Symbolic Logic, 5E by Irving Copi

 

Irving Copi

Hello, my self Sujit Sarkar, a mathematics student from Visva-Bharati University, when we were taking this course in 3rd semester we faced many problems such as how to check my answers so I have decided to create this blog hope it is helpful to all of the students of our university as well as other students who are following this book for this course.

First, let's discuss some basic questions which will help us to start this course. 

1) What is logic?

Logic is the study of the methods and principles used to distinguish correct from incorrect reasoning.

 

2) Why do we need?

When someone wants to make judgments that can be completely relied upon, their only solid foundation will be correct reasoning. Using the methods and techniques of logic—one can distinguish reliably between sound and faulty reasoning.

 

3) What is Proposition?

A statement; what is typically asserted using a declarative sentence, and hence always either true or false—although its truth or falsity may be unknown.

 

4) What is Statement?

A proposition; what is typically asserted by a declarative sentence, but not the sentence itself. Every statement must be either true or false, although the truth or falsity of a given statement may be unknown.

 

5) What is Inference?

A process by which one proposition is arrived at and affirmed based on some other proposition or proposition.

 

6) What are Premises?

In an argument, the propositions upon which inference is based; the propositions that are claimed to provide grounds or reasons for the conclusion.

 

8) What is symbolic logic?

Symbolic logic, also called formal or mathematical logic, studies the symbolic representations of logical expressions and reasoning processes. It uses symbols to represent logical relationships, allowing for the analysis of arguments and propositions systematically.

 

In symbolic logic, statements are represented with symbols like letters and characters. Logical operators such as conjunction (∧), disjunction (∨), negation (¬), implication (→), and biconditional (↔) express logical relationships between statements. These symbols and operators provide precise and unambiguous representations of logical relationships, making it easier to analyze complex arguments and draw valid conclusions.

 

Symbolic logic is important in various fields, including mathematics, philosophy, computer science, and linguistics. It provides a rigorous framework for reasoning and formalizing logical arguments, leading to advancements in fields like artificial intelligence, proof theory, and computational complexity theory.

Example:

   1. If Ned likes cheese, then he is a block.

   2. Ned likes cheese.

   3. Therefore, Ned is a block.

Now, when we turn these statements into ‘statement variables’ and symbolize the argument, it looks like this:

1. L → B
2. L

________

Therefore, B
3. B(2, 1, MP)

Each numbered line is a premise. For simplicity’s sake, this argument is only two premises long. The ‘Therefore’ denotes the conclusion of the argument. All steps following the premise with the ‘Therefore’ designator are steps to proving the conclusion correct. Proving a conclusion merely involves using various inferences to reach it with the information given. Think of it like a game, where the end-goal is the conclusion itself.

Indicators:
Conclusion indicator:
                                                        

therefore	for these reasons
hence	it follows that
so	I conclude that
accordingly	which shows that
in consequence	which means that
consequently	which entails that
proves that	which implies that
as a result	which allows us to infer that
for this reason	which points to the conclusion that
thus	we may infer

Premise indicators:

since	as indicated by
because	the reason is that
for	for the reason that
as	may be inferred from
follows from	may be derived from
as shown by	may be deduced from
inasmuch as	in view of the fact that

N.B:- If you find any mistake feel free to contact me.