http://training.criticalthinkeracademy.com/lecture/8721/3-valid-versus-invalid-arguments3. Valid vs Invalid ArgumentsAn argument has to satisfy the Logic Condition in order for it to qualify as a good argument. But there are two importantly different ways in which an argument can satisfy the Logic Condition.One way is if the argument isvalid. Another way is if the argument isstrong."Validity" and "strength" are technical terms that logicians and philosophers use to describe the logical "glue" that binds premises and conclusions together. Valid arguments have the strongest logical glue possible.In this lecture we're going to talk about "validity" and the difference between "valid" versus "invalid" arguments. In the next lecture we'll talk about "strength" and the difference between "strong" versus "weak" arguments.Together, these two concepts, validity and strength, will help us to specify precisely what it means for an argument to satisfy the Logic Condition.Valid vs InvalidWe've seen valid arguments before. Recall the Tom Cruise argument:1. All actors are robots.2. Tom Cruise is an actor.Therefore, Tom Cruise is a robot.This is an example of a valid argument.Here's thestandarddefinition of a valid argument:An argument is VALID if it has the following hypothetical or conditional property:IF all the premises are true, then the conclusion CANNOT be false.In this case we know that in fact the first premise is false (not all actors are robots) but the argument is still valid because IF the premises were true it would be IMPOSSIBLE for the conclusion to be false.In other words,in a hypothetical worldwhere all actors are robots, and Tom Cruise also happens to be an actor, then it's logically impossible for Tom Cruise NOT to be a robot.THAT is the distinctive property of this argument that we're pointing to when we call it valid that it'slogically impossiblefor the premises to be true and the conclusion false. Or to put it another way, the truth of the premisesguaranteesthe truth of the conclusion.These are all different ways of saying the same thing. Validity is the strongest possible logical glue you can have between premises and conclusion.Here's an example of an INVALID argument:1. All actors are robots.2. Tom Cruise is a robot.Therefore, Tom Cruise is an actor.The first premise is the same, "All actors are robots". But the second premise is different. Instead of assuming that Tom Cruise is an actor, we're assuming that Tom Cruise is a robot.Now, if these premises are both true, does it follow that Tom Cruise HAS to be an actor?No, it does not follow. It would follow if we said that ONLY actors are robots, but the first premise doesn't say that.All we can assume is that in this hypothetical world, anyone in the acting profession is a robot, but robots might be doing lots ofdifferentjobs besides acting. They might be mechanics or teachers or politicians or whatever. So in this hypothetical world the fact that Tom Cruise is a robot doesn't guarantee that he's also an actor.And THAT is what makes this an invalid argument.An argument is INVALID just in case it's NOT VALID.What this means is that even if all the premises are true, it's still possible for the conclusion to be false. The truth of the premises doesn't guarantee the truth of the conclusion.That's ALL it means to call an argument "invalid".In particular,itdoesn'timply that the argument isbad.As we'll see in the next lecture,invalid arguments can still be good arguments. Even if they don't guarantee the conclusion they can still give us good reasons to believe the conclusion, so they can still satisfy the Logic Condition.But like I said, we'll talk more about this later.A Cautionary Note About the TerminologyI'll end with a cautionary note about this terminology.We're using the terms "valid" and "invalid" in a very specific technical sense that is commonly used in logic and philosophy but not so common outside of these fields.As we all know in ordinary language the word "valid" is used in a bunch of different ways. Like when we say "that contract is valid", meaning something like the contract is legally legitimate or that it's executed with proper legal authority.Or when we say "You make a valid point", we mean that the point is relevant or appropriate, or it has some justification behind it.These are perfectly acceptable uses of the term "valid". But I just want to emphasize thatthis isn't how we're using the term in logic when we're doing argument analysis. It's important to keep the various meanings of "valid" and "invalid" distinct so there's no confusion.Note for example that when we use the terms valid and invalid in logic we're talking aboutproperties of whole arguments, not of individual claims.If we're using the terms in the way we've defined them in this tutorial thenit makes NO SENSE to say that an individual premise or claim is valid or invalid.Validity is a property that describes the logical relationship between premises and conclusions. It's a feature of arguments taken as a whole. Still, it's very common for students who are new to logic to confuse the various senses of valid and invalid, and make the mistake of describing a premise as invalid when what they mean is simply that it's false or dubious.So that's just a cautionary note about the terminology. If you keep the logical definition clear in your mind then you shouldn't have a problem.2. Invalid Forms Using ORLets talk about invalid argument forms that use OR.Consider this example again:1. Either youre with me or youre against me.2. Youre not with me.So, you must be against me.This argument is valid, because the disjunction states that both of these disjuncts cant be false, at least one of them must be true, so if you can eliminate one then the remainder has to be true.But what if I said something like this?1. College teachers have to have either a Masters degree or a Ph.D.2. Professor Smith has a Masters degree.Therefore, he doesnt have a Ph.D.Is THIS a valid argument?It doesnt seem so. After all, why cant it be the case that Professor Smith as BOTH a Masters AND a PhD? Generally this is the case, if you have PhD then you also have a Masters degree, since having a Masters degree is usually a prerequisite for attaining the PhD.But if so, then this inference is clearly INVALID.The general form of thisinvalidinference looks like this:1. A or B2. ATherefore, not-BIn this form youre affirming that one of the disjuncts is true, and on the basis of this, inferring that the remaining disjunct must be false.In general, this is not a valid inference when its logically possible for the two disjuncts to be true at the same time.In other words, itsinvalid when the OR is an INCLUSIVE OR.An inclusive OR is one that asserts that A is true, or B is true, OR BOTH may be true. The only case that it rules out is the case where both are FALSE.Now, as you might expect, the case is different if the OR is exclusive. Heres a clear example of an exclusive OR:1. The coin landed heads or tails.2. The coin landed heads.Therefore, the coin did not land tails.Here youre doing the same thing, youre affirming one of the disjuncts and inferring that the remaining disjunct must be false.But in this case the inference is VALID, since the OR is an exclusive or it excludes the case where both of the disjuncts can be true.So, this argument form1. A or B2. ATherefore, not-Bis VALID when the OR is an exclusive OR.Here are the OR forms side-by-side:1. A or B2. not-ATherefore, B1. A or B2. ATherefore, not-B

