Deductive reasoning in philosophy
Some philosophers, e.g. René Descartes, Immanuel Kant and Karl Popper, have claimed that they created a rational structure of theories, a structure that is based on deductive arguments only. A fallacy by them all is in their basis: The premises in every deductive argument about our perceived world are always based on probability arguments.
At least four important questions can be raised when dealing with "deductive" theory structures:
• How many observations (premises) is the philosopher lending against?
Definition of deduction
The definition is in accordance with David Hume's term "Relations of Ideas", a part of "Hume's fork" (Enquiry, Selby-Bigge 1902 p. 25).
With the term "ideas" Hume means memories and fantasies created by perceptions
Deductive "knowledge" about our world cannot be shown to exist
Sometimes philosophers erroneously claim that deduction about the world exists, that we can figure out things and create "true" statements about our perceived reality without references to observations. This was called synthetic a priori "knowledge" by Immanuel Kant.
Examples below show that pure deduction about our world seems to be non-existent, not even when performed as pure tautologies.
Example of "deduction"
A well known attempt to deduction was expressed by René Descartes:
The phrase contains the observations "I", "to think" and "to be".
A logically improved phrase is:
Without references to observations, the phrase becomes meaningless.
Correct pure deduction
A strict deductive statement becomes meaningless without reference to observations:
We do not know whether the tautology states that "nothing equals nothing",
Mathematical models as example of deduction
Mathematics and geometry may serve as examples of deduction, provided experiences from numbers, forms, equalities and inequalities that are based on observations are supposed to be given as premises. The strict logic is a characteristic of mathematical calculations.
Calculations concerning our perceived reality, e.g. quantum mechanics, relativity and statistical thermodynamics, are within philosophy sometimes believed to be purely deductive constructions.
The person that performed the calculations are however aware of that their value are determined by the correspondence between the premises and observations, or how well the consequences of the calculations agree with our perceived reality.