Intro to T of K 12: Conclusion and Paradoxes
Over the last 3 months we’ve been looking at knowledge:
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Value: intrinsic/instrumental
Definition: ability/propositional/JTB/Gettier
Structure: foundationalism/coherentism; rationalism/empiricism (innate)
We considered several problems for a theory of knowledge:
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Perception
Miracles
Induction
Scepticism
We ended by looking briefly at truth and relativism, and asking why we care about
knowledge. Pritchard argues that we care because we care about authenticity,1 and
ends his book with these words:
We care about knowledge because knowledge is crucial to a worthwhile,
valuable life. The questions of epistemology may be abstract, but their
importance to our lives is vital. Pritchard p159
For example: moral questions.
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Is morality objective?
What are human rights?
Are any values universal?
(These are actually metaphysical questions, but there are epistemological
equivalents – at this point epistemology and metaphysics tie closely together.)
Question for further thought – what is the value of philosophy?
eudaimonia. A topical question given the current funding climate.
Aristotle and
Peter Cave suggests in the preface to his book What’s Wrong With Eating People?
that every discussion we have contains some philosophical assumptions, and that
part of the goal of philosophy can be to disentangle these and to clarify our thought,
and this echoes Wittgenstein:
What is your aim in philosophy? – To show the fly the way out of the fly-bottle.
—Ludwig Wittgenstein, Philosophical Investigations, 309
Why do we want to do this?
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As an aside, this has Heideggerian echoes: “Dasein is ontically distinguished by the fact that, in its very Being,
that Being is an issue for it” (Being and Time 4: 32) http://plato.stanford.edu/entries/heidegger/ See also
here: http://en.wikipedia.org/wiki/Dasein
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Existentialism/pragmatism: in order to help us to lead a meaningful life.
Heidegger/Sartre for the former. William James/Peirce for the latter, also see
references here:
http://plato.stanford.edu/entries/pragmatism/#ColPapClaConPra
Analytic philosophy: knowledge for knowledge’s sake.
See here:
http://plato.stanford.edu/entries/analysis/
Maybe this is a matter of temperament, maybe both types of person are needed (cf
pure mathematicians and engineers).
Cave also suggests that “philosophy opens eyes; philosophy opens ‘I’s’.” (pp x-xi).
He compares our everyday lives to those of sleepwalkers, and this is reminiscent of
Heraclitus:
Though this Word is true evermore, yet men are as unable to understand it
when they hear it for the first time as before they have heard it at all. For,
though all things come to pass in accordance with this Word, men seem as if
they had no experience of them, when they make trial of words and deeds
such as I set forth, dividing each thing according to its kind and showing how
it is what it is. But other men know not what they are doing when awake, even
as they forget what they do in sleep. Heraclitus DK B1
http://www.heraclitusfragments.com/B1/index.html2
Philosophy can exercise our minds, and awaken them. It can also alert us to the
scary thought that maybe not all questions have answers (Wittgenstein makes a
remark somewhere about the real philosophical answer being the one that gives him
peace).
Tonight what I want to do is to end up by looking at some puzzles and paradoxes
from philosophy. There’s a multitude of sites dedicated to paradoxes on the internet,
some of which I have provided links to. Here’s a quote from one of them:
Logic is a powerful tool; it can be used to discern and to discover truth.
Sometimes, though, this tool falls into the hands of those who would abuse it.
Armed with the laws of logic and a few simple, plausible, and apparently
harmless assumptions, philosophers can construct proofs of the most absurd
conclusions. These proofs can give us pause; should we believe the
unbelievable? This is the power of a paradox.
The most interesting philosophical arguments are those that proceed from
undeniable premises, via inescapable logic, to incredible conclusions. When
philosophy proves what is plausible it is mundane; it is only when philosophy
appears to prove what is incredible that things really get interesting.
http://www.logicalparadoxes.info/
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"Blessed are the sleepy ones: for they shall soon fall off." Nietzsche Thus Spoke Zarathustra
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Though I am not sure I agree entirely with this sentiment – connected with this is my
dislike of some thought experiments. Maybe I am showing my bias towards
existentialism/pragmatism in wanting philosophy to be somehow connected with
“real” life.
