Deductive and Inductive Logic - Revision history

Hannibal: /* Review: Categories vs A Continuum */

Hannibal — Sat, 06 Oct 2012 13:14:09 GMT

Review: Categories vs A Continuum

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	==Review: Categories vs A Continuum==		==Review: Categories vs A Continuum==

-	It was the great thinker Galileo who ~~recognized and further~~ explicated upon the limitations of Aristotle's categorical paradigm that were first noted by the Sophists~~, long ago~~: we can create abstract categories like squares, and set up deductive arguments that speak about equivalenceis between such categories, but categories have no real world correlate - we live in a changing world of impreciseness, where everything falls somewhere along a continuum. This is not to say that deduction has no use, after all, geometry also deals with categories like circles and squares, and is quite useful. It is only to say that while deductive arguments give us 'certain' conclusions, we cannot apply these certain conclusions to the real world without error.	+	It was the great thinker Galileo who explicated upon the limitations of Aristotle's categorical paradigm that were first noted by his contemporaries, the Sophists: we can create abstract categories like squares, and set up deductive arguments that speak about equivalenceis between such categories, but categories have no real world correlate - we live in a changing world of impreciseness, where everything falls somewhere along a continuum. This is not to say that deduction has no use, after all, geometry also deals with categories like circles and squares, and is quite useful. It is only to say that while deductive arguments give us 'certain' conclusions, we cannot apply these certain conclusions to the real world without error.

Hannibal at 20:54, 28 March 2010

Hannibal — Sun, 28 Mar 2010 20:54:31 GMT

←Older revision		Revision as of 20:54, 28 March 2010
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	</pre>		</pre>

-	We can call a deductive logical system an a priori system. This means that we can make up such a system without any observation or experimental examination.We can create a set of categories like squares or circles or letters, and a set of self ~~consitent~~ rules that follow a set of definitions, all without having to ever experience such "things".	+	We can call a deductive logical system an a priori system. This means that we can make up such a system without any observation or experimental examination.We can create a set of categories like squares or circles or letters, and a set of self consistent rules that follow a set of definitions, all without having to ever experience such "things".

-	http://~~candleinthedark~~.com/brain.gif Philosophers like to say that a "brain in vat" set apart from the rest of the universe could create an a priori system.	+	http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/brain.gif Philosophers like to say that a "brain in vat" set apart from the rest of the universe could create an a priori system.

	==Inductive Logic==		==Inductive Logic==
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	Inductive arguments are not like mathematical equations at all, they are akin to predictions - i.e. they are probable claims. They don't work with abstract entities like categories or definitions, they work with empirical claims from the physical world outside of our imaginations. The "real world" outside of our imaginations does not give us a set of abstract categories, it gives us a set of imprecise entities that exist along an imprecise continuum. For this reason, inductive arguments do not posses the certainty of deductive arguments. All inductive arguments are uncertain and open to questioning.		Inductive arguments are not like mathematical equations at all, they are akin to predictions - i.e. they are probable claims. They don't work with abstract entities like categories or definitions, they work with empirical claims from the physical world outside of our imaginations. The "real world" outside of our imaginations does not give us a set of abstract categories, it gives us a set of imprecise entities that exist along an imprecise continuum. For this reason, inductive arguments do not posses the certainty of deductive arguments. All inductive arguments are uncertain and open to questioning.

-	http://~~candleinthedark~~.com/zaius.jpg <br>	+
		+	http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/zaius.jpg <br>
	'''"Don't speak to me in absolutes, the evidence IS contestable!"'''<br>		'''"Don't speak to me in absolutes, the evidence IS contestable!"'''<br>
	(Dr Zaius to Cornelius, regarding archeological (inductive) evidence, in ''Planet of the Apes'' - one of the few instances where Hollywood's take on science was right on the money.)		(Dr Zaius to Cornelius, regarding archeological (inductive) evidence, in ''Planet of the Apes'' - one of the few instances where Hollywood's take on science was right on the money.)

Hannibal at 20:49, 28 March 2010

Hannibal — Sun, 28 Mar 2010 20:49:12 GMT

←Older revision		Revision as of 20:49, 28 March 2010
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	This syllogism works from a general rule: "all humans are mortal" to a specific conclusion: "Socrates is mortal". However, it is not necessary that deductive arguments move from general or universal statements, to specific or particular statements, for example, a deductive argument can work from particular premises, consider this disjunctive syllogism:		This syllogism works from a general rule: "all humans are mortal" to a specific conclusion: "Socrates is mortal". However, it is not necessary that deductive arguments move from general or universal statements, to specific or particular statements, for example, a deductive argument can work from particular premises, consider this disjunctive syllogism:
	<pre>		<pre>
-	If Socrates if human, then Socrates is mortal	+	If Socrates is a human, then Socrates is mortal
-	Socrates is human	+	Socrates is a human
	Therefore, Socrates is mortal		Therefore, Socrates is mortal
	</pre>		</pre>

Hannibal at 20:47, 28 March 2010

Hannibal — Sun, 28 Mar 2010 20:47:46 GMT

←Older revision		Revision as of 20:47, 28 March 2010
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	==Deductive Logic==		==Deductive Logic==

-	'''Deductive Logic''' is the method of non contradictory identification. It is based on the classical [[The Laws of Classical Logic\|axioms]] of Aristotelean logic. ''Deductive arguments'' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "~~premises~~" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].	+	'''Deductive Logic''' is the method of non contradictory identification. It is based on the classical [[The Laws of Classical Logic\|axioms]] of Aristotelean logic. ''Deductive arguments'' are akin to mathematical equations: they present a series of categories or definitions in a series of '''equivalencies'''. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premise" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].

	Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:		Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:

Hannibal: /* Review: Categories vs A Continuum */

Hannibal — Sat, 19 Apr 2008 18:33:16 GMT

Review: Categories vs A Continuum

←Older revision		Revision as of 18:33, 19 April 2008
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	==Review: Categories vs A Continuum==		==Review: Categories vs A Continuum==

-	It was the great thinker Galileo who recognized the limitations of Aristotle's categorical paradigm - we can create abstract categories like squares, and set up deductive arguments that speak about equivalenceis between such categories, but categories have no real world correlate - we live in a changing world of impreciseness, where everything falls somewhere along a continuum. This is not to say that deduction has no use, after all, geometry also deals with categories like circles and squares, and is quite useful. It is only to say that while deductive arguments give us 'certain' conclusions, we cannot apply these certain conclusions to the real world without error.	+	It was the great thinker Galileo who recognized and further explicated upon the limitations of Aristotle's categorical paradigm that were first noted by the Sophists, long ago: we can create abstract categories like squares, and set up deductive arguments that speak about equivalenceis between such categories, but categories have no real world correlate - we live in a changing world of impreciseness, where everything falls somewhere along a continuum. This is not to say that deduction has no use, after all, geometry also deals with categories like circles and squares, and is quite useful. It is only to say that while deductive arguments give us 'certain' conclusions, we cannot apply these certain conclusions to the real world without error.

Hannibal: /* Abduction */

Hannibal — Sun, 29 Jul 2007 20:49:28 GMT

Abduction

←Older revision		Revision as of 20:49, 29 July 2007
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	As a side note for later study (section to be added later), the logician Charles S. Peirce holds that we should also consider "abduction", which is defined as follows: "Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea" (Peirce, 1903:CP 5.171).		As a side note for later study (section to be added later), the logician Charles S. Peirce holds that we should also consider "abduction", which is defined as follows: "Abduction is the process of forming an explanatory hypothesis. It is the only logical operation which introduces any new idea" (Peirce, 1903:CP 5.171).

		+	http://www.uni-bielefeld.de/idm/personen/mhoffman/papers/abduction-logic.html

	==Review: Categories vs A Continuum==		==Review: Categories vs A Continuum==

Hannibal: /* References */

Hannibal — Sun, 29 Jul 2007 20:49:07 GMT

References

←Older revision		Revision as of 20:49, 29 July 2007
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	* Hurely, P. J. (2000) A Concise Introduction to Logic - 7th Edition		* Hurely, P. J. (2000) A Concise Introduction to Logic - 7th Edition
		+	* Pierce, C. S. (1903) P Collected Papers of Charles Sanders Peirce (Volumes I-VI, ed. by Charles Hartshorne and Paul Weiß, Volumes VII-VIII, ed. by Arthur W. Burks). Cambridge, Mass.: Harvard UP.

Hannibal: /* Deductive Logic */

Hannibal — Wed, 04 Jul 2007 05:14:02 GMT

Deductive Logic

←Older revision		Revision as of 05:14, 4 July 2007
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	==Deductive Logic==		==Deductive Logic==

-	''Deductive Logic'' is the method of non contradictory identification. It is based on the classical [[~~Axiom~~\|axioms]] of Aristotelean logic. '''Deductive arguments''' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premises" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].	+	'''Deductive Logic''' is the method of non contradictory identification. It is based on the classical [[The Laws of Classical Logic\|axioms]] of Aristotelean logic. ''Deductive arguments'' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premises" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].

	Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:		Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:

Hannibal: /* Deductive Logic */

Hannibal — Wed, 04 Jul 2007 05:13:02 GMT

Deductive Logic

←Older revision		Revision as of 05:13, 4 July 2007
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	==Deductive Logic==		==Deductive Logic==

-	''Deductive Logic'' is the method of non contradictory identification. It is based on the classical [[~~Axioms~~\|axioms]] of Aristotelean logic. '''Deductive arguments''' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premises" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].	+	''Deductive Logic'' is the method of non contradictory identification. It is based on the classical [[Axiom\|axioms]] of Aristotelean logic. '''Deductive arguments''' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premises" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].

	Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:		Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:

Hannibal: /* Deductive Logic */

Hannibal — Wed, 04 Jul 2007 05:12:46 GMT

Deductive Logic

←Older revision		Revision as of 05:12, 4 July 2007
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	==Deductive Logic==		==Deductive Logic==

-	'''Deductive arguments''' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premises" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].	+	''Deductive Logic'' is the method of non contradictory identification. It is based on the classical [[Axioms\|axioms]] of Aristotelean logic. '''Deductive arguments''' are akin to mathematical equations: they present a series of categories or definitions in a series of equivalencies. For this reason, the conclusion of a deductive argument necessarily follows from its premises, in the same way that ''4'' follows from the "premises" of ''2+2=''. In the opinion of this author, the most elegant form of a deductive argument is Aristotle's syllogistic logic, or [[Classical Logic\|classical deductive logic]].

	Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:		Generally, it is held by logicians that deductive arguments work from general rules to specific conclusions. For example, consider this categorical syllogism:
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	We can call a deductive logical system an a priori system. This means that we can make up such a system without any observation or experimental examination.We can create a set of categories like squares or circles or letters, and a set of self consitent rules that follow a set of definitions, all without having to ever experience such "things".		We can call a deductive logical system an a priori system. This means that we can make up such a system without any observation or experimental examination.We can create a set of categories like squares or circles or letters, and a set of self consitent rules that follow a set of definitions, all without having to ever experience such "things".

-	http://candleinthedark.com/brain.gif Philosophers like to say that a "brain in vat" set apart from the rest of the universe could create an a priori system.	+	http://candleinthedark.com/brain.gif Philosophers like to say that a "brain in vat" set apart from the rest of the universe could create an a priori system.

	==Inductive Logic==		==Inductive Logic==