The Laws of Classical Logic - Revision history

Hannibal: /* Self Evident Nature of Axioms */

2019-01-19T20:06:53Z

Self Evident Nature of Axioms

←Older revision		Revision as of 20:06, 19 January 2019
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	==Self Evident Nature of Axioms==		==Self Evident Nature of Axioms==

-	Seeing as axioms are the foundation to classic logic, it is not possible to use classical logic to justify them ~~anymore~~ than it would be possible to use a building's second floor as its foundation. Any attempt to do so is doubly folly, seeing as the axioms of logic, as well as logic itself, is prescriptive, not descriptive. It's not a element of the universe that we need to verify as true or false, it is a system. In addition, any natural attempt to give logic a psychological justification would be viciously circular, since all reasoning, including that to produce the justification, already assumes the validity of logical rules of inference.	+	Seeing as axioms are the foundation to classic logic, it is not possible to use classical logic to justify them any more than it would be possible to use a building's second floor as its foundation. Any attempt to do so is doubly folly, seeing as the axioms of logic, as well as logic itself, are prescriptive, not descriptive. It's not an element of the universe that we need to verify as true or false, it is a system. In addition, any natural attempt to give logic a psychological justification would be viciously circular, since all reasoning, including that to produce the justification, already assumes the validity of logical rules of inference.

-	Finally, Aristotle found any attempt to logically justify axioms as unnecessary: he held that the axioms of classical logic are ''self evident''. It was said that they ~~are~~ are self evident because 1) all syllogisms rely on them, and 2) because they can be defended through [[Retortion\|retortion]].	+	Finally, Aristotle found any attempt to logically justify axioms as unnecessary: he held that the axioms of classical logic are '' self-evident''. It was said that they are self-evident because 1) all syllogisms rely on them, and 2) because they can be defended through [[Retortion\|retortion]].

-	A defense through [[Retortion\|retortion]] occurs whenever an argument must rely upon the very principle it seeks to challenge or overturn. Any attempt to form a syllogism to refute the axioms of classical logic will have to rely on the very axioms it seeks to overturn, leading to an implicit avocation of the axiom, which leads to a self refutation (we call this type of self refutation the Stolen concept fallacy.) See the [[Informal Fallacies]] section for more on this.	+	A defense through [[Retortion\|retortion]] occurs whenever an argument must rely upon the very principle it seeks to challenge or overturn. Any attempt to form a syllogism to refute the axioms of classical logic will have to rely on the very axioms it seeks to overturn, leading to an implicit avocation of the axiom, which leads to a self-refutation (we call this type of self-refutation the Stolen concept fallacy.) See the [[Informal Fallacies]] section for more on this.

	==Necessity and Contingency==		==Necessity and Contingency==

Hannibal: /* For Advanced Students */

2015-04-30T02:49:58Z

For Advanced Students

←Older revision		Revision as of 02:49, 30 April 2015
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	The following section delves into the matter of axioms more deeply, and requires knowledge of symbolic logic. Those following the [[Course in Logic 101]] will learn everything required to grasp this section in later lessons, and can skip this section for now, if desired.		The following section delves into the matter of axioms more deeply, and requires knowledge of symbolic logic. Those following the [[Course in Logic 101]] will learn everything required to grasp this section in later lessons, and can skip this section for now, if desired.

-	As stated above, some logical systems to not require any axioms at all. For example, the set of axioms for the sentential, or propositional, logic is {} - the empty set!	+	As stated above, some logical systems do not require any axioms at all. For example, the set of axioms for the sentential, or propositional, logic is {} - the empty set!

	So how does such a system "get off the ground"?		So how does such a system "get off the ground"?

Hannibal: /* What these axioms are NOT */

2012-10-06T13:10:07Z

What these axioms are NOT

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	It is also important to avoid conflating or confusing the so called [[laws of thought]] with set of nomological (Physical) laws for the universe. Logic is not cosmology. It is not descriptive of how the universe works'. It is prescriptive: it sets forth a method of examining arguments.		It is also important to avoid conflating or confusing the so called [[laws of thought]] with set of nomological (Physical) laws for the universe. Logic is not cosmology. It is not descriptive of how the universe works'. It is prescriptive: it sets forth a method of examining arguments.

-	The universe is not 'logical', it merely '''is'''.	+	The universe is not 'logical' (or illogical), it merely '''is'''. When a star radiates within a certain spectrum of light, appearing to us as "red" this is simply due to this physical cause and not due to its 'adherence' to logic.

	It is also important not to confuse classical logic with psychology. The so called laws of thought are not rules for human behavior, they don't even cover all human thought: in our dreams, we are able to imagine contradictions, like being both the victim and the attacker, or being both young and old at the same time - human thought contains rational, irrational and non rational thought - both logic and emotions, impulses and instincts.		It is also important not to confuse classical logic with psychology. The so called laws of thought are not rules for human behavior, they don't even cover all human thought: in our dreams, we are able to imagine contradictions, like being both the victim and the attacker, or being both young and old at the same time - human thought contains rational, irrational and non rational thought - both logic and emotions, impulses and instincts.

