Introduction to Formal Logic

 

1.1  Parts of Arguments: Premises/Conclusion

Indicator words are usually helpful:

Premise Indicator Words:

Since, as indicated by, because, following that, it may be inferred from (and others listed on page 3)

Conclusion Indicator Words:

therefore, thus, so, it follows that, it may be inferred that (and others listed on page 2)

 

 

1.2  Recognizing Arguments

Distinguishing Arguments from non-arguments:

1.  Are the indicator words used with statements meant as evidence for other statements, or as inferences from other statements?

2.  Is the inferential relationship between the statements one in which the inferred statement is evidenced by the others and vice versa?

Non-inferential passages and statements:

Warning, Advice, Belief/Opinion, Loosely Associated Statements, Exposition, Illustration/Example, Conditional Statement, Explanation

Conditional Statements:

* Every conditional statement is comprised of two component statements.  The statement immediately following the “if” is called the antecedent, and the statement immediately following the “then” is the consequent.

* A sufficient condition is one which obtains when a thing or event is all that is needed for the existence or occurrence of another thing or event. (Being a tiger is a sufficient condition for being an animal.)

* A necessary condition is a more strict condition, and it is one which obtains whenever a thing or event cannot occur without the occurrence of another thing or event. (Being an animal is a necessary condition for being a tiger.)

 

Introduction to Formal Logic 1.1 

Some key definitions:

Logic: the science that evaluates arguments.

Argument: a group of statements one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion).

Statement: a sentence that is either true or false.

Premise: a statement in an argument that sets forth evidence or reasons.

Conclusion: the statement in an argument that the premises are claimed to support or imply.

Conclusion indicators: words that provide a clue in identifying the conclusion (therefore, so...)

Premise indicators: words that provide a clue in identifying the premises (since, because...)

Inference: the reasoning process used to produce an argument.

Proposition: the information content of a statement.

Truth value: the attribute by which a statement is either true or false.

 

A first step in analyzing an argument is to restructure it.  For example, the argument “Socrates must be mortal, since he is a man and all men are mortal” is restructured as:

 

Socrates is a man.                                   premises

All men are mortal.

Therefore, Socrates is mortal.                 conclusion

 

More samples to do together:

 

1.  Only a fool or a daredevil smokes cigarettes, since cigarette smoking is a leading cause of cancer.

 

2.  The French are the most intelligent people in the world.  For it takes years and years for adult Americans to learn to speak the French language well.  But in France even little children speak it well.

 

Section 1.2:

Typical kinds of nonarguments.  Special emphasis on conditional statements and explanations.  Even though conditional statements are not by themselves arguments, they may serve as premises or conclusions of arguments.  Here is an argument containing a conditional statement as a premise:

If the air pressure lowers, then the barometer falls.         Note the form: “If (antecedent), then (consequent).”

The air pressure just lowered.

Therefore the barometer just fell.

 

and this is an argument with a conditional statement as a conclusion:

 

The higher the altitude, the lower the air pressure.

At higher altitudes the barometer falls.

We may conclude that if the air pressure lowers, then the barometer falls.

 

Are these arguments, or not?

1. The reason the beaker exploded is that it contained nitroglycerine and was shaken violently.

2. Several nations now possess the technology to manufacture nuclear weapons, even though they may not actually build such weapons.  Thus, the world is in much greater danger of a nuclear confrontation than one might think.

 

 

Introduction to Formal Logic

1.2  Recognizing Arguments

Distinguishing Arguments from non-arguments:

1.  Are the indicator words used with statements meant as evidence for other statements, or as inferences from other statements?

2.  Is the inferential relationship between the statements one in which the inferred statement is evidenced by the others and vice versa?

Non-inferential passages and statements:

Warning, Advice, Belief/Opinion, Loosely Associated Statements, Exposition, Illustration/Example, Conditional Statement, Explanation.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Conditional Statements:

* Every conditional statement is comprised of two component statements.  The statement immediately following the “if” is called the antecedent, and the statement immediately following the “then” is the consequent.

* A sufficient condition is one which obtains when a thing or event is all that is needed for the existence or occurence of another thing or event.

* A necessary condition is a more strict condition, and it is one which obtains whenever a thing or event cannot occur without the occurrence of another thing or event.

Introduction to Formal Logic 1.1 

Some key definitions:

Logic: the science that evaluates arguments.

Argument: a group of statements one or more of which (the premises) are claimed to provide support for, or reasons to believe, one of the others (the conclusion).

Statement: a sentence that is either true or false.

Premise: a statement in an argument that sets forth evidence or reasons.

Conclusion: the statement in an argument that the premises are claimed to support or imply.

Conclusion indicators: words that provide a clue in identifying the conclusion (therefore, so...)

Premise indicators: words that provide a clue in identifying the premises (since, because...)

Inference: the reasoning process used to produce an argument.

Proposition: the information content of a statement.

Truth value: the attribute by which a statement is either true or false.

 

A first step in analyzing an argument is to restructure it.  For example, the argument “Socrates must be mortal, since he is a man and all men are mortal” is restructured as:

 

Socrates is a man.                                 premises

All men are mortal.

Therefore, Socrates is mortal.               conclusion

 

More samples to do together:

 

1.  Only a fool or a daredevil smokes cigarettes, since cigarette smoking is a leading cause of cancer.

 

2.  The French are the most intelligent people in the world.  For it takes years and years for adult Americans to learn to speak the French language well.  But in France even little children speak it well.

 

Section 1.2:

Typical kinds of nonarguments.  Conditional statements.  Even though conditional statements are not by themselves arguments, they may serve as premises or conclusions of arguments.  Here is an argument containing a conditional statement as a premise:

If the air pressure lowers, then the barometer falls.                 Note the form: “If (antecedent), then (consequent).”

The air pressure just lowered.

Therefore the barometer just fell.

 

and this is an argument with a conditional statement as a conclusion:

 

The higher the altitude, the lower the air pressure.

At higher altitudes the barometer falls.

We may conclude that if the air pressure lowers, then the barometer falls.

 

Are these arguments, or not?

1. The reason the beaker exploded is that it contained nitroglycerine and was shaken violently.

2. Several nations now possess the technology to manufacture nuclear weapons, even though they may not actually build such weapons.  Thus, the world is in much greater danger of a nuclear confrontation than one might think.