Critical & Creative Thinking - OER & More Resources: Logic Terms

Excerpts:

An argument is a piece of reasoning with one or more premises and a conclusion. Arguments are usually divided into two kinds, deductive and inductive.

Deductive

A deductive argument is one that derives the truth of the conclusion from the truth of the premises. If the argument form, or structure of the argument, is valid, then the conclusion will always follow from the premises. The hard determinism argument below is an example of a deductive argument that makes use of two modus ponens arguments in which the conclusion of the first serves as the premise of the second, or so it appears.

Inductive  

Unlike deductive arguments, inductive ones promise only probability, not certainty. Thus, if one argues that having watched several different newscasts in several different cities on many different nights one may infer that newscasts emphasize, in Bob Inman's phrase, "mayhem and misery", then one is making an inductive argument. (In this case, an inductive (or empirical) generalization. Another kind of inductive argument is an argument from analogy. Inductive arguments are judged by their reliability, where one expects only a high degree of probability, not one hundred percent reliability as with deduction.

Excerpts:

argument
An Argument is a group of statements including one or more premises and one and only one conclusion. The point of an argument is to give the receiver of the argument good reason to believe new information.

deductive argument
An argument in which the premises are intended to provide necessary support for the conclusion. Deductive arguments are either valid or invalid.

factual claim
One of the implied parts of every argument. the speaker implies that the premises are true. (without this claim they wouldn't be premises, only loosely associated statements.)

fallacy of ambiguity
A group of informal fallacies in which the inferential link is faulty because of some ambiguity in the language of the argument.

fallacy of grammatical analogy
A group of informal fallacies in which the inferential link is faulty even though they are grammatically analogous to other good arguments.

fallacy of presumption
a group of informal fallacies in which the information in the conclusion of an argument is actually assumed in the premises, thus not actually proving anything new.

fallacy of relevance
a group of informal fallacies pertaining to the inferential relationship in arguments. The premises are in some way logically irrelevant to the conclusion, though they may have psychological or emotional relevance.

fallacy of weak induction
a group of informal fallacies pertaining to the inferential relationship in inductive arguments. The premises are irrelevant to the conclusion, but this fact is obscured in some way.

false cause fallacy
An informal fallacy of weak inductuion in which the arguer tries to claim a causal relationship about two events that are most likely just coincidental.

false dichotomy
An informal fallacy of presumption based on a disjunction when there are actually more than two choices.

formal fallacy
An invalid argument in which the problem has to do with the form of the argument.

inductive argument
An argument in which the premises are intended to provide probable support for the conclusion. It is conceivable, in an inductive argument, that the premises are all true but the conclusion is false, this is just unlikely. (The sun will come up in the east tomorrow morning, because it always has in the past is an inductive argument)

inference
A jump of reasoning from known information to new information. (See inferential relationship)

inferential claim 
see: claim of inference

inferential relationship
The relationship between the premises and conclusion in a good argument. See modus ponens.

informal fallacy
A bad (invalid or unsound) argument, where the problem has to do with the contingent content of the argument, and can't be detected by looking at the form itself.

Abstract: Along with others we believe there has been a distinct paradigm shift in the psychology of deductive reasoning.

Many authors have moved away from a model of rational reasoning based on extensional bivalent logic in favour of a
Bayesian approach in which all premises and conclusion are represented with a degree of uncertainty.

This leaves the important question of whether deductive reasoning is now distinct from inductive inference, which has traditionally been studied in separate literatures.

We argue that induction remains both logically and psychologically distinct from the probabilistic deduction of the new paradigm.

Although both forms of inference lead to conclusions with degrees of uncertainty, inductions cannot be probabilistically valid.

That is, their conclusions are by their nature more uncertain than their premises.

By contrast, valid deduction from uncertain premises cannot increase that uncertainty.

The two forms of inference also have distinct purposes: induction adds new beliefs whereas deduction draws out implications from what is already believed.

Abstract:

Peirce conceived inquiry as performed in three stages, which correspond to three classes of inferences:

abduction or retroduction, deduction, and induction.