Historical Introduction to Philosophy/Logic

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Introduction to Logic[edit]

Logic is the underpinnings of reason and argument. To be logical is to follow a pattern of reasoning that doesn't contain flaws or weaknesses. A true logical debate puts forward the best possible arguments from both sides and allows the evidence to carry the conclusion rather than fallacies that appeal to attacks, emotions, or trickery.

Valid and Invalid Arguments[edit]

An argument is said to be valid, (or have a valid inference) if it is impossible for all of the premises to be true and the conclusion to be false. Another way of stating the same thing is that if an argument is valid, then the conclusion must be true given the condition that all premises are true.

On the other hand, an argument is said to be invalid (or have an invalid inference) if it is possible to have all true premises and a false conclusion (no matter how remote the possibility).

An example of a valid argument (known as disjunctive syllogism)

    The battery is bad or the fuse is shot.
    The battery is not bad.
    Hence the fuse is shot.

Observe that if all of the premises to this argument are true, then the conclusion must be true.

On the other hand, the following argument is invalid.

    If it rains, then the streets will be wet.
    It did not rain.
    Therefore the streets are not wet.

In this case, even if all the premises are true, the conclusions could still be false - for example, in the case that a week of snow melts causing the streets to get wet (without it having rained).

There is a common confusion about the meaning of the terms valid and invalid. The terms, as used in logic refer to relationships between the truth of the premise and the truth of the conclusion (as given in the above definitions). Outside of logic and the context of philosophy the terms are often used as if they were synonymous with "true" in the case with valid, and "false" in the case with invalid. These non-logical meanings are not correct in the context of logic. For example, the elements of an argument are premises and the conclusion, each of which can be true or false, but the entire argument as a whole is either valid or invalid (not true or false). Just like the individual members of a family are male or female, the family as a whole might be classified as "traditional" or "non traditional" (not, male or female).

Some logicians restrict the use of the terms valid and invalid to a set of arguments which are classified as being deductive. Other logicians ignore this classification and simply state that all arguments have an inference which can be objectively classified as being valid or invalid.


Why study logic? Simple...to be a better person, to able to tackle an argument and break down the components into manageable chunks, to weed out poor arguments and expose them to light for the weaknesses that they are.

Logical Arguments/Syllogisims[edit]

All arguments can be broken down into basic structures that can be analyzed for accuracy. Let's look at an example:

Fallacies[edit]

Invalid deductive arguments and weak deductive arguments constitute fallacies, though not every invalid argument can be classified as a fallacy. Certain patterns of mistakes lead to the formation of a fallacy.

Formal and Informal Fallacies[edit]

Informal fallacies are quite syntactical in nature attributable to mistakes in language, inability to put across a message or due to poor sentence construction. However, formal fallacies constitute a much graver set of mistakes that are flaws in the argument or the structure of the argument. They cannot be altered even if their premises are changed.

Logical Fallacies[edit]

  • Fallacies of Relevance
    • Straw Man - A method of creating a weaker form of an argument and then attacking that weaker position. The opponents argument is first distorted into something that can be easily demolished by the opponent.
  • Ad Hominem - Differs from Straw Man in that the argument is not attacked, rather the person himself. The opponent may dig up the past history of the person in order to reduce the acceptance of his arguments by the public. This is usually seen in elections to public offices.
  • Red Herring - Shifting the focus of the argument to distract away from original point. An example may be to argue about animal rights and then say animals should not eat plants as plants too have rights.
  • Begging the Question (circular logic) - The conclusion is the same as the assertion, no argument is being made only a statement.
  • Appeals:
    • to Emotion (Ad Populam) - the basic tenet of this fallacy is "a lot of people do this so we should do too." Classic "toothpaste advertising" is a good example: "3 out of four dentists use and approve Crest Extra Strength Whitening!" The ad never says, specifically, that you should too, and yet viewers immediately are tricked into thinking they should. This is because most viewers believe that dentists are trust able, yet most likely no dentists were even asked their opinion on it.
    • to Belief
    • to Popularity
    • to Fear
    • to Ridicule
    • Fallacies of Defective Induction

the premises here are irrelevant but the inductive conclusions drawn from this are very weak.

  • Hasty Generalization - One example may be that the person takes for granted what happens in a small universe and applies it in general life, without factoring in deviance and luck.
  • False Cause - Correlation is not the same as the causes for it.
  • Appeal to Authority - Citing an 'expert' with no additional context...the expert could easily be a novice in terms of the discussion unless directly related to the problem. (i.e. Bill Gates being cited as an expert on Nuclear War instead of technology). It does not mean, however, that the 'expert' is not right, but it creates a weakness in the argument and is best to be avoided.
    • Fallacies of Presumption
  • Accident - A general rule that cannot be applied for exceptions.
  • Complex Question - The question consists of definitive suggestions.
  • Begging the Question (circular logic) - The conclusion is the same as the assertion, yet no argument is being made, only a statement.
    • Fallacies of Ambiguity
  • Equivocation - Use of same words in different senses in the same argument.
  • Amphiboly - An argument based on an Amphibolous construction.
  • Accent - When the focus is on the wrong word. Modern logicians have extended this to selective quoting.
  • Composition - Since every part has the same character, the whole body of text does not necessarily share the same view.
  • Division - The inversion of Composition, where the whole piece does not necessarily imply the character of the various parts, yet by connotation it can be assumed.
  • Bandwagon Thinking - Also could be called Mob Rule or Rule of the Majority...using the power of a crowd as evidence of argument rather than actual evidence.
  • Post Hoc Ergo Propter Hoc (After the fact, therefore because of it) - supposing that because circumstance B follows circumstance A, it must therefore have been caused by it.
  • The 'Only Game in Town' Fallacy - supposing that since there is only one available explanation, this explanation is therefore the correct one.
  • "Scapegoating" - blaming a single person for a problem seemingly unsolvable such as the murder of the Lindbergh baby.
  • False Dilemma - presenting two options, disproving one and making the claim that the other option is the only answer when there could be others not explored.
  • Slippery Slope - assuming a small effect will produce a much larger effect down the road without accurate causation.

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