A logical argument starts with the matter… what you actually say. We may break this up into arguments and examples.
The next consideration is the method... how you say what you say (organization of thought and of delivery.) We start with a clear idea of what we are going to say. We bring unity (consistency) and logic to what we say. Most importantly we develop our arguments using premises, inferences, and conclusions. Use the ‘truth table’ (*) to test all logical connections.
Matter and method will need one more element to bind for a successful presentation of logical arguments... manner. When presenting our arguments, we should be aware of the following... need for simplicity, clarity, and tact... no need for shouting... and no need for ego display. Furthermore, care should be taken to avoid the myriad of fallacies that would pop up out of the blue from habit or lack of diligence.
Definitions of terms:
Premise = proposition used to advance an argument ... often indicated by phrases such as “because,” “since,” “obviously,” etc.
Inference = when a premise has been accepted and a new proposition is derived ... often indicated by phrases such as “therefore,” “ … implies that…,” etc.
Conclusion = the final stage of all inferences, the wrapping up …often indicated by phrases such as “it follows that,” “we conclude that,” etc.
Deductive Argument = provides conclusive proof of its conclusion ... we need to differentiate ‘false implications’ from logical conclusions.
Inductive Argument = either valid or invalid inferences are made depending on the premises.
(*) Truth Table:
Where the symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. "T" and "F" represent true and false (or valid and invalid) respectively.
Premise Conclusion Inference
A B A=>B
F F T
F T T
-- If the premise is false and the inference valid, the conclusion can be true or false.
T F F
-- If the premises are true and the conclusion false, the inference must be invalid.
T T T
-- If the premise is true and the inference valid, the conclusion must be true.
Argumentum ad hominem = "argument directed at the man", the abusive kind where instead of trying to disprove the truth of an assertion, the arguer attacks the person or people making the assertion.
Argumentum ad ignorantiam = "argument from ignorance". This fallacy occurs whenever it is argued that something must be true simply because it has not been proved false. Or, equivalently, when it is argued that something must be false because it has not been proved true. (Note that this is not the same as assuming that something is false until it has been proved true, a basic scientific principle.)
Argumentum ad misericordiam = appeal for pity or special pleading.
Argumentum ad populum = appeal to the gallery or appealing to the people.
Argumentum ad verecundiam = The Appeal to Authority uses the admiration of the famous to try and win support for an assertion.
The Fallacy of Accident = The Fallacy of Accident is committed when a general rule is applied to a particular case whose "accidental" circumstances mean that the rule is inapplicable.
Converse accident / Hasty generalization = the reverse of the fallacy of accident.
Sweeping generalization / Dicto simpliciter = A sweeping generalization occurs when a general rule is applied to a particular situation in which the features of that particular situation render the rule inapplicable. A sweeping generalization is the opposite of a hasty generalization.
Non causa pro causa / Post hoc ergo propter hoc = these are known as False Cause fallacies.
Cum hoc ergo propter hoc = this fallacy is similar to Post Hoc Ergo Propter Hoc. It asserts that because two events occur together, they must be causally related, and leaves no room for other factors that may be the cause(s) of the events.
Petitio principii / Begging the question = this fallacy occurs when the premises are at least as questionable as the conclusion reached.
Circulus in demonstrando = this fallacy occurs when one assumes as a premise the conclusion which one wishes to reach. Often, the proposition will be rephrased so that the fallacy appears to be a valid argument. (A circular argument.)
Ignoratio elenchi = the fallacy of Irrelevant Conclusion consists of claiming that an argument supports a particular conclusion when it is actually logically nothing to do with that conclusion.
Equivocation = … occurs when a key word is used with two or more different meanings in the same argument.
Amphiboly = … occurs when the premises used in an argument are ambiguous because of careless or ungrammatical phrasing.
Accent = … another form of fallacy through shifting meaning.
Fallacies of composition = One Fallacy of Composition is to conclude that a property shared by the parts of something must apply to the whole. The other Fallacy of Composition is to conclude that a property of a number of individual items is shared by a collection of those items.
Fallacy of division = … the opposite of the Fallacy of Composition.
The slippery slope argument = … states that should one event occur, so will other harmful events .... "A is based on B" fallacies / " ... is a type of ... " fallacies / Fallacy of the False Cause."
Undistributed Middle = these fallacies occur when one attempts to argue that things are in some way similar without actually specifying in what way they are similar.
Affirmation of the consequent = this fallacy is an argument of the form "A implies B, B is true, therefore A is true". To understand why it is a fallacy, examine the truth table for implication given earlier.
Denial of the antecedent = this fallacy is an argument of the form "A implies B, A is false, therefore B is false". Again refer to the truth table.
Converting a conditional = this fallacy is an argument of the form "If A then B, therefore if B then A".
Argumentum ad antiquitatem = this is the fallacy of asserting that something is right or good simply because it is old, or because "that's the way it's always been."
Argumentum ad novitatem = this is the opposite of the Argumentum ad Antiquitatem; it is the fallacy of asserting that something is more correct simply because it is new or newer than something else.
Argumentum ad crumenam = the fallacy of believing that money is a criterion of correctness; that those with more money are more likely to be right.
Argumentum ad lazarum = the fallacy of assuming that because someone is poor he or she is sounder or more virtuous than one who is wealthier.
Argumentum ad nauseam = this is the incorrect belief that an assertion is more likely to be true the more often it is heard.
Bifurcation = ... also referred to as the "black and white" fallacy, bifurcation occurs when one presents a situation as having only two alternatives, where in fact other alternatives exist or can exist.
Plurium interrogationum / Many questions = this fallacy occurs when a questioner demands a simple answer to a complex question.
Non sequitur = ... an argument where the conclusion is drawn from premises which are not logically connected with it.
Red herring = This fallacy is committed when irrelevant material is introduced to the issue being discussed, so that everyone's attention is diverted away from the points being made, towards a different conclusion.
Reification / Hypostatization = ... occurs when an abstract concept is treated as a concrete thing.
Shifting the burden of proof = .... The burden of proof is always on the person making an assertion or proposition. Shifting the burden of proof, a special case of Argumentum ad Ignorantiam, is the fallacy of putting the burden of proof on the person who denies or questions the assertion being made. The source of the fallacy is the assumption that something is true unless proven otherwise.
Straw man = The straw man fallacy is to misrepresent someone else's position so that it can be attacked more easily, then to knock down that misrepresented position, then to conclude that the original position has been demolished. It is a fallacy because it fails to deal with the actual arguments that have been made.
The extended analogy = the fallacy of the Extended Analogy often occurs when some suggested general rule is being argued over. The fallacy is to assume that mentioning two different situations, in an argument about a general rule, constitutes a claim that those situations are analogous to each other.
Tu quoque = this is the famous "you too" fallacy. It occurs when an action is argued to be acceptable because the other party has performed it.
For instance: “You’re just being randomly abusive.”
“So? You've been abusive too.”
This is a personal attack, and is therefore a special case of Argumentum ad Hominem.
Audiatur et altera pars = Often, people will argue from assumptions which they do not bother to state. The principle of Audiatur et Altera Pars is that all of the premises of an argument should be stated explicitly.
Argumentum ad logicam = this is the "fallacy fallacy" of arguing that a proposition is false merely on the grounds that it has been presented as the conclusion of a fallacious argument. Remember always that fallacious arguments can arrive at true conclusions.