Scie 326 Unit 9

• Principles of Reason

  1. Principle of non-contradiction
  2. Principle of sufficient reason
  3. Principle of the identity of indiscernibles
• Principle of non-contradiction


  asserts that every statement involving a contradiction is to be judge false, and every statement that is the negation of a falsehood is to be judge true. In analytic cases, the appearance of a contradiction in an argument indicates an error in the argument. Example- Necker cube
• Principle of sufficient reason


  there can be no fact real or existing, no statement true, unless there be a sufficient reason why it should be so and not otherwise. "Nothing ever comes to pass without a cause".
• Principle of the identity of indiscernibles

  two things that cannot be in any way distringuished from each other are considered indentical. Example- If we are speaking at the higher level (that of genus), we can consider lions and tigers to be the same; at the local level (of species), we cannot.
• What are the four polarities of reason

  1. Top down/bottom up2. Deduction/Induction3. Analysis/synthesis4. Functional/structural
• Hypothetico-deductive argument


  An argument that scientific inquiry proceeds by formulating a hypothesis in a form that could conceivably be falsified by a test on observable data. If I make a hypothesis, and from that hypothesis deduce a logically valid conclusion that can be empirically tested, then, if the conclusion turns out to be empirically false, it must be the case that either the hypothesis, or some other assumption involved in the deduction, is false.
• Four Polarities in the hypothetico-deductive argument

  the prescribed rules of procedure are to begin with data, and by induction or abduction, to generate an explanatory hypothesis. (In general, it is a good idea to consider several distinct hypotheses, and choose that which seems most likely for further testing.) Then the reasoner assumes the truth of the hypothesis, and deduces further consequences that can be tested observationally or experimentally. That is, we begin with a bottom-up approach, studying the basic components of a system and attempting to generate a synthesis that describes and explains the system's structure and behavior. Once this synthesis is formalized as a hypothesis, we are in a position to take a top-down approach in which we can deduce further system properties, and make predictions about components and their interactions. These, in turn, are compared to empirical data. If there is a fit, we feel more confident in our hypothesis. If there is a misfit (contradiction), we need to change or adjust the hypothesis until we are able to find a fit.
• Three laws of Aristotelian Logic

  1. Law of Identity2. Law of Contradiction3. Law of the Excluded Middle
• Law of Identity


  A thing is equal to itself
• Law of Contradiction


  No thing is equal to anything other than itself.
• Law of the Excluded Middle

  No thing can have both a property and its opposite, or negation.
• What does Aristotelian logic deal with?

  questions of identity, and in particular, universal and unchanging identity: that which a thing must have in order to be entitled to its name. What is it, for example, that makes a rose a rose, and not a carnation; or allows us to talk about roses and know that we are both talking about the same thing?
• Is this syllogism valid?Mice have sharp teethSome animals with sharp teeth eat cheeseTherefore mice eat cheese

  S= MiceP= Sharp TeethM= eats cheeseAll S are PSome P are MTherefore, All S are MThis is INVALID
• Is this syllogism valid?Dogs are not giraffesCats are not giraffesTherefore, dogs are cats


  S= DogsP= GiraffesM= CatsAll S are not PAll M are not PTherefore, All S is MThis is INVALID
• Is this syllogism valid? Species in danger of extinction ought to be protected, Smallpox virus is in danger of extinction, Therefore, the smallpox virus ought to be protected.

  S= Danger of extinction P= Ought to be protected M= Smallpox virus All S is P. All M is S. Therefore, All M is P. This is VALID
• Is this syllogism valid? All fish have legs, All animals with legs can jump over the moon, Therefore fish can jump over the moon.

  S= Fish P= Legs M= Jump over the moon. All S is P. All P is M. Therefore, all S is M. This is VALID
• You are shown four cards, two labeled with the letters A and K and two with the numbers 2 and 7. You are told that these cards follow the rule that if there is a vowel on one side, then there is an even number on the other side. Which cards must you turn over in order to test this rule?


  Wason Card Problem for deductive reasoningThe answer is A and 7The only way to falsify an "if X, then Y" statement ("if vowel, then even number") is by finding an instance of "X and not Y" ("vowel and odd number"). D and 4 are irrelevant, because these cards cannot combine a vowel and odd number.
• In terms of truth tables, what do the following symbols mean? 1. ^ 2. v 3. --> 4. <-->

  1. AND 2. OR 3. implies 4. if and only if
• What is the importance of the contrapositive in the hypothetico-deductive method?

  The contrapostive proves the principle of non-contradiction.