Here we will examine two kinds of logic: deductive reasoning (a la Sherlock Holmes), in which we reason from general principles to specific instances and inductive reasoning, in which we reason from particular, observed phenomena to generalizations about the world.


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Deductive Reasoning


Deductive reasoning moves from the general to the specific as in the example below:

All dogs are mammals, Fido is a dog, therefore Fido is a mammal. We go from ALL dogs (the general) to FIDO (specific). These are called SYLLOGISMS. the structure of the logical syllogism is always the same. They each have:

  • Two PREMISES and one CONCLUSION
  • Have three terms, each of which occur twice (dogs, mammals, Fido)
  • Have QUANTIFIERS such as ‘all’, or ‘some’ or ‘no’

Consider the following example:

Premiss A: All humans are mortal
Premiss B: I am human
Conclusion C: Therefore I am mortal

If you agree with the conclusion you are thinking rationally and deductively in particular. It would be foolish to propose the truth of Premiss A and of Premiss B while denying the truth of conclusion C.

This is what is known as logical validity. The actual truth of A or B could be questionable but the syllogism is still valid as the conclusion follows from the premisses.
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So, STATEMENTS can be true or false but ARGUMENTS are valid or invalid. Don’t confuse the two! An argument can be VALID and still not be TRUE! Pure logic is ONLY concerned with the STRUCTURE of an argument.
  • A) I am either a Kibberschtupperuhn or a crocklebinder or both.
  • B) I am not a Kibberschtupperuhn
  • Therefore:

We can use Venn Diagrams to determine the validity of an argument:

Premiss A:Socrates is a man
Premiss B:All men are mortal
Conclusion C:Therefore Socrates is mortal
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source: billbreitmayer.com

Using Venn diagrams determine whether or not each of these are valid. (Examples from van de Lagemaat, pp. 117-8)

1. All Italians eat spaghetti. Giovanni Ross eats spaghetti. Therefore Giovanni Rossi is an Italian

2. No Martians have red noses. Rudolph has a red nose. Therefore Rudolph is not a Martian

3. All bull-fighters are brave people. Some brave people are compassionate Therefore bull-fighters are compassionate.

4. Some Monks are Tibetans. All Tibetans are good at yoga. Therefore some Monks are good at yoga.

5. Some astrologers are frauds. Some frauds are not wealthy. Therefore some astrologers are not wealthy.

6. All bobos have dogs. No doctors have dogs. Therefore no bobos are doctors.

7. All rookies are red-heads. All red-heads are runners. Therefore all rookies are runners.

8. No alphas are betas. No gammas are betas. Therefore no gammas are alphas.

Examples of faulty reasoning, deductive logic and valid premises.

Proving that a woman is a witch through logic in Monty Python'sThe Life of Brian.
"She's a witch! burn her!"


So:
Both witches and wood burn
Both wood and ducks float
Therefor, if a woman weighs the same as a duck, she is a witch.

Dumb Penguins
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Make up arguments which are:

  • Logically valid, true premises
  • logically valid; one true premiss; one false premiss; true conclusion
  • Logically invalid; true premises; false conclusion
  • Logically valid; false premises; true conclusion
  • logically valid with true premises and false conclusion (Is this possible?)

Which one above is the most credible?

Conclusions on deductive reasoning

For the conclusion of a logical argument to be true, the logic must be correct (Valid) and the premises must be true. To undermine an argument, you can fault the logic (The argument is invalid!) or you can dispute the premises of the argument.

Advantages:

  • Deduction if done correctly gives us precise and direct answers.
  • If an argument is valid, and in addition it started from true premises, then it is called a sound argument. Sound arguments must arrive at a true conclusion.

Problems:

  • The fact that an argument is valid doesn't necessarily mean that its conclusion holds. It may have started from false premises.

  • Attempts at logic often seems valid but on further examination they often are not (Being validly logical all the time is hard to do).

  • Many of the premisses used in deductive reasoning are generalizations made using INDUCTIVE REASONING so the soundness of the premiss relies on a form of logic that can not bring certainty.

  • Belief bias

  • agreement of terms

  • factual disputes

  • etc.