-	Finally, there is no reason to hold that these axioms are "immaterial", or transcendental. Such claims are matters of theology or dualistic philosophy, and are merely incidental issues in logic qua logic. These claims are usually based on [[Informal_Fallacies#Arguments_from_Ignorance\|arguments from ignorance]]. An incomplete physical account for abstractions is not a positive argument for an immaterial account for abstractions. Second, 'immateriality' is a negative concept, and a negative definition devoid of a universe of discourse, is meaningless. Unless someone can show how something immaterial can exist, how something immaterial can act without violating the principle of conservation of ~~energyand~~ how something ~~immateriality~~ can interact with physical brains, then the claim that these logical laws that people create are transcendent or immaterial remains incoherent.	+	Finally, there is no reason to hold that these axioms are "immaterial", or transcendental. Such claims are matters of theology or dualistic philosophy, and are merely incidental issues in logic qua logic. These claims are usually based on [[Informal_Fallacies#Arguments_from_Ignorance\|arguments from ignorance]]. An incomplete physical account for abstractions is not a positive argument for an immaterial account for abstractions. Second, 'immateriality' is a negative concept, and a negative definition devoid of a universe of discourse, is meaningless. Unless someone can show how something immaterial can exist, how something immaterial can act without violating the principle of conservation of energy and how something immaterial can interact with physical brains, then the claim that these logical laws that people create are transcendent or immaterial remains incoherent.

Hannibal: /* The Axioms of Classical Logic */

2010-08-18T00:47:40Z

The Axioms of Classical Logic

←Older revision		Revision as of 00:47, 18 August 2010
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	*[[The Law of Noncontradiction]]: Metaphysically, this law asserts:: "Nothing can be both A and not-A." For propositions: "A proposition, P, can not be both true and false."		*[[The Law of Noncontradiction]]: Metaphysically, this law asserts:: "Nothing can be both A and not-A." For propositions: "A proposition, P, can not be both true and false."

-	All of our ''syllogisms'' rely on these laws - that any thing is equal to itself, that tautologies must be true, and that contradictions must be false. Classical logic holds that everything has a definite, non-contradictory nature. A metaphysical law of identity would hold that to be perceived or even exist at all it must have a definite, non-contradictory nature~~, but for our purposes, it is enough to say that If A is true, then A is true!~~	+	All of our ''syllogisms'' rely on these laws - that any thing is equal to itself, that tautologies must be true, and that contradictions must be false. Classical logic holds that everything has a definite, non-contradictory nature. A metaphysical law of identity would hold that to be perceived or even exist at all it must have a definite, non-contradictory nature.

	==Self Evident Nature of Axioms==		==Self Evident Nature of Axioms==

Hannibal: /* Necessity and Contingency */

2010-04-14T19:10:23Z

Necessity and Contingency

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	==Necessity and Contingency==		==Necessity and Contingency==

-	An understanding of [[The Laws of Classical Logic\|axioms]] be further advanced if the concepts of [[Necessity and Contingency\|necessity]] and [[Necessity and Contingency\|contingency]] are introduced. A [[proposition]] is said to be a '''necessary proposition''' if it's negation necessarily entails a contradiction. [[The Laws of Classical Logic\|Axiom]]s are considered to be [[Necessity and Contingency\|necessary]] [[proposition\|propositions]].	+	An understanding of [[The Laws of Classical Logic\|axioms]] can be further advanced if the concepts of [[Necessity and Contingency\|necessity]] and [[Necessity and Contingency\|contingency]] are introduced. A [[proposition]] is said to be a '''necessary proposition''' if it's negation necessarily entails a contradiction. [[The Laws of Classical Logic\|Axiom]]s are considered to be [[Necessity and Contingency\|necessary]] [[proposition\|propositions]].

	A proposition is said to be a '''contingent proposition''' if it can be either true or false. As we will learn later, [[Categorical Propositions]] are one type of statement that can be either true or false.		A proposition is said to be a '''contingent proposition''' if it can be either true or false. As we will learn later, [[Categorical Propositions]] are one type of statement that can be either true or false.

Hannibal: /* Self Evident Nature of Axioms */

2009-06-21T20:24:45Z

Self Evident Nature of Axioms

←Older revision		Revision as of 20:24, 21 June 2009
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	==Self Evident Nature of Axioms==		==Self Evident Nature of Axioms==

-	Seeing as axioms are the foundation to classic logic, it is not possible to use classical logic to justify them anymore than it would be possible to use a building's second floor as its foundation. Aristotle found any attempt to logically justify axioms as unnecessary: he held that the axioms of classical logic are ''self evident''. It was said that they are are self evident because 1) all syllogisms rely on them, and 2) because they can be defended through [[Retortion\|retortion]].	+	Seeing as axioms are the foundation to classic logic, it is not possible to use classical logic to justify them anymore than it would be possible to use a building's second floor as its foundation. Any attempt to do so is doubly folly, seeing as the axioms of logic, as well as logic itself, is prescriptive, not descriptive. It's not a element of the universe that we need to verify as true or false, it is a system. In addition, any natural attempt to give logic a psychological justification would be viciously circular, since all reasoning, including that to produce the justification, already assumes the validity of logical rules of inference.
		+
		+	Finally, Aristotle found any attempt to logically justify axioms as unnecessary: he held that the axioms of classical logic are ''self evident''. It was said that they are are self evident because 1) all syllogisms rely on them, and 2) because they can be defended through [[Retortion\|retortion]].

