In assessing a deductive argument, we must first determine whether it is valid.

## Validity[]

Validity has to do with the formal characteristics of an argument, whether the propositions in the argument preserve the truth along the premises to the conclusion. For example, consider this valid argument - a hypothetical syllogism:

Premise 1: If A is true, then B is true Premise 2: If B is true, then C is true Conclusion: Therefore, if A is true, then C must be true

Here we can see that the truth of *premise 1* is is carried over, or preserved in *premise 2*, through the the fact that term *B* appears in both premises. The use of this repeated term connects *premise 1* and *premise 2*. Provided *A* is true, then the truth of *A* is carried through each premise to the conclusion. The conclusion only contains propositions contained in the premises that were connected by the connecting term "B", so we know that the conclusion must necessarily follow from the premises, and must, necessarily, be true if proposition *A* is true.

A deductive argument therefore, is valid if and only if the conclusion must necessarily follow from the premises. So we may test a deductive argument for validity by checking to see if there is any possibility that the premises could be true and the conclusion false. If so, the form of the argument must be invalid, there must be a place where the 'truth" of the propositions is not being carried through to the conclusion.

To get a clearer idea of what "preserving truth" in arguments really means, consider the idea of a set of directions designed to get you to a destination - a road map. Imagine you have a set of directions on how to get to from Soho to Little Italy.

http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/roadmap-4.gif

We will consider you and your car to represent the "Truth" and we will consider the roads as "premises", and your final destination as the "conclusion" that your car/the truth, want to reach to support your argument.

If I told you to start out from Soho by taking Broome Street towards Lafayette (at the center of the map) and then to turn right down Mulberry Street (look for the name at the top right of the map), each step would take YOU along the path to your destination, Little Italy. We would "preserve the truth" by carrying you along the roads/premises, by getting you to your destination/conclusion!

However, if I told you instead to turn left onto Lafayette, you would end up lost. You'd never reach your destination. The invalid set of directions - or a invalid set of premises , wouldn't allow you to reach the destination, or conclusion - even though your destination, Little Italy, is still a real place.

When we say that an argument is invalid, nothing is necessarily being said about the truth value of the premises or even the truth value of the argument's conclusion. As David Coss states, all that is being said when we declare an argument to be invalid is that the argument does not support its conclusion, because the argument does not preserve truth value through all the premises, to the conclusion. Or, using our example from above, the directions don't get you to your destination, even though the destination actually does exist.

At the same time, a valid argument does not necessarily mean that the conclusion is true! Using our example from above, I could tell you that by taking Broome street to Mulberry, you will end up at China Town - the directions would take you to the place I wish to direct you to, but I would be wrong about the destination. This means that at least one of my premises must be false.

Copi, in his Introduction to Logic (10th Edition), presents a classic example of this point: "This point was made forcibly by Abraham Lincoln in one of his debates with Stephen Douglas, in 1858. Lincoln was attacking the Dred Scott decision, which obliged the return of slaves, who had escaped into northern states, to their owners in the south

"(I believe the following) syllogistic argument... follows (from The Dred-Scott decision), and submit it to the consideration of men capable of arguing whether... the argument has any fault in it: Nothing in the Constitution or laws of any state can destroy a right distinctly and expressly affirmed in the Constitution of the United States. The right of property in a slave is distinctly and expressly affirmed in the Constitution of the United States. Therefore, nothing in the Constitution or laws of any state can destroy the right of property in a slave. I believe that no fault can be pointed out in that argument (i.e., it is valid); (AND) assuming the truth of the premises, the conclusion, so far as I have capacity at all to understand it, follows inevitably. There is a fault in it as I think, but the fault is not in the reasoning, but the false-hood in fact is a fault of the premises. I believe that the right of the property in a slave is not distinctly and expressly affirmed in the Constitution, and Judge Douglas thinks it is. I believe that the Supreme Court and the advocates of that decision may search in vain for the place in the Constitution where the right of property in a slave is distinctly and expressly affirmed. I say, therefore, that I think one of the premises is not true."

