About deduction



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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?
• What is the probability that the premises correspond with our perceived reality?
• Is the logical structure of the arguments really strict logical?
• In case premises together with strict logic are not able to demonstrate the quality of the structure, are the consequences in accordance with our perceived reality?



Definition of deduction

Deductive arguments concerning our perceived reality
create relations between observation results

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:


"Cogito, ergo sum" -

"I think, therefore I am"

The phrase contains the observations "I", "to think" and "to be".

A logically improved phrase is:

  Something that I experience like "I" experiences that it "thinks",
therefore what I experience like "I" has an experience that
it does, what I from experience know as "being".

Without references to observations, the phrase becomes meaningless.

Correct pure deduction

A strict deductive statement becomes meaningless without reference to observations:


"klombumba" equals "klombumba"

We do not know whether the tautology states that "nothing equals nothing",
"something equals something" or "1 equals 1".


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.



A statement

Albert Einstein:


Pure logical thinking can give us no knowledge whatsoever of the world of experience; all knowledge about reality begins with experience and terminates in it.

Conclusions obtained by purely rational processes are, so far as Reality is concerned, entirely empty.

But if experience is the beginning and end of all our knowledge about reality, what role is there left for reason in science?

A complete system of theoretical physics consists of concepts and basic laws to interrelate those concepts and of consequences to be derived by logical deduction.

It is these consequences to which our particular experiences are to correspond, and it is the logical derivation of them which in a purely theoretical work occupies by for the greater part of the book.

Einstein A., Philosophy of Science 1 (1934) 163


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