Logic Chapter 3a - Salmon

(Originally written September 8, 2005 in Book 1)

Logic
Wesley Salmon

Chapter 3 - Inductive

Inductive arguments provide conclusions whose contents exceed that of their premises. (Deductive arguments stay within the confines of their premises).

Inductive arguments state if the premises are true then the conclusion may not always be true, but that it is probably true.

Induction by enumeration is the simplest inductive argument. This form of inductive argument draws a conclusion about all of a class based on the premise of observing a sample of that class. For example:

All X's we examined had 1Y
Therefore, all X's have 1 Y

It doesn't have to be all it can be a percentage as well:

75% of the X's observed had 1 Y
Therefore, 75% of all X's have 1 Y

Form:
Z% of the observed members of F are G
Therefore, Z% of F are G

-If Z is equal to exactly 0 or 100, then it is a universal generalization
-If Z is equal to 1-99, then it is a statistical generalization

The fallacy of insufficient statistics is the fallacy of making a conclusion prior to collecting enough evidence to warrant such a conclusion.

The fallacy of biased statistics consists of being an inductive generalization upon a sample which is known to be unrepresentative or one which there is good reason to believe may be unrepresentative of the population.

In a statistical syllogism the form is:

Z% of F are G
X is F
Therefore, X is G

The value of Z determines the strength of the syllogism. If Z is close to 100 then it is a strong argument. But, if Z is equal to 50 then the premises offer no support for the conclusion. If Z is less than 50 then the premise offers evidence for the opposite of the conclusion.

The argument from authority form is:

X asserts P
Therefore, P

A frequent method of attempting to support a conclusion is to create some person, institution or writing to assert a conclusion. Even though the form is fallacious, sometimes it can be correct to use an authority. In these cases, the authority must be reliable. He/she/it must be known to be honest and well informed and known to have based their judgment upon objective evidence which could be examined and verified. Here is the correct from for an argument from authority:

X is a reliable authority concerning P
X asserts P
Therefore, P

It can be misused however if the authority is misquoted or misinterpreted. It can be misused if the authority is the authority only an authority based on glamour, prestige or popularity, but has no real special competence in any field of learning. It can be misused if an authority makes a conclusion outside of his realm of expertise. It can be misused because the authority may express opinions about matters that they could not possibly have evidence for. It can be misused because authorities don't always agree and because people use the authorities that match their biases. For example, some one could cite a well respected theologian that has all the authority in the world concerning the theological and philosophical arguments pertaining to the existence of God for an argument concerning the validity of a trickle-down economy. While the well respected theologian is a learned and celebrated scholar, his economic viewpoint is not one from authority. His expertise is elsewhere and thus, he is no longer an expert. Likewise, an argument based on authority about the existence of God can be shaded by misrepresenting or piecemeal quoting said expert to support previously held biases.

The argument against the man is a similar inductive argument. It concludes that an argument is false because it was made by a certain person. It has the form:

X is a reliable anti-authority on P
X asserts P
Therefore, Not-P

The misusers of this argument tend to be emotional appeals rather than argument at all. This type of argument could be fallacious, but at the same time, it is also utterly biased.