For this reason, it is important to make sure that we use the term "valid" only to refer to arguments that have the proper form - arguments that give proper directions to the conclusion, while remembering that proper form means nothing if we have false premises. Validity has to do with the form, and 'Truth" has to do with examining the individual premises, Both invalid and valid arguments can contain either true of false premises, in fact, of the 8 possible permutations between true and false premises and true and false conclusions in valid and invalid arguments, there is only one set of premises and conclusions we will not see: a set of ALL true premises with a false conclusion. To best represent all the possible permutations, I've replicated two tables from Copi's Introduction to Logic (10th Edition):

Invalid Arguments True Conclusion False Conclusion True Premises Yes Yes False Premises Yes Yes Valid Arguments True Conclusion False Conclusion True Premises Yes NO! False Premises Yes Yes

## Soundness[]

If an argument is valid, then the argument can be contested truth-wise by examining the truth value of its premises. However IF the premises in a valid argument are accepted as true, there is no choice BUT to accept the conclusion, no matter how counter-intuitive or emotionally unsatisfying it may be. This is what Socrates was all about - leading you to accept the truth of his premises and the validity of argument, until you had no choice but to accept his conclusion. Such a valid argument is called a Sound argument*.

May all your deductive arguments be sound arguments.

## Strength[]

In inductive arguments, no such absolutism can exist - arguments can only be weak or strong. Strength is determined on the basis of the assumption that if its premises are true, its conclusion is probably true - however, like deductive arguments, strength and weakness have no more direct bearing on the absolute truth or falsity of the premises and conclusions than validity or invalidity.

Examples: http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/hat.jpg I met a Texan once who wore a goofy hat. I bet all Texans wear goofy hats.

This argument does not violate the rules of logic, but it is weak

I have met 90% of the citizens of Texas - and all of them were wearing goofy hats - it follows that the rest of the citizens wear goofy hats.

This argument is strong

I have met 99% of the citizens of Texas - and all of them were wearing goofy hats - it follows that the rest of the citizens wear goofy hats.

This argument is even stronger (Notice, that as things have turned out, the weak argument has as much truth value as the strongest. This can become especially annoying when someone not well versed in logic claims "But I argued the same thing!" Again, the point is not the truth of the conclusion, but whether one has A right to believe based on the evidence as they present it)

## Cogency[]

A cogent argument is the inductive equivalent of a sound argument. The last of these arguments is both a strong and a cogent argument. It is an argument that is both strong AND has true premises - pointing to a conclusion that is MOST LIKELY a truthful conclusion - but NOT absolutely a true conclusion. (as Francis Bacon (?) said, one needed only to find one white crow to disprove the contention all crows are black) This implies that, unlike deductive arguments, all inductive arguments are open to the possibility to being one day disproved - an important concept to remember when considering the value of science.

In general, the two main ways of creating a cogent argument are by providing strong evidence in the premise, or, conversely, making a weak conclusion - by using words such as: probably true, possibly true, it may be, etc. Inductive conclusions should be as far from being absolute statements as possible.

One of the key things I hope people pick up about induction is that they can vary in degrees. A deductive argument is either valid and sound, or its not. A deductive argument cannot be very sound. Deduction is a cut and dry system that for the most only concerns itself with the syntax of the argument.

Induction however, can vary in degrees of cogency based on its probability.

For instance, the more properties X and Y share, the greater the probability that a given medical treatment will work on them both. This is critical in medical research.

If X has properties - A, B, C, D and F and Y has properties A, B, C and D then chances are, Y has property F.

Hence, when working with induction, ask yourself "how cogent is the argument?" not just "is the argument cogent?"

## Review[]

A **valid deductive argument** with true premises is a **sound argument**.
A **strong inductive argument** with a set of likely-to-be- true premises is a **cogent argument**.

With this knowledge under your belt, you are more than prepared for the next section - on fallacies in arguments.

- For now, I will leave aside cases where an argument may be valid and sound, yet trivial. (I.e. circular logic, re-assertions of a conclusion, etc.)

Those following the Course in Logic 101 should proceed to the next section: Formal and Informal Logic

## References[]

- Copi, I. M, Cohen, C., (2001), "Introduction to Logic", 11th Edition.
- Hurely, P. J. (2000) A Concise Introduction to Logic - 7th Edition