Logic

What is logic?

• Logic (from the Ancient Greek: λογική, logike) is the use and study of valid reasoning. The study of logic features most prominently in the subjects of philosophy, mathematics, and computer science.

Informal logic is the study of arguments as presented in

ordinary language, as contrasted with formal logic, the

presentations of arguments in an artificial, formal, or technical

language.

A simple definition of inductive reasoning is using observation to

formulate an idea or theory. In this sense, inductive reasoning moves from the specific to the general.

Arguments based on experience or observation are best expressed

inductively.

Inductive reasoning involves finding the path that leads to a solution.

Inductive reasoning is the ability to combine pieces of information that

may seem unrelated to form general rules or relationships.

It is a primary attribute in scientific theory formulation. As an example of inductive reasoning, in a murder trial you have the evidence, and the goal is to use inductive reasoning to

determine the probability of the defendant’s guilt.

In contrast to deduction, inductive reasoning depends on working with cases, and developing a conjecture by examining instances and testing

an idea about these cases.

It is frequently used in mathematics and is a key aspect of

scientific reasoning, where collecting and analyzing data is the

norm.

A simple definition of deductive reasoning is taking a known idea or theory and applying it to a situation (often with the intention of testing

whether it is true).

In this sense, deductive reasoning moves from the general to the

specific.

Arguments based on laws, rules, or other widely accepted principles are best expressed deductively

(e.g. the Declaration of Independence).

Precis: In the “Declaration of Independence” (1776) Thomas Jefferson, et al., argue that the

American colonists have certain rights being denied by the British and therefore have the right to be

independent of British rule.

The authors of the document develop this thesis with careful

reasoning and compelling evidence: “grievances” that specify outrages carried out against the colonists by

the British.

The purpose of the document is to declare to the world the intentions

of the colonists and to provide a rational justification for them.

The audience is British authorities but also a “candid world” that has its eye on the rebellious colonists and might question their decision.

Formal logic, as its name states, is formal in the sense that it has a particular structure that is rigid,

unlike the casual flexibility of informal logic.

In logic and philosophy, an argument is an attempt to

persuade someone of something, by giving reasons for accepting a particular conclusion as evident

In formal logic, the argument is carefully structured or formed,

arriving at a conclusion that is self-evident (i.e. requires no

explanation).

A formal argument is based on premises, statements that define

what the argument is about.

A syllogism is a miniature deductive argument comprising three parts:

Major premiseMinor premise

Conclusion

Aristotle’s famous syllogism begins with a major premise, a general

statement on which his argument is based:

All homo sapiens are mortal.

Aristotle then applies that idea to a specific situation (Socrates) by

saying: Socrates is a homo sapien

This leads us to his conclusion:Therefore, Socrates is mortal.

Major premise: All people are mortal

Minor premise: Socrates is a person

Conclusion: Therefore, Socrates is mortal

Although it seems obvious, the conclusion “follows logically” from the premises because the premises are properly structured to make the

conclusion valid.

A valid logical argument is one in which the conclusions “follow”

logically from its premises, and its conclusions are consequences of its

premises.

There are six rules for determining the validity of a syllogism.

Because they’re technical and our study of syllogisms is cursory, we’ll not spend time learning the rules.

Suffice it to say, that in formal logic, when the form of an argument is

valid, the conclusion follows logically and is thereby valid.

Because of this, when challenging a formal logic argument, one

challenges the premises, not the conclusion.

Validity is a function of form. Just because an argument is valid in its

form does not mean it’s necessarily true.

If the premises are false, then the conclusion will be false, even if it is

properly arranged logically.

If an argument is both valid and true, it is said to be sound.