VALID AND INVALID ARGUMENTS

Valid Arguments

If an argument is valid, then it meets the following criteria:

If all the premises are true, then the conclusion must be true.
(In other words, the truth of the conclusion is guaranteed if all the premises are true)
OR
It is impossible to have a false conclusion if all the premises are true
OR
The premises of a valid argument entail the conclusion.

Conclusions deduced from a set of premises together with the premises themselves form a valid argument.

Here are some common examples of valid arguments::

If John makes this field goal, then the U of A will win. John makes the field goal . Therefore the U of A wins The Logical Name for this argument is Modus Ponens (this argument goes by other names as well, but this is the traditional name and the one used by Cohen and Copi in our textbook)	The general form of this argument is: If P then Q P Therefore Q
If the patient has malaria, then a blood test will indicate that his blood harbors at least one of these parasites: P. falciparum, P. vivax , P. ovale and P. malaria Blood test indicate that the patient harbors none of these parasites Therefore the patient does not have malaria. The Logical Name for this argument is Modus Tollens	The general form of this argument is: If P then Q Not Q Therefore Not P
Either The Patriots or the Philadelphia Eagles will win the Superbowl The Patriots lost Therefore The Eagles won The Logical name for this argument is Disjunctive Syllogism, more commonly known as Process of Elimination	The general form of this argument is: Either P or Q Not P Therefore Q
If John gets a raise, then he will buy a house. If John buys a house, he will run for a position on the neighborhood council. Therefore, if John gets a raise, he will run for a position on the neighborhood council The logical name for this argument is Hypothetical Syllogism	The general form of this argument is: If P then Q If Q then R Therefore If P then R

Invalid Arguments

If an argument is invalid, then it is possible for the conclusion to be false even if all the premises are true.
Invalid arguments come in all sorts of flavors, and students of Logic should be aware of the many different types.
One type of invalid argument is simply called a Logical Fallacy. These arguments are instances of pseudo-reasoning. The conclusion of a logical fallacy either does not depend on the truth of the premises at all (in such a case, we say the truth of the conclusion is independent of the truth of the premises) or the conclusion only follows very weakly from the premises. Unfortunately for those who are lovers of reason, logical fallacies are simply everywhere and one of the major goals of this class will be learning to recognize such fallacies when they occur.

Inductive arguments are another special case of invalid arguments - depending on the case, many inductive arguments have quite strong conclusions. Inductive arguments are not logical fallacies - since their conclusions are many times strongly inferred from the premises, however inductive arguments do not guarantee the truth of their conclusion, even if all of the premises are true (which makes them invalid).

WE WILL SAY that conclusion(s) arrived at by induction are strongly or weakly inferred from the premises.
The the conclusions of logical fallacies do not follow from the premises. By the way, "non-sequitor" is the Latin term used to describe conclusion(s) which do not follow from sets of premises!

Here are some examples:

Logical Fallacies

I have always liked Michael J. Fox, and now his battle with Parkinson's disease is really sobering.
He certainly is a man acquainted with grief.
He is also a vegetarian, therefore not eating meat is probably not a good idea.

The conclusion is that one should not be a vegetarian, which seems to take its strength from the fact that Michael J. Fox is now not healthy. In other words, there is an innuendo (which is disguised by the first statement which states a personal like toward Michael J. Fox) that tries to connect Parkinson's disease with being a vegetarian. In other words, this is an example of false cause and hasty generalization. Since no causal links between vegetarianism and Parkinson's disease have been stated, and from one case you can not generalize to other cases.

The Powerball has reached a near-record jackpot of $210 million dollars. Almost anyone would like that kind of money, and one thing is for sure, if you don't play, you can't win. Therefore Play Powerball!

In this case the conclusion is that one should play Powerball. The reason for this conclusion seems to follow from three true premises. 1) The Jackpot has reached a near-record high. 2) Almost anyone would like that kind of money and 3) You can't win if you don't play.
However, there is an additional unstated true premise which makes the conclusion very weak, specifically that the odds of wining the powerball are one chance in 120,526,770. This by definition is extremely improbable! (Go here to see how this figure was calculated)

Inductive Arguments

Every Banana plant that I have grown outside always dies immediately at the first touch of frost. Therefore, the banana plant growing outside will die too when we get our first frost.	The conclusion to this argument certainly is not guaranteed, even if the premise is true. The strength of the conclusion increases with the number of banana plants the person has grown, and also knowing that no other important fact about banana plants has changed (such as genetic variants which enable them to survive below freezing temperatures)
I have always owned Ford vehicles, and have always been pleased with their performance and reliability - therefore I should buy another Ford this time too.	Again, the same considerations listed above apply to this conclusion as well. If the person had only owned one Ford in his life, the conclusion would be weak. If the person had owned several Fords, then the conclusion does seem to be somewhat strong (certainly many other factors need to be considered before coming down on the side of just how strong the conclusion really is) - but this argument, like many inductive arguments, argues from past experience to future expectations - which is nicely illustrated in the next argument paraphrased from the Philosopher David Hume.
I have eaten toast with butter an jam every morning for the most of my life. Therefore I may eat toast with butter and jam this morning, and it will not poison me. (The toast I ate yesterday will not poison me today!)	Again, this argument is inductive, and most would say the conclusion is strongly inferred from the premises. Of course additional information may change things (NOTE: To state that the servant poisoned the toast to kill the master does not necessarily change the argument's conclusion, since in this case it is neither the toast nor the jam that kills the master, but rather the poison placed in it!)

FINAL NOTE:
Ways to tell the two types of arguments apart!

FOR VALID arguments, the addition of extra premises can not change the conclusion - a valid conclusion deduced from a set of premises can never be changed by the addition of new premises.
Also, it is inconceivable for the premises of a valid argument to be true and the conclusion to be false (just try it!)

FOR INVALID arguments, the addition of new premises will many times strengthen or weaken a given conclusion.
Also, it is conceivable for the conclusion of an invalid argument to be false even if it does have true premises!