Always validInvalid if OR is inclusive,valid if OR is exclusive

http://www.kslinker.com/VALID-AND-INVALID-ARGUMENTS.html

ALL ARGUMENTS CAN BE CLASSIFIED INTO TWO TYPES, VALID AND INVALID.In our class even inductive arguments will be considered a sub-type of invalid arguments. The major difference between these two types of arguments is explained in what follows.

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

If all the premises are true, then the conclusionmustbe true.(In other words, the truth of the conclusion is guaranteed if all the premises are true)ORIt is impossible to have a false conclusion if all the premises are trueORThe premises of a valid argumententailthe conclusion.

Conclusionsdeducedfrom a set of premises together with the premises themselves form avalidargument.

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 .Thereforethe U of A wins

The Logical Name for this argument isModus 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 QPThereforeQ

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 andP. malariaBlood test indicate that the patient harbors none of these parasitesThereforethe patient does not have malaria.

The Logical Name for this argument isModus TollensThe general form of this argument is:If P then QNot QThereforeNot P

Either The Patriots or the Philadelphia Eagles will win the SuperbowlThe Patriots lostThereforeThe Eagles won

The Logical name for this argument isDisjunctive Syllogism, more commonly known as Process of EliminationThe general form of this argument is:Either P or QNot PThereforeQ

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 isHypothetical SyllogismThe general form of this argument is:If P then QIf Q then RThereforeIf P then R

Invalid ArgumentsIf an argument isinvalid, then itis possiblefor the conclusion to befalse 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 weaklyinferredfrom 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 FallaciesI 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 areone chance in 120,526,770. This by definition is extremely improbable! (Gohereto see how this figure was calculated)

Inductive ArgumentsEvery 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!