Argumentation and Logic

One of our first “philosophical society” meetings we decided to discuss argumentation and logic. we figured it was a good point to start in order to build a foundation for later topics and discussions that could be potentially be divisive.

I wrote up a worksheet that could be a helpful resource for us (below). Most of the information was gathered from Craig and Morleand (2003) as well as Koukl (2009). However, there is also some info from wikipedia (very academic).

Argumentation and Logic

  • Argumentation can be
    • Deductive: premises guarantee truth of conclusion
    • Inductive: premises render conclusion more probable than competitors
  • Deductive Arguments
    • Must be both formally and informally valid
      • Formally: follow rules of logic
      • Informally- Arguments can still be fallacious even if it follows rules of logic
        • g. reasoning in a circle
      • ALSO, premises must be true
      • A “sound argument” has both true premises and is logically valid
        • It also has premises that are more plausible than their contradictories
          • Certainty for premises is NOT a must
            • The question is whether the contradictory is as or more plausible than the premises


  • If we are utterly uncertain or ignorant of a premises’ truth the argument will be of little use to us HOWEVER
  • If we are warranted in believing the premises to be true, then the argument warrants us in accepting the conclusion.
    • The premises must be more plausible than their denials.
  • An argument can be sound and informally valid and STILL not be a good one!
  • Certainty is an unrealistic ideal
    • Were we required certainty for premises then skepticism would follow
  • One can present a bad argument for a true conclusion
  • Some may deny premises because they do not like where the conclusion leads

The above info is from (moreland & craig, 2003)

  • Sentential or Propositional logic
    • Most basic level of logic
      • Only 9 rules to learn
    • Symbolic Logic
      • P and Q stand for two different sentences the arrow (>) stands for connecting words “if…then…”
        • g. “if P then Q”
        • Or “P implies Q”
      • P>Q, “P” is sufficient condition of “Q”, and “Q” is a necessary condition of “P”
      • The following is logically fallacious (affirming the consequence)
        • 1 P>Q
        • 2 Q
        • 3 P
          • (P) is sufficient but (Q) is the necessary condition. In other words, (Q) does not imply (P). Only the opposite would be true.
        • Propositional Logic- most basic logic
        • 9 rules below:
          • Modus Ponens
          • Modus Tollens
          • Hypothetical syllogism
          • Conjunction
          • Simplification
          • Absorption
          • Addition
          • Disjunctive syllogism
          • Constructive Dilemma

The above info is from (moreland & craig, 2003)

  • Argumentation tactics
    • Reductio Ad Absurdum
      • In order to defeat another’s argument you show that their assumptions/reasoning lead to contradictions or absurdities when carried out (Koukl)
    • Define terms so that there is not confusion
    • Ask questions
      • This helps in several ways
        • Buys you time to gather your thoughts (especially if you are ignorant of their argument)
        • Allows you to understand their argument better
        • Lets you know if they really have a sound argument or if it has internal contradictions
        • Shows that you care and are listening
        • Puts you in the drivers seat of the conversation (Koukl)
      • Understand who has the burden of proof
        • Whoever makes an assertion is the one who must defend their assertion first
          • Do not let the burden of proof be shifted until they have provided adequate evidence for their assertion. (Koukl)
        • Fallacies (popular ones)
          • Straw man
            • When someone tries to misrepresent their opponent’s argument by slightly changing it and showing how absurd the changed argument or premise is (even though it really isn’t the argument being asserted)
          • Begging the question/arguing in a circle/circular reasoning
            • Conclusion that one is attempting to prove is included in the initial premises of an argument, often in an indirect way that conceals this fact (Wikipedia)
          • Genetic Fallacy
            • Argues that a belief is false or mistaken because of the way the belief originated
          • False Dichotomy
            • that involves a situation in which only limited alternatives are considered, when in fact there is at least one additional option. (wikipedia)
          • Argument to moderation
            • is an informal fallacy which asserts that the truth can be found as a compromise between two opposite positions. (wikipedia)
          • Ad hominem
            • is a general category of fallacies in which a claim or argument is rejected on the basis of some irrelevant fact about the author of or the person presenting the claim or argument (wikipedia)
          • Argument from authority
            • while authorities can be correct in judgments related to their area of expertise more often than laypersons, they can still come to the wrong judgments through error, bias, dishonesty, or falling prey to groupthink. Thus, the appeal to authority is not a generally reliable argument for establishing facts (wikipedia)
          • Red herring
            • A diversionary tactic and ultimately irrelevant to the argument. used to refer to something that misleads or distracts from the relevant or important issue. It may be either a logical fallacy or a literary device that leads readers or characters towards a false conclusion. (wikepedia)
          • Argument from ignorance
            • Arguing that a claim is false because there is not sufficient evidence that the claim is true
          • Equivocation:
            • Using a word in such a way as to have two meanings
          • Amphiboly
            • Formulating premises in such a way that their meaning is ambiguous
          • Composition:
            • Inferring that a whole has a certain property because all of its parts have that property
              • Sometimes wholes DO have the properties of the parts but not always

The above info is from (moreland & craig, 2003) and WIKIPEDIA

  • Inductive reasoning
    • Bayes’s Theorem
      • Formula for calculating probability of a hypothesis on given evidence
        • Can be helpful. Although impossible to do with precision
      • Inference to the best explanation
        • More apt to be useful than deductive in some cases
          • From a pool of live options we select the explanations that, if true, best explains the data.
        • Commonly acknowledged criteria that go toward making an explanation the best:
          • Explanatory scope- the best hypothesis (H) will explain a wider range of data than will rival H’s
          • Explanatory power- the best H will make the observable data more epistemically probable than rival H
          • Plausibility- Best H will be implied by a greater variety of accepted truths AND its negation implied by fewer accepted truths than rival H
          • Less ad Hoc- Best H will involve fewer new suppositions not already implied by existing knowledge than rival H
          • Accord with accepted beliefs- the best H when conjoined with accepted truths, will imply fewer falsehoods than rival H
          • Comparative superiority- the best H will so exceed its rivals in meeting the above conditions that there is little chance of a rival H exceeding it in fulfilling those conditions.

The above info is from (moreland & craig, 2003)

Exercise: evaluate the following argument (is it logically sound, are the premises true?)

  1. If an outline proposes facts from unreliable sources, then the outline is necessarily false.
  2. The majority of information in this outline comes from two sources: 1) philosophers who are theists (more specifically Christians) and 2) Wikipedia. (Christian philosophers are unreliable because of their assumptions and biases and Wikipedia is not a reliable source for college papers)
  3. Therefore, this outline is untrustworthy and necessarily false in what it states


J.P. Moreland & William Lane Craig (2003) Philosophical Foundations for a Christian Worldview. Chapter 2. Argumentation and logic

Koukl, Greg (2009) Tactics


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