Propositions Mathematics and logic are obviously closely related.
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Transcript of Propositions Mathematics and logic are obviously closely related.
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Propositions
Mathematics and logic are obviously closely
related
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Proposition……..any statement that can be asserted or denied (i.e. said to be true
or false)
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Examples of propositions
Snow is white
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Examples of propositions
Liquid nitrogen is very cold.
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Examples of propositions
Pigs have wings
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Examples of propositions
Polish men are very sensitive and understanding
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IB students are not very enthusiastic
Examples of propositions
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4 kinds of propositions
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1. Analytic propositions (2 types)
Propositions that can be shown to be true just by analyzing (thinking about) them.
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1. Analytic propositions - 2 types
Definitional truths;
All bachelors
are unmarried men
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1. Analytic propositions – 2 types
Truths of reason; If Eerik is taller than Rami, and Rami is taller than Bartosz, Eerik must be taller than Bartosz
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2. Empirical Propositions
Their truth can be determined by appeal to evidence based on perception
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2. Empirical Propositions
Pandas eat bamboo
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2. Empirical Propositions
Smoking can damage your health
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2. Empirical Propositions
Hitler was a woman
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3. Value judgments
A statement that contains a value word such as “good”, “bad”, “right”, “wrong”, “beautiful”, “ugly”……..
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3. Value judgments
Harder to establish the truth as two people may have different values
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3. Value judgments
Kirsten Dunst is beautiful
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3. Value judgments
Mr Porter is the World’s best TOK teacher
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3. Value judgments
Rap isn’t good music
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4. Metaphysical propositions
Neither analytic, empirical nor value judgment. This leaves statements about the nature of ultimate reality
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4. Metaphysical propositions
God exists
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4. Metaphysical propositions
Free will is an illusion
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4. Metaphysical propositions
The past does not exist
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Importance of knowing which type of proposition
Because all 4 types can be justified in different ways, it is important to know which type of proposition we are dealing with when looking at a knowledge claim
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State whether the following propositions are analytic,
empirical, value judgment or metaphysical
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God is the creator of all things
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Mozart was a great composer
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Bananas are yellow
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Smith is a courageous man
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Napoleon was defeated at Waterloo in 1815
YouTube - Duel and duelality part2
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You ought to eat more cabbage
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Every event has a cause
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A straight line is the shortest distance between two points
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Vedran said that a telescope has two lenses
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All mass murders are insane
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It’s not that simple!
In “real life” there are grey areas and complications
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Factual/verbal disputes
Analytical/empirical propositions
What looks like a factual dispute can sometimes become a verbal dispute about the meaning of words
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John is bald
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Abortion is murder
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Nelson Mandela is a terrorist
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Nominal Fallacy
Assuming we have explained something just because we have named it
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Nominal Fallacy
“Why is iron attracted to a magnet?”
“Because iron is magnetic”
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Nominal Fallacy
“Why are there many tribal wars in Papua New Guinea?”
“The people there are very aggressive”
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Nominal Fallacy
“Why is lead heavy”
“Because it is very dense”
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Nominal fallacy
Try to spot the nominal fallacies in the following;
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Nominal Fallacy?
“What caused the baby’s death”
“Sudden Infant Death Syndrome”
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Nominal Fallacy?
“Why did the water pipes burst?”
“Because the temperature fell below zero(freezing), and when water freezes it expands”
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Nominal Fallacy?
“What caused the earthquake”
“A sudden movement of rocks beneath the earth’s surface”
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Nominal Fallacy?
“What caused the earthquake?”
“It was an act of God”
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Nominal Fallacy?
“Why does sugar dissolve in water?”
“Because it is soluble”
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Nominal Fallacy?
“Why did the apple fall to the ground?”
“Because of gravity”
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Nominal Fallacy?
“Why did the apple fall to the ground?”
“Because of gravity”
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Nominal Fallacy?
“Why did Peter Sutcliffe murder 13 people”
“Because he is insane”
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Nominal Fallacy?
“Why did the stock market fall yesterday?”
“Because of a technical adjustment and profit-taking by investors”
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Nominal Fallacy?
“Why did he win the lottery?”
“Because he is a lucky person”
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Empirical propositions and value judgements
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Empirical propositions and value judgements
Many words have positive and negative connotations that can blur the distinction between a fact and a value
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Connotations
Blair is a murderer
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Connotations
Cristina is a spinster
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Connotations
Albert is brainy
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Connotations
Can you think of some propositions of your own in which an empirical proposition is turned into a value judgement by a connotation?
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Relevant facts
Some empirical facts may be relevant to the justification of value judgements
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Relevant facts
Gary is a bad man
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Relevant facts
Tiger is a good golfer
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Relevant facts
The British School is a good school
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Empirical propositions and metaphysics
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Empirical propositions and metaphysics
Some empirical facts may be relevant to the justification of our metaphysical beliefs
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Empirical propositions and metaphysics
God created the universe in six days about 6000 years ago.
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Push hard enough!
If you push an empirical proposition hard enough, it collapses into a metaphysical one.
Empirical proposition
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Push hard enough!
If you push an empirical proposition hard enough, it collapses into a metaphysical one.
Metaphysical proposition
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Push hard enough!I know that my car is parked outside
But how can you be sure you are not
dreaming?
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Push hard enough!I know that all
metals expand when heated.
But how can you be sure the laws
of physics will hold tomorrow
?
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Push hard enough!
I know that World War 2 started in
1939
But how can you be
sure the past really
exists?
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Fortunately we have seen that you
don’t need complete certainty to say you “know”
something!