The Science of Logic

Introduction

­­­­­­­­­­­Logic is the system of methods that used to evaluate and create arguments.

The study logic enables an individual or a group will be able to make better decisions and make fewer mistakes.

If you do not study logic, I have to tell you something. And I am telling you this as a friend. “You might as well donate yourself for biological research, asshole”.

I think I might have crossed a line.

Basic Concepts

Defining a Statement

In logic, a statement is a meaningful declarative sentence or a component of a sentence that can act as a meaningful declarative sentence that is either true or false.

True and false are the two possible values of a statement.

Examples of sentences that are statements:

  • Socrates is a man.
  • A triangle has five sides.
  • Van Gogh was a painter and George R.R Martin is an author.

The first statement is true.

The second statement is false.

The third statement consists of two statements and both of them are true.

Defining Argument, Premises and Conclusion

An argument is a group of statements. The statements that make up an argument are divided into one or more premises and one conclusion.

The premises are the statements that claim to provide the reasons or evidence, and the conclusion is the statement that the evidence is claimed to support or imply.

In other words, the conclusion is the statement that is claimed to follow from the premises.

Recognizing Arguments

Not all passages contain arguments. Because logic deals with arguments, it is important to be able to distinguish passages that contain arguments from those that do not.

Two conditions must be fulfilled for a passage to contain an argument:

  1. The passage must contain a premise.
  2. The premise must lead to a conclusion.

It is not necessary that the premises present actual evidence or true reasons nor that the premises actually support the conclusion. But at least the premises must claim to present evidence or reasons, and there must be a claim that the evidence or reasons support or imply something.

Deduction and Induction

Arguments can be divided into two groups:

  1. Deductive
  2. Inductive

A deductive argument claims that its conclusion is supported by its premises conclusively. The premises are claimed to support the conclusion in such a way that it is impossible for the conclusion to be false when the premises is true.

An inductive argument claims that its conclusion is supported by its premises inconclusively. The premises is claimed to support the conclusion in such a way that it is improbable for the conclusion to be false when the premises is true.

Thus, deductive arguments are those that involve absolute reasoning and inductive arguments are those that involve probabilistic reasoning.

Examples:

The meerkat is closely related to the suricat.

The suricat thrives on beetle larvae.

Therefore, probably the meerkat thrives on beetle larvae.

The meerkat is a member of the mongoose family.

All members of the mongoose family are carnivores.

Therefore, it necessarily follows that the meerkat is a carnivore.

The first of these arguments is inductive, the second deductive.

The distinction between inductive and deductive arguments lies in how strongly the conclusion follows from the premises.

Examples:

All saleswomen are extroverts.

Elizabeth Taylor is a saleswoman.

Therefore, Elizabeth Taylor is an extrovert.

The vast majority of saleswomen are extroverts.

Elizabeth Taylor is a saleswoman.

Therefore, Elizabeth Taylor is an extrovert.

In the first example, the conclusion follows with strict necessity from the premises. If we assume that all saleswomen are extroverts and that Elizabeth Taylor is a saleswoman, then it is impossible that Elizabeth Taylor not be an extrovert. Thus the argument is deductive.

In the second example, the conclusion does not follow from the premises with strict necessity, but it follows with some degree of probability. If we assume that the premises are true, then based on that assumption it is only probable that the conclusion is true. Thus, the argument is inductive.

Evaluation of arguments

Validity of Deductive arguments

The validity test checks whether the premises supports the conclusion. It does not check whether the premises and conclusion are true.

This is a test for deductive arguments.

In a valid deductive argument, the premises support the conclusion.

In an invalid deductive argument, the premises do not support the conclusion.

There are no arguments that are almost valid and almost invalid.

When checking for validity, the premises are assumed to be true even when it is not. This is because this test only checks whether the premises support the conclusion. It does not check whether the premises and conclusion are true or false.

Strength of Inductive arguments

The strength test checks whether the conclusion that follows from the premises is probable or improbable. It does not check whether the premises and conclusion are true.

This is a test for inductive arguments.

In a strong inductive argument, the conclusion that follows the premises is probable.

In a weak inductive argument, the conclusion that follows the premises is improbable.

There are no arguments that are almost strong and almost weak.

When checking for strength, the premises are assumed to be true even when it is not. This is because this test only checks whether the premises support the conclusion. It does not check whether the premises and conclusion are true or false.

