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:
- John is a human (premise 1)
- Humans breath (premise 2)
- John breaths (conclusion)
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.
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:
- Rare things are expensive (premise 1)
- A cheap Ferrari is rare (premise 2)
- A cheap Ferrari is expensive (conclusion)
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 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 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.
See the 'topics KCard.
See the 'arguments' KCard.