A Concise Introduction to A Concise Introduction to Logic.
In this brief assessment of A Concise Introduction to Logic written by Craig DeLancey; I will attempt to unfurl his magnificent introduction to logic onto you whilst giving praise when merited and owning up when it becomes obvious that some of these concepts begin to drift over my head.
The book, itself, is almost Zen. In the sense that it is strewn with philosophy and rules that seem trivial but eventually will make sense in the long run and can impact your life extremely well.
A Concise Introduction to Logic begins with the definition of logic as the ability to recognise an argument. It also states that every undertaking in life requires you to evaluate an argument, sometimes two, several or many. Logic helps you understand life or at least what it entails.
Logic is a skill and therefore it puts the onus on the user. If you use it poorly, you will be made a fool of, you will be taken advantage of and you will eventually be disenfranchised.
This book will help you learn how to use logic to its fullest, whether or not you actually want to is an entirely different question.
We will begin with the lighter stuff, as we were fortunate enough to do in the book.
First, we discover the logic of sentences, this is known as prepositional logic or sentential logic. This is the most basic we are going to get with logic as it outlines only the logic of sentences.
Declarative sentences are the most important. We know declarative sentences because they are either true or false.
We need sentences to be precise to be able to pursue them logically. To assess how precise a sentence is, is to ascertain the truth value of a sentence. If a sentence is vague it is not clear what conditions are true, If the sentence is ambiguous we cannot tell if it is true at all and if a sentence has both truth and no truth value it is confusing and therefore hard to apply logic to.
In short, we want our language to either be true or false. This is called the principal of bivalence.
Seemingly explaining basic language in the context of logic, the author continues to show clever math through tables, language, semantics and syntax to engage the student and help tackle the huge doctrine of logic.
I will not go into the syntax and semantics that the author did, because I am afraid I might get it wrong, but I will describe the feeling you get once you understand a logical argument through this language.
It is like grasping algebra (which I never really did). But I believe that’s what it would be like. Except the meaning behind logic and truth is much more profound then “x+y=z”
After Delancey nails language to the door with Greek letters and Logical Syntax, DeLancey begins to describe arguments further. He explains that our language is now complex enough for us to develop the idea of using our logic not just to describe things, but also to reason about those things.
An argument in the sense of trying to persuade someone that something is true is an ordered list of sentences. We call one of these sentences the conclusion and the rest is called a premise.
You would be likely to say “an argument is good if the premise is true and the conclusion is true” but this is weak, because it doesn’t necessarily make a good argument. The premise could have nothing to do with the conclusion and the conclusion could still be true. This is not a good argument because it is not valid.
A valid argument is an argument for which, if and only if the premise is true then the conclusion is true.
You can have a valid argument that is false but does this make it a bad argument? A bad argument is not only an invalid argument but also an argument that is not sound. A sound argument is a valid argument with true premises. Finally, Arguments sometimes need a hypothesis, there are four ways to assess a hypothesis’ relevance.
1. The more a hypothesis can predict correctly, the better it is.
2. It is preferred that the hypothesis might lead to a new direction of research
3. A hypothesis can cohere with an existing theory.
4. the simplest hypothesis is preferable.
To discern an argument, we must learn how to use and understand certain language such as “and” and “or”
“and” is an adjunction and “or” is a disjunction. An adjunction is a false if either aspect of the argument is false e.g. I will get you flowers and chocolates. A disjunction is a false only if both aspects of the argument is not fulfilled e.g. I will get you flowers or chocolate.
There are many more but to cover them would be as tedious to write as it is tedious to read. To elaborate, this is basic knowledge, only outlined in the book to help understand the syntax and semantics of logic.
It is important for the reader to understand that without proper syntax, arguments in logic can become lost in translation; just as without grammar, communication can become muddled and incoherent.
Logic is meaningless without dialogue and to understand the dialogue you need to understand these terms.
Primitives: True, false, Refer and Identity are primitive words.
Domain of discourse: Not only sounds cool but explains what it is in the name.
Predicates: Are adjective phrases that identify a relation between any number of things.
Derivation: this is the process of proving an argument through syntax.
An Indirect Derivation: This is slightly more difficult, but can be discerned as if something is not, not true then it is true. And if it is not, not false then it is false.
Logic is the maths of philosophy, this is because logic and truth are morally correct. Theistic philosophers strive to answer the question, did good and bad come before religion? Do gods have strict moral codes as well?
The author attempts to answer the question, but only ends up showing the argument through logical means and defining it. Not actually answering any question. Can this be only what logic does? assess arguments? Thankfully, it is not. Logic is also the pursuit of truth through simplification of arguments.
Delancey boldly takes us to first order logic. I am barely going to cover this topic because it is mostly just more syntax and semantics.
First order logic only translates more diverse words into syntax such as Everything, Something, Nothing, All, Some, No, All and only. These words are called quantifiers.
It also adds a few rules. An example of one is an inference rule, this allows us to write down a sentence that must be true based on the fact that previous sentences are true.
First order logic helps us understand predicates further as well (these are adjective phrases, right?). It outlines that predicates have things called arities. An arity is the smallest number of things a predicate can relate to.
Delancey has given us all this information not only so we can dive deeper into philosophy and its discussion through logic but so we can go even further afield with the study of advanced logic…
Which brings us to advanced logic. If you couldn’t get your head around the syntax and semantics of prepositional or first order logic, you have no chance here.
First, DeLancey begins with axiomatic prepositional logic. It’s not only a mouthful but it’s also trigonometry; or to be more precise, prepositional logic in a trigonometrical layout. This is a brand new easier method compared to traditional prepositional logic.
He then describes mathematical induction, which is a deductive method of logic. Mathematical induction shows how conditional derivation works by deduction.
Set theory is apparently a useful tool for logicians and philosophers because it groups things into a set and allows them to determine the identity of a set by its elements.
This goes on for a while, leaving us to wonder what we did to deserve logic and how enigmatic it really is.
Delancey even takes us back to trig class with axiomatic first order logic. This is the same as axiomatic prepositional logic but with first order rules applied. Meaning we can now use the usual negation and conditional syntax of first order logic, making the arguments much more in depth, usable and succinct.
The book finally finishes on one final note on peano arithmetic. Which I am not sure how to portray logically. I can say that it helps combine logic with maths in a way that connects it intrinsically whilst atomising the deities of logic and math into accessible principles.
A Concise Introduction to Logic has no observable conclusion except; I believe as itself, and that is how I will end this essay.