Classical Logical Paradoxes
The four main paradoxes attributed to Eubulides, who lived in the fourth century BC,
were “The Liar,” “The Hooded Man,” “The Heap,” and “The Horned Man”
http://www.iep.utm.edu/par-log/
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Liar: self-reference
Horned man: “when did you stop beating your wife?
Heap: Sorites paradox (vagueness)
Hooded Man: epistemic
Zeno’s paradoxes: http://www.logicalparadoxes.info/
The Arrow/Achilles and the Tortoise: infinity
Other paradoxes
Theseus’s ship: identity (also cf Only Fools and Horses and Terry Pratchett, who
have both used this joke).
The paradox of the stone: omnipotence
The unexpected hanging
The Barber: set theory
Catch-22
There was only one catch and that was Catch-22, which specified that concern for
one's own safety in the face of dangers that were real and immediate was the
process of a rational mind. Orr was crazy and could be grounded. All he had to do
was ask; and as soon as he did, he would no longer be crazy and would have to fly
more missions. Orr would be crazy to fly more missions and sane if he didn't, but if
he was sane he had to fly them. If he flew them he was crazy and didn't have to; but
if he didn't want to he was sane and had to.
The paradox of the court
The Paradox of the Court is a very old problem in logic stemming from ancient
Greece. It is said that the famous sophist Protagoras took on a pupil, Euathlus, on
the understanding that the student pay Protagoras for his instruction after he had
won his first case (in some versions: if and only if Euathlus wins his first court case).
Some accounts claim that Protagoras demanded his money as soon as Euathlus
completed his education; others say that Protagoras waited until it was obvious that
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Euathlus was making no effort to take on clients and still others assert that Euathlus
made a genuine attempt but that no clients ever came. In any case, Protagoras
decided to sue Euathlus for the amount owed.
Protagoras argued that if he won the case he would be paid his money. If Euathlus
won the case, Protagoras would still be paid according to the original contract,
because Euathlus would have won his first case.
Euathlus, however, claimed that if he won then by the court’s decision he would not
have to pay Protagoras. If on the other hand Protagoras won then Euathlus would
still not have won a case and therefore not be obliged to pay. The question is: which
of the two men is in the right? http://listverse.com/2010/05/28/11-brain-twistingparadoxes/
Categories of paradoxes
W. V. Quine (1962) distinguished between three classes of paradoxes:
A veridical paradox produces a result that appears absurd but is demonstrated to
be true nevertheless. Thus, the paradox of Frederic's birthday in The Pirates of
Penzance establishes the surprising fact that a twenty-one-year-old would have had
only five birthdays, if he was born on a leap day. Likewise, Arrow's impossibility
theorem demonstrates difficulties in mapping voting results to the will of the people.
The Monty Hall paradox demonstrates that a decision which has an intuitive 50-50
chance in fact is heavily biased towards making a decision which, given the intuitive
conclusion, the player would be unlikely to make.
A falsidical paradox establishes a result that not only appears false but actually is
false due to a fallacy in the demonstration. The various invalid mathematical proofs
(e.g., that 1 = 2) are classic examples, generally relying on a hidden division by zero.
Another example is the inductive form of the horse paradox, falsely generalizes from
true specific statements.
A paradox which is in neither class may be an antinomy, which reaches a selfcontradictory result by properly applying accepted ways of reasoning. For example,
the Grelling–Nelson paradox points out genuine problems in our understanding of
the ideas of truth and description.
A fourth kind has sometimes been described since Quine's work.
A paradox which is both true and false at the same time in the same sense is called
a dialetheism. In Western logics it is often assumed, following Aristotle, that no
dialetheia exist, but they are sometimes accepted in Eastern traditions[which?] and
in paraconsistent logics. An example might be to affirm or deny the statement "John
is in the room" when John is standing precisely halfway through the doorway. It is
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reasonable (by human thinking) to both affirm and deny it ("well, he is, but he isn't"),
and it is also reasonable to say that he is neither ("he's halfway in the room, which is
neither in nor out"), despite the fact that the statement is to be exclusively proven or
disproven. http://en.wikipedia.org/wiki/Paradox
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