	A defense through [[Retortion\|retortion]] occurs whenever an argument must rely upon the very principle it seeks to challenge or overturn. Any attempt to form a syllogism to refute the axioms of classical logic will have to rely on the very axioms it seeks to overturn, leading to an implicit avocation of the axiom, which leads to a self refutation (we call this type of self refutation the Stolen concept fallacy.) See the [[Informal Fallacies]] section for more on this.		A defense through [[Retortion\|retortion]] occurs whenever an argument must rely upon the very principle it seeks to challenge or overturn. Any attempt to form a syllogism to refute the axioms of classical logic will have to rely on the very axioms it seeks to overturn, leading to an implicit avocation of the axiom, which leads to a self refutation (we call this type of self refutation the Stolen concept fallacy.) See the [[Informal Fallacies]] section for more on this.

Hannibal at 13:53, 21 June 2009

2009-06-21T13:53:32Z

←Older revision		Revision as of 13:53, 21 June 2009
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-	Classical logic rests upon a foundation of [[~~axioms\|~~axiom]]. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic\|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics<sup>1</sup> and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments that may or may not mirror basic metaphysics. The universe isn't subject to any laws of logic at all. The universe merely exists. However, because I feel there is a clear relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.	+	Classical logic rests upon a foundation of [[axiom\|axioms]]. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic\|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics<sup>1</sup> and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments that may or may not mirror basic metaphysics. The universe isn't subject to any laws of logic at all. The universe merely exists. However, because I feel there is a clear relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.

	===The Axioms of Classical Logic===		===The Axioms of Classical Logic===

Hannibal at 13:53, 21 June 2009

2009-06-21T13:53:15Z

←Older revision		Revision as of 13:53, 21 June 2009
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-	Classical logic rests upon a foundation of [[axioms]]. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic\|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics<sup>1</sup> and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments that may or may not mirror basic metaphysics. The universe isn't subject to any laws of logic at all. The universe merely exists. However, because I feel there is a clear relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.	+	Classical logic rests upon a foundation of [[axioms\|axiom]]. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic\|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics<sup>1</sup> and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments that may or may not mirror basic metaphysics. The universe isn't subject to any laws of logic at all. The universe merely exists. However, because I feel there is a clear relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.

	===The Axioms of Classical Logic===		===The Axioms of Classical Logic===

Hannibal at 13:52, 21 June 2009

2009-06-21T13:52:50Z

←Older revision		Revision as of 13:52, 21 June 2009
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-	Classical logic rests upon a foundation of axioms. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic\|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics<sup>1</sup> and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments that may or may not mirror basic metaphysics. The universe isn't subject to any laws of logic at all. The universe merely exists. However, because I feel there is a clear relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.	+	Classical logic rests upon a foundation of [[axioms]]. The axioms of classical logic, are a set of [[a priori]] abstractions that humans create, in order to make [[Classical Logic\|categorical syllogisms]]; their existence is contingent upon sentient brains. Some may argue, like myself, that these laws have correlates to basic laws of metaphysics<sup>1</sup> and that this accounts for the 'utility' of logic, but it does not follow that logical rules are rules for the universe - they are rules for arguments that may or may not mirror basic metaphysics. The universe isn't subject to any laws of logic at all. The universe merely exists. However, because I feel there is a clear relationship between the metaphysical status of these concepts and their application to logic, I will address both concepts in my definitions.

	===The Axioms of Classical Logic===		===The Axioms of Classical Logic===

Hannibal: /* What these axioms are NOT */

2009-05-24T17:21:00Z

What these axioms are NOT

←Older revision		Revision as of 17:21, 24 May 2009
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	===What these axioms are NOT===		===What these axioms are NOT===

-	These axioms are axioms for classical logic. Not "all logic".	+	These axioms are axioms for classical logic. Not all thought or even all logic.

	It is also important to avoid conflating or confusing the so called [[laws of thought]] with set of nomological (Physical) laws for the universe. Logic is not cosmology. It is not descriptive of how the universe works'. It is prescriptive: it sets forth a method of examining arguments.		It is also important to avoid conflating or confusing the so called [[laws of thought]] with set of nomological (Physical) laws for the universe. Logic is not cosmology. It is not descriptive of how the universe works'. It is prescriptive: it sets forth a method of examining arguments.