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KCard : Argumentation
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Syllogism
A syllogism is a construction where some premises
(usually shared by all and accepted to be true) are used to introduce a
conclusion (which is new for the listeners). There is normally a logical link between the premises
and the conclusion, like in this example:
This example is in the standard from A-B and B-C so
A-C. There are precise rules which must be respected for
a syllogism to be valid. These rules can be found in the literature. If a
rule is transgressed then it becomes a sophism. Sophism
A sophism is a syllogism which isn't valid. This
means that it looks true but it isn't, more precisely, the structure is right
but the content of the premises is false. This isn't always easy to notice,
like the following example which is obviously false but it takes a little
thinking to find where the error actually is:
This example follows the structure A-B and C-A so
C-B (if premises 1 and 2 were inverted it would have the structure A-B and
B-C so A-C and nothing would be changed, it would still be false). When the objects are simple and well known (like
above) it is easy to spot that there is a fallacy and then if necessary
locate it (which even in the simple example above isn't so simple). But
imagine when more complex matters are at play (like in politics with terms
such as 'global economy', 'unemployment', 'delocalisation',
...) how difficult it can be to detect these constructs. Many books explore the mechanism of syllogism and
sophism and provide guidance towards the rules which must be respected by a
syllogism or can be transgressed by a sophism. When complex matters are
involved in the construct it can be helpful to have some knowledge of these
formal rules to help identify valid and invalid cases. Induction
Induction is the process of extrapolating some
examples to obtain a general rule/theory. This is sometimes similar to
generalisation which is probably one of the most basic and common cognitive
processes used for learning. An important comment is that it seems this process
can in fact lead to errors, here is an example, try
to answer the following question 'quickly' before reading the answer: a hiker
leaves from the valley at 8:00 and arrives at the top of the mountain at
17:00. Next day he goes back down and leaves at 08:30 and arrives at 15:00 (of
course he goes faster down than up). Question: is it possible that there be a
specific time at which the hiker was at exactly the same location on both
days? Think about it before reading on. Most people give
the bad reply because they implicitly use induction to find the answer. They
think of a few specific times (usually near the ends and around the middle)
and evaluate that at these times the hiker isn't at the same locations on the
two days. These few specific times are then extrapolated/generalised
(induction mechanism) to conclude that the assertion is never true. With in depth thinking most people do however find
the correct answer (graphing the problem on a time-position diagram gives the
correct answer explicitly, that is, yes, there has to be a time at which on
both days the hiker is at exactly the same location), in particular people
used to scientific thinking shouldn't fall for this example (but following
our experience they do). However, once again (as in the sophism example), the
example above uses very simple and common concepts making reflection simple.
Imagine how this can lead to confusing with complicated concepts (see sophism
examples). Deduction
Deduction unlike induction is based on logical
inferences to conclude a rule/theory from some premises. See above
'syllogism' and 'sophism' which are examples of this. Topics
See the 'topics KCard. Other techniques
See the 'arguments' KCard. |
Ideas to develop
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