Logic

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Logic argumentation theory

• 04/05/2004

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What is an argument?

• An argument is a set of propositions where one of
  the set (the conclusion) is supposed to follow
  from the others (the premises). If it is the case
  that the premises are true, and the conclusion
  does indeed follow from the premises, then the
  argument provides evidence or rational grounds or
  a reason that the conclusion is true.

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What are propositions?

• Propositions are any grammatical form that can be
  either true or false. Another way of putting this
  is to say that propositions are the meaning of
  the sentences which say something true or false.
• An argument is not just a pile of propositions.
  If a collection of propositions constitutes an
  argument there are specific putative relations
  between the propositions that make it an argument.

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Premise and conclusion

• The relations that make collections of
  propositions into an argument can be
  characterized as follows. The premise or premises
  of an argument are those propositions in the
  argument from which the conclusion is said to
  follow. The conclusion is that proposition which
  is said to follow from the premise or premises.
• It should be noted that the terms premise and
  conclusion are relative terms.

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Why arguing?

• The value of arguments is that they are a way of
  finding out what is rational to believe or think
  true. We know that if an argument is a good
  argument, the premises are true and the
  conclusion follows from the premises, then we are
  rationally justified in believing the conclusion
  of that argument or accepting it as true.

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What is logic?

• Logic hopes to identify the general form of those
  collections of propositions where the conclusion
  really does follow from the premises. Once one
  knows the forms of good argument, one can
  confidently slot particular propositions into
  those forms, and be sure that the outcome is a
  good argument in that particular case. This is
  because any proposition slotted into a good
  argument form will be a good argument.
• Similar to a recipe in a cookery-book

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Logic and rhetoric (1)

• There are many ways to get someone to hold
  certain beliefs r accept certain propositions
  that are not arguments brainwashing, depriving
  someone of sleep and repeating something again
  and again threatening, flattering, an orator,
• What may as a matter of fact get someone to hold
  a certain belief or accept certain propositions
  as true is a purely psychological matter, and has
  no bearing on whether something is a good
  argument or not.

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Logic and rhetoric (2)

• Presenting someone with an argument is one way,
  it so happen sometimes a good way, to get someone
  to believe something or to hold a proposition
  true. But this is not its prime aim or part of
  the essential nature of arguments. The prime aim
  of an argument is to present a rational
  justification for a belief or for the truth of a
  proposition, and this is totally independent of
  whether it in fact convinces anyone or not

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Validity

• Propositions are true or false. Arguments are
  valid or invalid.
• An argument is valid if the conclusion follows
  from the premises. The conclusion follows from
  the premises if to assert the premises but deny
  the conclusion would be a contradiction or
  inconsistent.

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Soundness

• Validity is not enough for good reasoning.
  Arguing validly without regard to the truth of
  the premises only tells us what follows given
  those premises it does not give a reason for
  thinking the conclusion true.
• In a sound argument, because both the premises
  are true and the argument valid, a reason has
  been given for the conclusion being true. Indeed
  it must be the case that the conclusion is true
  if the argument has both true premises and is
  valid.

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Informal fallacies

• objective fallacies affirming the consequent,
  denying the antecedent
• Irrelevant factors ad hominem, ad populum, etc.
• Misleading factors strawman, too complex
  questions, etc.
• Problematic premises false dilemma, petitio
  principii