PHL245H5 Lecture 1: PHL247 notes
PHL247
LECTURE ONE:
Reasoning versus mere thinking
• When we think we can – if we choose – merely let thoughts come to us in a relatively
ado ode eg. I hug. M shoe is tight. That sue looks good.
• When we reason we make inferences from premises to conclusions eg. I hug.
When people are hungry they should eat. I should eat).
• Only statements can serve as premises
• Statements can be true or false
• Arguments reason from premises to conclusions by means of inference
INFERENCE
• 1. Amy has three children
• 2. All people who have three children are excellent mothers
• 3. Therefore Amy is an excellent mother
• This is a aguet i the tehial sese ot a fight
• We are inferring 3 (the conclusion) from 1 and 2 (the premises)
• The premises and the conclusion are all statements
• Signs of inference include words like thus, therefore, as a result, consequently…
• The conclusion doesnt always come at the end of an argument – and may even be
merely implied rather than explicitly stated
Deductive and inductive arguments
• Deductive arguments deal in absolutes. Example: All cats are animals. All animals are
living beings. Therefore a cat is a living being.
• Inductive arguments deal with degrees of probability. Example: Most cats have four
legs. Morris is a cat. Therefore Morris probably has four legs.
Deductive arguments can be valid or invalid – But they are absolute (Not a matter of degree)
• EXAMPLE OF AN INVALID DEDUCTIVE ARGUMENT
• All students are either under twenty five or over twenty five
• Students under twenty five are young
• Sonya is twenty six
• Therefore Sonya is not a student
• IF the olusio as “oa is ot a oug studet this ould e alid
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Another invalid Deductive argument
• If you give me ten dollars, I will buy a burrito for lunch
• You didt gie e te dollas
• So I did not buy a burrito for lunch
• (Getting $10 from you was one way to guarantee I would buy a burrito for lunch, but
nothing says it was the only way. Maybe someone else gave me money or I already had
some).
A similar, but valid argument
• If you give me ten dollars, I will buy a burrito for lunch
• I did not buy a burrito for lunch
• Therefore you did not give me ten dollars
• (This is valid because the argument guaranteed that if you gave me ten dollars for lunch
the I ould u a uito, ad I didt
Invalidity – a taste of symbolic logic
• Denying the antecedent
• If P then Q (If you give him candy, he will be happy)
• Not P You dot gie hi ad
• Therefore not Q (Therefore he is not happy)
• Problem: He might be happy for some other reason (he is happy that Auston Matthews
has recovered from his concussion)
Invalidity - a bit more symbolic logic
• If P then Q
• Not Q
• Therefore P – If instead we said Therefore NOT P this would be valid
• If P then Q
• Not P
• Therefore not Q
• You ould hae Q ee if P does ot otai, ou just at hae oth P ad ot Q
Validity is a type of logical strength
• When a deductive argument is logically strong it is VALID
• This does not mean the conclusion is true
• It only means that IF the premises are true, then the conclusion MUST be true
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Deductive arguments can be valid and yet not sound
• 1. Amy has three children
• 2. All people who have three children are excellent mothers
• 3. Therefore Amy is an excellent mother
• THIS IS A VALID DEDUCTIVE ARGUMENT BUT IT IS NOT SOUND
• SOUNDNESS REQUIRES LOGICAL VALIDITY PLUS TRUE PREMISES
Deduction, Validity and Soundness
• 1. Amy has three children
• 2. All people who have three children are excellent mothers
• 3. Therefore Amy is an excellent mother
• The argument is valid because the premises, if true, guarantee the truth of the
conclusion.
• The premise that all people who have three children are excellent mothers is false.
Some people who have three children are not mothers at all (but fathers) and some
women who have three children are not even adequate mothers
• Since a premise is false the argument is not sound
Arguments that are not sound can still have true conclusions
• All professors love chocolate
• Amy is a professor
• Amy loves chocolate
• The argument is valid (so logically strong that this is a DEDUCTIVE argument in which the
conclusion is guaranteed to be true if the premises are true). However the premises are
false (there are some professors who do not love chocolate) so it is not SOUND
• Even though it is not a sound argument, the conclusion still happens to be true
Deductive arguments are valid or invalid but for inductive arguments logical strength comes
in degrees
• For deductive arguments, that deal with absolute assertions, they are either completely
logically strong (valid) or completely not (invalid)
• Inductive arguments, that deal with degrees (most, many, probably…), logical strength
comes in degrees
An inductive argument with some logical strength
• 1. Amy knows a lot of professors
• 2. Most of those professors are professors of philosophy
• 3. Amy knows Professor Raffman
• 4. Professor Raffman is a philosophy professor
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Document Summary
Reasoning versus mere thinking: when we think we can if we choose merely let thoughts come to us in a relatively (cid:396)a(cid:374)do(cid:373) o(cid:396)de(cid:396) (cid:894)eg. i(cid:859)(cid:373) hu(cid:374)g(cid:396)(cid:455). That su(cid:396)e looks good(cid:895): when we reason we make inferences from premises to conclusions (cid:894)eg. i(cid:859)(cid:373) hu(cid:374)g(cid:396)(cid:455). I should eat): only statements can serve as premises, statements can be true or false, arguments reason from premises to conclusions by means of inference. Deductive and inductive arguments: deductive arguments deal in absolutes. Maybe someone else gave me money or i already had some). If you give me ten dollars, i will buy a burrito for lunch. Invalidity a taste of symbolic logic: denying the antecedent. Validity is a type of logical strength: when a deductive argument is logically strong it is valid, this does not mean the conclusion is true. It only means that if the premises are true, then the conclusion must be true. Deductive arguments can be valid and yet not sound: 1.
