Use of Reason and Logic RATIONALISM

 A Rationalist approach to knowledge is based on the belief that we can ascertain truth by thinking and reflection alone. RATIONALISM

 Reasoning is a collective endeavor by which people construct meaning together by exchanging, modifying, and improving their ideas and opinions.  When someone offers a claim (to knowledge) it is appropriate to ask for their reasons.  Any disagreement in reasoning (or the validity of their reasons) requires argument in order to maintain consistency. REASON

 Reasoning, from an argumentative standpoint, is the drawing of inferences or conclusions from known or assumed facts.  When solving a problem, one must understand the question, gather all pertinent facts, analyze the problem i.e. compare with previous problems (note similarities and differences), perhaps use pictures or formulas to solve the problem. USING REASON

 Reason has a place in nearly all the Areas of Knowledge as well as in our everyday experiences.  Think of 1 way you use reason when attempting to formulate knowledge about the natural world…  How do you know whether or not to leave the house with or without a raincoat or umbrella (without the weatherman or your iPhone / computer)? REASON

 Central to the Rationalist approach is Logic.  Logic can be simply defined as a way of thinking that uses different modes of reasoning to determine which reasons are valid and invalid (fallacies), with a goal of finding the truth.  It’s not raining, but the clouds are dark, low, and they look threatening. Therefor, there’s a good chance of rain. I should bring my raincoat or umbrella. REASON & LOGIC

 The two Forms of Logic that we will apply in our examination of Rationalism are:  Deductive Logic.  Inductive Logic. TYPES OF LOGIC Induction Specific Observations to General Conclusion Deduction Specific Conclusion from General Statements Specific General

 Deductive Logic is where given the truth of some information, the conclusion must also be true.  Another Example:  A: All humans are mortal (major premise)  B: I am Human (minor premise)  C: Therefore, I am mortal (conclusion)  The above example is a syllogism: an argument composed of 2 statements of evidence (premises) followed by a conclusion. DEDUCTIVE LOGIC

 Deductive arguments involve the claim that the truth of its premises guarantees the truth of its conclusion;  The terms valid and invalid are used to characterize deductive arguments.  A deductive argument succeeds when, if you accept the evidence as true (the premises), you must accept the conclusion.  BE CARFEUL, DO NOT CONFUSE TRUTH WITH VALIDITY! DEDUCTIVE REASONING

Valid:Invalid: an argument is valid if and only if it is necessary that if all of the premises are true, then the conclusion is true; if all the premises are true, then the conclusion must be true; it is impossible that all the premises are true and the conclusion is false. We can test for invalidity by assuming that all the premises are true and seeing whether it is still possible for the conclusion to be false. If this is possible, the argument is invalid. These terms apply only to DEDUCTIVE arguments and apply only to the arguments themselves, not the premises. VALID AND INVALID ARGUMENTS

(Premise #1) All math teachers are over 7 feet tall. (Premise #2) Mr. D. is a math teacher. (Conclusion) Therefore, Mr. D is over 7 feet tall. Valid or Invalid? VALID, but definitely not true LETS TRY THIS OUT!

VENN DIAGRAMS  Venn Diagram: A diagram consisting of various overlapping figures contained in a rectangle called the universe. This is an example of all A are B. (If A, then B.) B A

(Premise #1) Some professors wear glasses. (Premise #2) Mr. Einstein wears glasses. (Conclusion) Therefore, Mr. Einstein is a professor. Valid or Invalid? INVALID, but definitely not true

VENN DIAGRAMS This is an example of some A are B. (At least one A is B.) The yellow oval is A, the blue oval is B.

EXAMPLE #1 Construct a Venn Diagram to determine the validity of the given argument.  All smiling cats talk.  The Cheshire Cat smiles.  Therefore, the Cheshire Cat talks. VALID OR INVALID???

EXAMPLE #1 X is Cheshire Cat; Argument is Valid Things that talk Smiling cats x

EXAMPLE 2 Construct a Venn Diagram to determine the validity of the given argument.  No one who can afford health insurance is unemployed.  All politicians can afford health insurance.  Therefore, no politician is unemployed. VALID OR INVALID?????

