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logic. THE SCIENCE OF REASONING. What is logic?. Logic is the Study of the principles and concepts of good reasoning . Yes, there is such a thing as bad reasoning . Logicians are not interested in why people reason the way they do.
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logic THE SCIENCE OF REASONING
What is logic? • Logic is the Study of the principles and concepts of good reasoning. • Yes, there is such a thing as bad reasoning. • Logicians are not interested in why people reason the way they do. • Logicians are interested in the principles of reasoning.
Any sentence has a Subject and a Predicate. • A simple subject-predicate sentence can be either universal: ‘All bachelors are unmarried men’ or particular: ‘My house is small’
A sentence is Analytic if, and only if, the predicate concept is “contained in” the subject concept. • For example: • ‘All triangles are three-sided figures’ • SUBJECT: Triangles • PREDICATE: Three-sided figures • Triangles are defined as three-sided figures
Another example: • ‘All objects occupy space’ • Objects are defined as things that occupy space • The predicate concept ‘occupying space’ is contained in the subject concept ‘object’ • Philosophers call these statements ‘tautologies’ • Tautologies are empty truths like ‘A = A’ or ‘Plato is either Greek or he is not Greek’ or ‘A rose is a rose’
A judgment is synthetic if and only if it is not analytic. (Duh!) • Or, a judgment is synthetic just when the predicate concept is not contained in the subject concept. • For example: • ‘All bachelors are tall’ • SUBJECT: Bachelors • PREDICATE: Tall • Here the predicate concept is not contained in the subject concept • Being tall does not mean being a bachelor and vice versa
Synthetic! • ‘New York City in the winter is lovely’ ‘The Sun will rise tomorrow’ Synthetic
Consider these two statements: • ‘All bachelors are unmarried’ • ‘Some bachelors are happy’ • While we know both to be true, how we know differs.
‘All bachelors are unmarried’ • How do you know that all bachelors are unmarried?
A judgment is a priori if it can be known independently of experience: • If I tell you that I have a triangle in my pocket, you know it has three sides without the need to see it. • True in all possible worlds(?)
‘Some bachelors are happy’ • How do you know this?
Definition of ‘bachelor’ does not include the concept of happiness. • Bachelor: ‘A man who is not and has never been married.’ (Merriam-Webster) • How do you know? Through experience
There are prime numbers larger than Graham’s number1. 1. Graham's number is bigger than the number of atoms in the observable Universe, which is estimated to be 1082.
The shortest distance between two points is a straight line.
Hitting a billiard ball with a cue stick makes the ball move onto the table.
Great Job! Now, let’s discuss arguments
ARGUMENT DEFINITION • A group of statements in support of a conclusion. A paper, A Speech, A book, An article, An oral presentation, can be arguments. But to be arguments they require a conclusion. Conclusion: the main point or thesis.
Good argument • A Good argument has • True premises. • And a conclusion that follows from the premises eithernecessarily or probably. NECESSARILY and PROBABLY imply 2 different ways to argue.
The 2 ways are 1. DEDUCTION2. INDUCTION If the conclusion follows necessarily, the argument is DEDUCTIVE. If it follows probably, it is INDUCTIVE. • If you are in Brooklyn, you are in the US. • You are in Brooklyn. • It follows that… How does it follow? You are in the US
DEDUCTIVE means that given the premises, the conclusion either follows necessarilyor it doesn’t follow at all—all or nothing! • Given the premises, if the conclusion does follow necessarily, a deductive argument is called is VALID. • Given the premises, if the conclusion does not follow at all, a deductive argument is called INVALID.
Note that an argument can be deductively VALID, even if it contains one or more false premises. For example: • If you live in Brooklyn you are in South America. • You live in Brooklyn. • Therefore, you are in South America. • In this case we call the argument UNSOUND.
A Valid ARGUMENT that has ALL TRUE PREMISES is called sound • All physical objects occupy space. • My book is a physical object. • Therefore, my book occupies space.
What if the conclusion does not fallow at all?Then the argument is invalidfor example: • If you leave your car out on the street and it rains, your car get wet. • Your car is wet. • It follows that it rained.
Careful!An argument can be invalid even if it contains all true premises. • To be president of the US one must be 35 or older. • Trump is older than 35. • Therefore, Trump is the president of the US.
Often arguments are intended to support the conclusion with a matter of probability: • Every time I come to your house, your cat rubs against me. • I’m coming to your house later today. • Therefore, your cat will rub against me. • Here the premises are not meant to support the conclusion necessarily. • Given the premises, conclusion does not follow necessarily. • Does it not follow at all? No! • So how does it follow? • It follows probably.
INDUCTION • Given the premises, an argument is called INDUCTIVE just if the conclusion follows probably. There are three kinds of inductive arguments: • Inductive Generalizations. • Arguments from Analogy. • Causal Arguments.
1. INDUCTIVE GENERALIZATION • To move from a sample to a general conclusion about a population. • This desk is brown. • That desk is brown. • Therefore, all desks are brown.
2. ARGUMENTS FROMANALOGY • Using an analogy between two or more things (also people, events, etc.) in order to support a conclusion about one of them. • This book is boring. • That book has the same author and same plot. • Therefore, that book must also be boring. • Earth has oxygen. • Planets that have oxygen might have life. • Europa has oxygen. • Therefore, there might be life on Europa.
