Term
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Definition
| Statements that cannot possibly be true. e.g. p & -p, 1=0 |
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Term
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Definition
| Statements that are always true. e.g. p or –p, 1+1=2 |
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Term
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Definition
| Statements that may or may not be true depending on how the world actually is. E.g. p, p --> q,…. |
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Term
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Definition
| An argument is deductively valid if and only if it is (logically) impossible that its conclusion is false while its premises are true. |
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Term
All flurgs are turvy
This is a flurg
--
This is turvy |
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Definition
| valid purely in virtue of form |
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Term
Papa Smurf if blue
--
Papa Smurf is coloured |
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Definition
| valid in virtue of their content (as well as their form) |
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Term
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Definition
| An argument is inductively strong if and only if it is improbable that its conclusions are false given that its premises are true (and it is not deductively valid). |
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Term
The moon is square
--
Therefore the moon has four corners. |
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Definition
| Unjustified premise - Justification requires good reasoning and justified premises |
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Term
The moon is round
--
Therefore the moon is white |
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Definition
| Bad reasoning – the conclusion can be false while the premise(s) are true |
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Term
If P then Q
P
--
Therefore Q |
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Definition
Valid.
Conditional Arguments - Affirming the antecedent |
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Term
If P then Q
Q
--
Therefore P |
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Definition
Invalid.
Conditional Arguments - Affirming the consequent |
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Term
If P then Q
-P
--
Therefore Q |
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Definition
Invalid.
Conditional Arguments - Denying the antecedent |
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Term
If P then Q
-Q
--
Therefore -P |
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Definition
Valid.
Conditional Arguments - Denying the consequent |
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Term
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Definition
| There is no good reason to think that the past will resemble the future. |
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Term
| Responses to the Problem of Induction |
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Definition
1. Circular reasoning is okay.
2. Using induction is part of the meaning of ‘rational’.
3. Pragmatic vindication – if anything will work, induction will.
4. We don’t need induction, just falsification (Popper). |
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Term
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Definition
| A hypothesis designed to fit a piece of data. |
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Term
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Definition
| A (non-analytic) sentence is meaningful if only if there is a procedure that would determine whether it is true or false. |
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Term
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Definition
| Science proceeds not by confirming theories, but by falsifying them. |
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Term
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Definition
| A theory is scientific if and only if it is falsifiable. |
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Term
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Definition
| A sentence is scientific if and only if it is testable. |
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Term
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Definition
| The degrees of belief of actual agents. |
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Term
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Definition
| the degrees of belief that an agent ought to have. |
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Term
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Definition
| the probability of an attribute A in a finite reference class B is the relative frequency of actual occurrences of A within B. |
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Term
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Definition
| Probability is propensity / disposition / tendency of a certain experimental setup to produce a certain result. |
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Term
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Definition
| If A and B are mutually exclusive, then P(A or B) = P(A) + P(B) |
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Term
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Definition
| P(A or B) = P(A) + P(B) – P(A and B) |
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Term
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Definition
If A and B are not correlated, then P(A and B) = P(A) * P(B).
--
P(A and B) = P(A|B) * P(B)
--
P(B|A) = P(A and B) / P(A) |
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Term
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Definition
| A is correlated with B if and only if the proportion of A among those with B is greater than the proportion of A among those without B. |
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Term
confidence interval for the frequency of the value in the population:
Sample size of 250.
f(R) = 0.56 |
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Definition
The margin of error for 250 is +- 0.06, so:
P(R) = 0.56 +-0.06 |
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Term
| 60-70% of the red marbles in the population are large, which doesn’t overlap with the 25-35% of the non-red marbles in the population are large |
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Definition
| evidence for a correlation in the population |
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Term
| Causation - Constant conjunction |
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Definition
| A causes B = Events of type A are constantly conjoined with events of type B. |
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Term
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Definition
Where A and B are actual events,
A causes B = If A were not to occur, then B would not occur = In the closest world in which not A, not B |
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