EXAMPLES X=politician. The argument is valid. People who can afford Health Care. Politicians X Unemployed

 Deductive Logic is Flawed…. Surprised?  All that matters is that the Premises are true.  A correctly reasoned syllogism only guarantees a valid answer. Whether or not its true is a different matter.  Premise #1 : When an evenly weighted coin is randomly flipped in the air, the probability of it landing on heads and tails is equal.  Premise #2: The coin is evenly weighted and is being randomly flipped.  Conclusion: its chances of landing on heads and tails is equal. PROBLEM OF DEDUCTION…

 Does the result rely on previous results?  How do we know the sides are evenly weighted?  How can we determine if the actual toss of the coin is random?  Actually, this is all superstition! The odds are 50/50. PROBLEM OF DEDUCTION

DEDUCTIVE LOGIC Meet: Jackson! When Jack was nearly 2 years old, he identified this as “dog”

 Jack also recognized these as dogs:  Jack noticed all these dogs had 4 legs and a tail. DEDUCTIVE LOGIC

 On his First Trip to the Zoo, here were the other “dogs” that Jack pointed out: DEDUCTIVE LOGIC

 Why would Jack ever believe this?  Deductive Logic  Jack made specific conclusions from a set of general observations.  All dogs have 4 legs and a tail.  The animals at the zoo had 4 legs and tails.  Those animals were dogs too. DEDUCTIVE LOGIC

Lets Summarize ………

From vague To specific DEDUCTIVE REASONING

 The process of reasoning from known facts to conclusions. When you reason deductively, you can say “therefore” with certainty. If your facts were firm to begin with, then your conclusions will also be firm.

A DEDUCTIVE ARGUMENT True Premise True Premise True Conclusion

 The process of reasoning from known facts to conclusions. When you reason deductively, you can say “therefore” with certainty. If your facts were firm to begin with, then your conclusions will also be firm. DEDUCTIVE REASONING

 is one in which it is impossible for the premises to be true but the conclusion false.  It is supposed to be a definitive proof of the truth of the claim (conclusion).  Premise  All men are mortal.  Premise  Socrates was a man.  Conclusion  Socrates was mortal.  If the premises are true (and they are), then it simply isn't possible for the conclusion to be false.  If you have a deductive argument and you accept the truth of the premises, then you must also accept the truth of the conclusion. A DEDUCTIVE ARGUMENT

 Inductive logic is the reverse of Deductive Logic… Inductive Logic allows a general conclusion to come from a collection of specific observations.  Observing that something is true many times, then concluding that it will be true in all instances  Using the data to make a prediction  (SO) The sun has risen everyday of my life.  (GC) The sun will rise tomorrow.  (SO) I’ve never had food poisoning.  (GC) All food is safe to eat.  (SO) When I drop a baseball it falls to the ground.  (GC) Every time I drop something, it will fall. INDUCTIVE LOGIC Are you starting to see a problem with this line of thinking???

 Thunderstorms occur when clouds are low, dark, and dense.  Currently, the clouds are low, dark, and dense.  It probably will rain. INDUCTIVE REASONING

 A chicken sees a farmer every morning and is subsequently given a handful of feed.  This “philosophical” chicken inductively greets the farmer every morning, expecting food.  Until the day the farmer snaps its neck. CONSIDER THIS INDUCTIVE LOGIC…

From specific To vague INDUCTIVE REASONING

 is one in which the premises are supposed to support the conclusion.  If the premises are true, it is unlikely that the conclusion is false.  The conclusion probably follows from the premises.  Premise  Socrates was Greek.  Premise  Most Greeks eat fish.  Conclusion  Socrates ate fish.  Even if both premises are true, it is still possible for the conclusion to be false (maybe Socrates was allergic to fish).  Words which tend to mark an argument as inductive include probably, likely, possibly and reasonably. AN INDUCTIVE ARGUMENT

A INDUCTIVE ARGUMENT True Premise True Premise Probably True Conclusion

 Example:  January has been cold here in Siberia. Today is January 14, so it is going to be another cold day in Siberia. INDUCTIVE REASONING

 Simply put, the “problem of inductive logic is that we begin drawing general conclusions from specific observations.  My friend had terrible service a Red Knapp’s yesterday (SO), therefor Red Knapp’s is a bad restaurant (GC).  All the 9/11 hijackers were Muslim (SO), therefor all Muslims are terrorists (GC).  Sadly, most of what a developing child learns about the world comes from inductive logic. PROBLEM OF INDUCTION

More to come… Got it? Good! Time for a quiz! Good Luck!! PROBLEM OF INDUCTION