Degrees of probability for Inductive arguments

Unlike the validity and invalidity of deductive arguments, the strength and weakness of inductive arguments have varying degrees of probability. To be considered strong, an inductive argument must have a conclusion that is more probable than improbable. In other words, the likelihood that the conclusion is true must be more than 50 percent, and as the probability increases, the argument becomes stronger.

Example

This barrel contains 100 apples.

Three apples selected at random were found to be ripe.

Therefore, probably all 100 apples are ripe.

This barrel contains 100 apples.

Eighty apples selected at random were found to be ripe.

Therefore, probably all 100 apples are ripe.

The first argument is weaker and the second is stronger. This is because the sample taken from the barrel in the second argument is bigger.

Good and Bad Deductive arguments

A good deductive argument is valid and has true premises.

A bad deductive argument is invalid and/or has false premises.

Good and Bad Inductive arguments

A good inductive argument is strong and has true premises.

A bad inductive argument is weak and/or has false premises.

Language usage

Language has two functions.

  1. convey information
  2. express and evoke feelings

These statements accomplish their respective functions using two distinct kinds of words.

  1. Informative words: are words that convey information
  2. Emotional words: are words that express or evokes feelings.

Sometimes, depending on the situation a person or a group might have an emotional response even if an informative word is used.

Sometimes, depending on the situation a person or a group might be able to get information from an emotional word.

Example

The death penalty, which is legal in thirty-six states, has been carried out most often in Georgia. However, since 1977 Texas holds the record for the greatest number of executions.

The death penalty is a cruel and inhuman form of punishment in which hapless prisoners are dragged from their cells and summarily slaughtered only to satiate the bloodlust of a vengeful public.

The first statement is intended to convey information.

The second is intended to express and evoke feelings.

Defects of emotion and emotional words in arguments

The use of emotion in arguments can be used to deceive other people and hence must be removed and only then must the argument be analysed.

Example

Consider the word “harvest”. This word evokes feelings associated with honest, hardworking farmers being rewarded for their labor in planting and tending their crops.

To capitalize on this positive feeling, wood products companies speak of harvesting the trees in 200-year-old forests, even though they had nothing to do with planting them.

In all of these cases, the use of the word “harvest” is specifically calculated to elicit a favorable or agreeable response from the listener.

Vague and ambiguous informative words

Vague informative words

They are words that allow for a continuous range of interpretations. The meaning is imprecise.

Example

Words such as “fresh”, “rich”, “poor”, and ‘‘normal’’ are vague.

How fresh does something have to be in order to be called fresh?

How much money must someone have in order to be called rich or poor?

When is something considered normal?

Vagueness affects statements and hence it affects arguments.

Example

Consider the statement, “Today our job situation is more transparent”.

Firstly, what is the meaning of “job situation”?

Does it refer to finding a job, keeping a job, filling a job, completing a job, or bidding on a job?

Secondly, what exactly does it mean for a job situation to be “transparent”? Does it mean that the job is more easily perceived or comprehended? That the job is more easily completed? That we can anticipate our future job needs more clearly?

Ambiguous informative words

They are words that can be interpreted as having more than one meaning in a given context.

Example

Words such as “bank”, “sound” and ‘‘race’’ are ambiguous.

Does it reference a financial institution or the shoreline of a river?

Does it reference loudness or physical strength of an object?

Does it reference a running race or about the human race?

Ambiguity affects statements and hence it affects arguments.

Example

“College students are turning to vegetables.”

Does this mean that the students are changing into vegetables or that they are incorporating more vegetables into their diet?

Difference between vagueness and ambiguity

Vagueness allows for a continuous range of interpretations.

Ambiguity allows for multiple discrete interpretations.

In a vague statement there is a blur of meaning, whereas in an ambiguous statement there is a collection of clear meanings, only one of which is correct.

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5 thoughts on “The Science of Logic

  1. Here’s a great quote on logic you might enjoy.
    “Mike’s love of the scientific method, of logic and proofs and truth, induces resentment for humankind’s general lack of precision. Grandiose announcements of the strongest and fastest and most beautiful often irritate him, because people generally have short memories and tend to assign superlatives to individuals and situations with a frequency that is statistically invalid. There can be only one strongest, after all, only one fastest, and only one (per beholder, anyway) most beautiful.”

    The God Particle by Richard Cox

    Liked by 1 person

  2. And this one is a personal favorite of mine:

    “You can’t disprove the facts. It’s pure logic.”
    “Logic, my dear Zoe, merely enables one to be wrong with authority.”
    – Doctor Who, The Wheel In Space

    Liked by 1 person

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