« Text, more text, even more Text | Main | Acro is the Game »
March 22, 2005
Logic: Deductive and Inductive
I have never bothered to understand the fine line between inductive and deductive logic, but my physics and philosophy teachers forced me to reconsider… So what do official definitions say?
“Deductive logic = this refers to the application of general rules to specific cases. Begins with general statements and moves to the particulars. Inductive Logic = Examines the particulars or specifics in an attempt to develop generalization.”
However, this misses out paradoxes, probabilistic statements and specific cases. A better definition of the the two would be as follows: Deductive logic = you lose information, Inductive logic = you gain information. Part of the definition is that it dispels myths that deductive logic is somehow “better” than inductive logic. Read on for my analysis.
In deductive logic, you lose information. Deductive logic relies on the validity of its base propositions. Many claim that deductive logic arguments are the only ones “full-proof,” but this is only a red herring, for we are concerned with the truth and not with the validity of the argument. Deductive logic may be a localization of a well-established fact, but it can also be seen as a logical interpolation of two (or more) assertions into one. This itself is tricky process which may require typographical properties of logical quantifiers (and, or, for all) as well as jumps outside the system (which cannot be definitely explained in the system). It is not merely inductive logic in reverse, where the premises follow the conclusion.
In inductive logic, you gain information. You extrapolate the qualities of the particulars onto a more general subset of this universal. To do this, you make a leap forward, even in the case when you have a base object and an ordering schemata (such as mathematical induction), you may still suffer from ω-incompleteness (some may reject arguments based on indefinite existence, meaning a successive pyramid of true statements may not lead to a true statement in general, this gets much more complicated with unprovable statements from Gödelian incompleteness).
Another foundation of induction is Limit Theory, which states that objects tend to change little over little time. For instance, “if the sun rises today, most likely it will rise tomorrow”. In fact - it definitely will, for the “sun rising today” is not a specific event, meaning that the line between it happening and not happening is blurred (the famous the chicken and the egg paradox). But the two propositions are different, and perhaps even conflicting. One describes timeless attributes the other describes state-of-being. Yet (its arguable that) both are able to provide absolute certainty (or the same certainty) of knowing the truth as deductive logic.
Posted by Oleg Ivrii at March 22, 2005 12:13 PM
Comments
Ohh, logic is fun.
Some interesting points...
Mathmatical induction relies exclusively on deductive logic. You are using the name in an attempt to confuse people.
Your references to limit theory are also interesting, as (like Occam's razor) there is no good reason why it should be true. Logical minimalism and it's close cousin uni-directional information entropy are both red herrings themselves, and neither need be true. In fact, there is good reason to believe that both concepts are not provable one way or another. But then we are back to Gödelian incompleteness and we are stuck exactly where we started (or prehaps we have learned something in the process...) ;D
Posted by: Nicholas Engelking at March 23, 2005 02:46 AM
Not trying to confuse anyone here. I don't even want to make the separation between inductive and deductive logic in the first place. I classify the two not by the fundamental difference of ideas (there is none), but by the conclusions they produce.
Inductively, Limit Theory is true. I am extrapolating mathematics onto a real world system. However, there is no deductive way to prove inside the system, or to show the fallacy of the contrary.
Posted by: Oleg Ivrii ![[TypeKey Profile Page]](http://oleg.moltenstudios.com/blog/nav-commenters.gif)
at March 23, 2005 10:46 AM