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induction, deduction
deduction
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About deduction

Return to "Theory of knowledge"

 
 

Some philosophers, e.g. René Descartes, Immanuel Kant and Karl Popper, have claimed that they created a rational structure of theories, a structure based on deductive arguments only. They have all made a mistake in their basic assumptions: They do not acknowledge that the premises in every deductive argument about our perceived world always ultimately are 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?

 
     

Deduction

 
 

Deductive arguments concerning our perceived reality create relations between perceptions or between inferences that ultimately are based on perceptions

 
 

The definition above 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 purely deductive arguments about the world are meaningful, that we can figure out things about our world without references to perceptions. Such arguments would, it they existed, represent "absolute knowledge", or what Immanuel Kant called synthetic a priori arguments.

Examples below show that pure deductive arguments about our world do not seem to exist, not even when expressed as pure tautologies.

 
     
 

A well-known claimed deduction was expressed by René Descartes:

 
 

"Cogito, ergo sum"
"I think, therefore I am"

 
 

The phrase contains the terms "I", "to think" and "to be" that ultimately are based on perceptions. By reformulating the phrase, it's real foundation becomes clear.

 
 

A brain, that from many previous perceptions has created an experience of a unity termed "I" is now reached by an additional perception that is inferred as "thinking". This perception is added to many previous perceptions that together have created an experience of "being".

 
     
 

Correct pure deduction

 
 

A strict deductive statement becomes meaningless without reference to perceptions:

 
 

"klombumba" is identical with "klombumba"

 
 

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

As soon as we insert a worldly object or concept into the tautology it becomes i relation between perceptions:

 
 

"an apple" is identical with "an apple"

 
 

Two different meanings may be ascribed to this tautology - either a synthesis or a real tautology. The synthesis implies that the specific object that now results in a perception is similar to the group of objects, or is included in the "set", that we from previous comparisons and generalizations from perceptions has defined as an "apple".

The tautology should actually be expressed as:

 
 

"this apple" is right now identical with "this apple"

 
 

The tautology now implies that the object that results in a perception exists, but does not provide additional knowledge. The apple in question is not identical with the same apple at a later time and is not identical with any other apple.

 
     
     

Mathematical models as examples of deduction

 
 

Mathematics and geometry are sometimes seen as examples of pure deduction, but presumes that worldly concepts like numbers, forms, equalities and inequalities, all based on perceptions, are supposed given as premises. The relations between these perceptions may be developed using strict logic because e.g. the number "one" is perceived with such clarity that it may be exactly defined.

Calculations concerning our perceived reality, e.g. quantum mechanics, relativity and statistical thermodynamics, are sometimes within philosophy claimed to be purely deductive constructions. But the persons that perform such calculations are however aware of that their value is determined by the correspondence between the premises and perceptions, or how well the consequences of the calculations agree with our perceived reality.

 
   

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 (1934), Philosophy of Science 1, p.163
     

 

       
 

 

       
 

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