that all humans are mortal (and in consequence, whether you have to accept that Sokrates is mortal). Whether these statements are actually true is a matter of biology, not logic.

• In other words, logics is a formal calculus, void of any semantics. Even more striking with Boole's algebra. "It is $1$ that $P=P$" ;-)
– user65203
Commented Jan 4, 2021 at 13:58
• @Yves Daoust That's not at all true. Standard logic of course defines a (truth-functional) semantics, and even in a formal calculus one can think about the "meaning" of a proof or inference rule, see proof-theoretic semantics. Commented Jan 4, 2021 at 14:05
• So what I said is $0$ ?
– user65203
Commented Jan 4, 2021 at 14:06
• @Yves Daoust Sorrry, I don't understand. How would the fact that we assume or define $P = P$ to be true mean that logic has no semantics? Commented Jan 4, 2021 at 14:08

For what it is worth, here is how I look at the notions of true and false in formal logic:

• To formally state that proposition $$A$$ is true, we simply write: $$A$$
• To formally state that proposition $$A$$ is false, we simply write: $$\neg A$$

Why then do we have $$T$$ for true, and $$F$$ for false in truth tables? Consider, for example, the truth table for $$\neg A\lor B$$:

This is just a convenient representation of the following with each line corresponding to a line in the above truth table:

1. $$A \land B \implies (\neg A \lor B)$$
2. $$A \land \neg B \implies \neg (\neg A \lor B)$$
3. $$\neg A \land B \implies (\neg A \lor B)$$
4. $$\neg A \land \neg B \implies (\neg A \lor B)$$

In each line, the antecedent corresponds to columns 1 and 2 of the truth table. And the consequent corresponds to column 3.

• thanks. but i don't get how this answers my question? i'm not asking about truth tables or $¬A∨B$.
– user851668
Commented Jan 19, 2021 at 22:41
• I used this truth table only as an example of how several results (theorems) of propositional logic can be visually summarized used T and F for truth values. Although some presentations of propositional logic formally encode truth values in proofs this way, I think they lead to unnecessary confusion and are not necessary. You won't usually see anything like them used in mathematical proofs. That said, I think truth tables are the best way to introduce students to propositional logic. Once you have mastered them, you are ready to study the basic methods of proof, to actually prove these results Commented Jan 20, 2021 at 4:10