Classical Logic - Revision history

Hannibal at 16:48, 5 July 2009

Hannibal — Sun, 05 Jul 2009 16:48:48 GMT

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	=== Let's get in the Mood ===		=== Let's get in the Mood ===

-	Oh yeah! http://~~candleinthedark~~.com/ladiesman.jpg	+	Oh yeah! http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg

	The mood of a syllogism is determined by the types of categorical propositions it contains (A, E, I, or O propositions, which again, are: A) All S are P (E) No S are P (I) Some S are P (O) Some S are not P)		The mood of a syllogism is determined by the types of categorical propositions it contains (A, E, I, or O propositions, which again, are: A) All S are P (E) No S are P (I) Some S are P (O) Some S are not P)
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	The mood and figure of a syllogism uniquely determine its form, and the form of an argument, from the viewpoint of logic, is its most important aspect. The validity or invalidity of a syllogism, (whose constituent propositions are all contingent, we will discuss this is more detail later) depends exclusively on its form, completely independent of its content. In fact, I've always held that this fact is one of the most impor..		The mood and figure of a syllogism uniquely determine its form, and the form of an argument, from the viewpoint of logic, is its most important aspect. The validity or invalidity of a syllogism, (whose constituent propositions are all contingent, we will discuss this is more detail later) depends exclusively on its form, completely independent of its content. In fact, I've always held that this fact is one of the most impor..

-	Excuse me, my man, my man... http://~~candleinthedark~~.com/ladiesman.jpg	+	Excuse me, my man, my man... http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg

	Yes?		Yes?

-	You gotta hit me with another picture. http://~~candleinthedark~~.com/ladiesman.jpg	+	You gotta hit me with another picture. http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg

-	http://~~candleinthedark~~.com/christina2.jpg	+	http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/christina2.jpg

-	Oh yeah! http://~~candleinthedark~~.com/ladiesman.jpg	+	Oh yeah! http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg

	Ok. Once the task of forming a categorical syllogism in standard form is accomplished, validity of the form can be ascertained according to the following table. You don't need to work it out on your own, it's already been done for you: thousands of years ago! Of the 256 possible permutations of mood and figure (64 types of mood X 4 types of figure), only 15 of the possible forms are valid. Here they are:		Ok. Once the task of forming a categorical syllogism in standard form is accomplished, validity of the form can be ascertained according to the following table. You don't need to work it out on your own, it's already been done for you: thousands of years ago! Of the 256 possible permutations of mood and figure (64 types of mood X 4 types of figure), only 15 of the possible forms are valid. Here they are:
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	Ok, now let's take a look		Ok, now let's take a look

-	http://~~candleinthedark~~.com/ladiesman.jpg ....at that fine lady again?	+	http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg ....at that fine lady again?

	Ok, one more...		Ok, one more...
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	http://www.nndb.com/people/752/000025677/christina_ricci_bubbles.jpg		http://www.nndb.com/people/752/000025677/christina_ricci_bubbles.jpg

-	http://~~candleinthedark~~.com/ladiesman.jpg Oh yeah!	+	http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg Oh yeah!

	==Syllogistic Rules and Syllogistic Fallacies==		==Syllogistic Rules and Syllogistic Fallacies==
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	===Rule 3 - and The Fallacy of Illicit Major and Illicit Minor===		===Rule 3 - and The Fallacy of Illicit Major and Illicit Minor===

-	If a term in distributed in the conclusion, it must be distributed in the premise. When a term is distributed in the conclusion, (~~let’s~~ say that P is distributed), then that term is saying something about every member of the P class. If that same term is not distributed in the major premise, then the major premise is saying something about only some members of the P class. Remember that the minor premise says nothing about the P class. Therefore, the conclusion contains information that is not contained in the premises, making the argument invalid.	+	If a term in distributed in the conclusion, it must be distributed in the premise. When a term is distributed in the conclusion, (letâ��s say that P is distributed), then that term is saying something about every member of the P class. If that same term is not distributed in the major premise, then the major premise is saying something about only some members of the P class. Remember that the minor premise says nothing about the P class. Therefore, the conclusion contains information that is not contained in the premises, making the argument invalid.

	If the rule is broken, the fallacy committed is either illicit major or illicit minor, depending on whether the Predicate or Subject is undistributed.		If the rule is broken, the fallacy committed is either illicit major or illicit minor, depending on whether the Predicate or Subject is undistributed.

Hannibal: /* Let's Look at Some Figures */

Hannibal — Sun, 05 Jul 2009 16:46:39 GMT

Let's Look at Some Figures

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	Now, we must examine some Figures		Now, we must examine some Figures

-	http://~~candleinthedark~~.com/christina.jpg	+	http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/christina.jpg

-	Oh yeah! http://~~candleinthedark~~.com/ladiesman.jpg	+	Oh yeah! http://i602.photobucket.com/albums/tt102/hanniballecturer/candleinthedark/ladiesman.jpg

	No, unfortunately, not that kind of figure.		No, unfortunately, not that kind of figure.

