Knowledge. Concepts. Knowledge ( “ knowing that__ ” ) as justified true belief Truth value Belief Justification Counterexample Sorites Paradox Mathematical Induction. What ’ s the point of this discussion?. We confuse truth with notions like belief , knowledge and justification .
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x knows that P
Correspondence with reality
How do we know? We stipulate that this is how we’ll understand truth value! We idealize…
We agree that removing one grain of sand from a heap won’t make it stop being a heap…
n. Therefore, a one-grain collection is a heap [by 2, n - 1]
Mathematical induction is a method of mathematical proof typically used to establish that a given statement is true of all natural numbers. It is done by proving that the first statement in the infinite sequence of statements is true, and then proving that if any one statement in the infinite sequence of statements is true, then so is the next one.
A proof by mathematical induction consists of two steps:
The basis (base case): showing that the statement holds for a natural number, n, e.g. when n = 1
The induction step: showing that if the statement holds for some n, then the statement also holds when n + 1 is substituted for n.
This proves that the statement
holds for all values of n.
So the dominos all fall!
However the same form of argumentgives us the Sorites Paradox.
Basis: A 100,000 grain collection is a heap.
Induction step: If an k-grain collection is a heap then an (k - 1)-grain collection is a heap.
So all the dominoes fall…and there seems no way to avoid the conclusion that a one-grain collection is a heap!
What should we do???
We’ll ignore the Sorites in this class...So now for some easier problems.(For further discussion see http://plato.stanford.edu/entries/sorites-paradox/)
Sorites seeking to impale a wet philosopher on the Horns of a Dilemma
I like chocolate
I don’t likechocolate
For any utterance of a context-dependent sentence, there’s a context-independent sentence that makes the same statement.
But we still haven’t answered the Big Question
Reality(“the World,” the way things are)
Roses are red.
A propositional attitude
Believing doesn’t make it so!
The relation between propositions and reality is completely separate from the relation between persons and propositions!
People disagree. Who’s to say? No one knows.
…but it’s alright to be wrong!
Having good reasons for what you believe
Knowledge doesn’t require certainty
Justification is relative to personsJustification
I think,therefore I am
It is wrong always,everywhere and foreveryone to believe anythingon insufficient evidence.
W. K. Clifford
Is it ever rational for a person to believe believe anything for which he has no compelling evidential reasons?
To be continued…