1. Basic Argumentation

2. 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.

3. 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.

4. 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

5. 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

6. 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

7. 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

8. 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.

9. 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.”

10. 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

11. 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.

12. 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

13. 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

14. 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

15. 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.