BASIC ARGUMENTATIO

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WHAT IS AN ARGUMENT? A group of

statements, in which some of them (the premises) are intended to support another statement (the conclusion).

An Argument is NOT: a quarrel, bickering or verbal fighting of any kind.

When we use the word “Argument” in logic, this is NOT what we mean.

INTRODUCTION TO LOGIC Deductive Arguments An argument whose

conclusion necessarily follows from the truth of the premises

A D.A. is “valid” if it is successful in providing logical support for its conclusion

A “valid” D.A. is such that if all its premises are true, it is guaranteed that the conclusion must be true.

This means that if all the premises are true, there is NO possible way that the conclusion could be false.

We say that a D.A. is “invalid” if the truth of the premises does NOT guarantee that the conclusion must be true.

INTRODUCTION TO LOGIC Deductive Arguments VALID does NOT equal

TRUE These are NOT

synonyms It is entirely possible for

a valid D.A. to be FALSE. To claim that an argument is a “deductively valid argument” only means that the argument has necessary logical STRUCTURE

Logical structure doesn’t refer to the actual contents of an argument, but to its construction: The particular way the premises and conclusion fit together.

The logical structure of a D.A. is “truth preserving” which means the truth of the premises are preserved onto the conclusion

INTRODUCTION TO LOGIC Simple

Deductive Arguments

Premise 1 – All politicians are liars

Premise 2 – Jim is a politician

Conclusion – Therefore it follows that Jim is a liar

Premise 1 – All men are mortal

Premise 2 – Socrates is a man

Conclusion – Therefore, Socrates is mortal

INTRODUCTION TO LOGIC Logic is

ABSOLUTE In each of these

following arguments, if the premises are true, the conclusion MUST be true. It is impossible for the premises to be true and the conclusion to be false.

The conclusion follows directly from the premises, and the order of the premises makes no difference

INTRODUCTION TO LOGIC Deductively

INVALID Arguments

Premise 1 – All politicians are liars

Premise 2 – All used car salesmen are liars

Conclusion – Therefore if follows that all used car salesmen are politicians

Premise 1 – If Socrates has no teeth, then he is mortal

Premise 2 – Socrates is mortal

Conclusion – Therefore, Socrates has no teeth

*These Conclusions do not logically follow from the Premises

INTRODUCTION TO LOGIC INDUCTIVE

Arguments An argument that is

intended to provide “probabilistic” support for its conclusion.

An I.A. is such that if all its premises are true, the conclusion is possibly true, or highly likely to be true, but not necessarily true

If an I.A. succeeds in providing probable (but not logically necessary) support for its conclusion, then it is said to be “strong.”

If an I.A. fails to provide good support for its conclusion, we call it “weak.”

The structure of an I.A. does NOT guarantee that if all the premises are true, the conclusion must necessarily be true. However, if the conclusion is “highly probable” then it should be generally accepted.

When a good Inductively strong argument has true premises, it is “cogent.” Bad inductive arguments are NOT cogent.

INTRODUCTION TO LOGIC INDUCTIVE

Arguments Due to the fact that

the truth of an inductive argument's conclusion cannot be guaranteed by the truth of its premises, inductive arguments are NOT “truth preserving.”

INTRODUCTION TO LOGIC Strong

INDUCTIVE Arguments

Premise 1 – Most dogs have fleas

Premise 2 – Bowser is a dog

Conclusion – Therefore it follows that Bowser probably has fleas

Premise 1 – 98% of snails are slimy

Premise 2 – There is a snail in my garden

Conclusion – Therefore, the snail in my garden is highly likely to be slimy

INTRODUCTION TO LOGIC Strong

INDUCTIVE Arguments

Be aware that it is entirely possible for all the premises to be true in these I.A.s, and for the conclusion to be false.

After all, just because most dogs have fleas, doesn’t mean that Bowser does, because it is possible that he is one of the few dogs that don’t.

Also, just because 98% of snails are slimy, doesn’t mean the one in my garden is necessarily slimy, because he might be part of the 2% that is not.

INTRODUCTION TO LOGIC Strong INDUCTIVE

Arguments Be aware that it is entirely

possible for all the premises to be true in these I.A.s, and for the conclusion to be false.

After all, just because most dogs have fleas, doesn’t mean that Bowser does, because it is possible that he is one of the few dogs that don’t.

Also, just because 98% of snails are slimy, doesn’t mean the one in my garden is necessarily slimy, because he might be part of the 2% that is not.

Good D.A.s definitely have a valid logical structure.

However, there is more to good deductive arguments than good logical structure.

Good D.A.s also have true premises.

EXAMPLE: Deductively Valid (but FALSE) Argument

Premise 1 – All pigs can fly Premise 2 – Charles is a pig Conclusion – Therefore it

follows that Charles can fly

INTRODUCTION TO LOGIC A good D.A. must have

true premises We say that a deductively

valid argument with true premises is “sound.”

A SOUND argument is a good argument which gives you good reasons for accepting its conclusions.

Deductively valid arguments can have TRUE or FALSE premises and TRUE or FALSE conclusions

Deductive valid arguments can have: False premises

and a false conclusion

False premises and a true conclusion

True premises and a true conclusion

INTRODUCTION TO LOGIC False Premises

and False Conclusion

All fish have wings

All fish are dogs Therefore it

follows that all dogs have wings

False Premises and True Conclusion

All crows don’t have wings

Everything that doesn’t have wings is black

Therefore, all crows are black

INTRODUCTION TO LOGIC True Premises

and True Conclusion

I have two feet On each foot I

have five toes Therefore, I

have ten toes

The support a D.A. gives for its conclusion is “absolute.” Either it is demonstrably true, or it is not. There is no possible “sliding scale” of truth or falsity.

However, as the support an I.A. gives is probabilistic, the likelihood of the truth of an I.A. goes on a scale from very unlikely to highly likely.