Hannibal: /* Major, Minor and Middle Terms */

Hannibal — Mon, 15 Dec 2008 21:03:36 GMT

Major, Minor and Middle Terms

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	Now, in order to figure out which proposition is '''major term''' and which is the '''minor term''', we look at the conclusion of the argument. The category referred to in the predicate of the conclusion is called the major term. So the major term in this argument is ''cowards'' This term appears in the first proposition, so the first premise in this argument is the '''major premise'''.		Now, in order to figure out which proposition is '''major term''' and which is the '''minor term''', we look at the conclusion of the argument. The category referred to in the predicate of the conclusion is called the major term. So the major term in this argument is ''cowards'' This term appears in the first proposition, so the first premise in this argument is the '''major premise'''.

-	The ~~classical approach~~ to syllogisms is to list the major premise first, but this need not be the case. Another aspect of major premises is that they a generalization about some category. Examples would include: "All A's are B," "Either A or B," or "If A, then B"?	+	The standard form to syllogisms is to list the major premise first, but this need not be the case, so we cannot rely upon this as a clue as to which premise is the major premise. Another aspect of major premises is that they a generalization about some category. Examples would include: "All A's are B," "Either A or B," or "If A, then B"?

	Now, for the minor term. The subject of the conclusion contains the minor term. In our example, the category of "heroes" would be the minor term. The second proposition of the categorical syllogism contains this term, so we will call it the '''minor premise''.		Now, for the minor term. The subject of the conclusion contains the minor term. In our example, the category of "heroes" would be the minor term. The second proposition of the categorical syllogism contains this term, so we will call it the '''minor premise''.

Hannibal: /* Major, Minor and Middle Terms */

Hannibal — Mon, 15 Dec 2008 21:00:42 GMT

Major, Minor and Middle Terms

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	We can first break down propositions by looking at their '''subject''' and '''predicate''': the first category in a proposition is called the '''subject''' and the second category is called the '''predicate'''. In our example, the subject of the first premise, ''No heroes are cowards'' would be the category of ''heroes''. The second category ''cowards'', would be the "predicate".		We can first break down propositions by looking at their '''subject''' and '''predicate''': the first category in a proposition is called the '''subject''' and the second category is called the '''predicate'''. In our example, the subject of the first premise, ''No heroes are cowards'' would be the category of ''heroes''. The second category ''cowards'', would be the "predicate".

-	Now, in order to figure out which proposition is '''major term''' and which is the '''minor term''', we look at the conclusion of the argument. The category referred to in the predicate of the conclusion is called the major term. So the major term in this argument is ''cowards'' It appears in the first proposition, so ~~we will call~~ this ~~premise~~ the '''major premise'''~~. The classical approach to syllogisms is to list the major premise first, but this need not be the case. Major premises always do make a generalization about some category, however~~.	+	Now, in order to figure out which proposition is '''major term''' and which is the '''minor term''', we look at the conclusion of the argument. The category referred to in the predicate of the conclusion is called the major term. So the major term in this argument is ''cowards'' This term appears in the first proposition, so the first premise in this argument is the '''major premise'''.

-	The subject of the conclusion contains the minor term. In our example, the category of "heroes" would be the minor term. The second proposition of the categorical syllogism contains this term, so we will call it the '''minor premise''.	+	The classical approach to syllogisms is to list the major premise first, but this need not be the case. Another aspect of major premises is that they a generalization about some category. Examples would include: "All A's are B," "Either A or B," or "If A, then B"?
		+
		+	Now, for the minor term. The subject of the conclusion contains the minor term. In our example, the category of "heroes" would be the minor term. The second proposition of the categorical syllogism contains this term, so we will call it the '''minor premise''.

	The 3rd item is the '''middle term'''. It occurs in both the major and the minor premise. It is the transitional device that connects the major premise to the minor premise. The middle term is the term that preserves truth along the premises, to the conclusion. It's like the equal sign in math. Can you identify the ''middle term'' in this argument? It is the category ''soldiers''.		The 3rd item is the '''middle term'''. It occurs in both the major and the minor premise. It is the transitional device that connects the major premise to the minor premise. The middle term is the term that preserves truth along the premises, to the conclusion. It's like the equal sign in math. Can you identify the ''middle term'' in this argument? It is the category ''soldiers''.

Hannibal: /* Major, Minor and Middle Terms */

Hannibal — Mon, 15 Dec 2008 20:55:30 GMT

Major, Minor and Middle Terms

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	We can first break down propositions by looking at their '''subject''' and '''predicate''': the first category in a proposition is called the '''subject''' and the second category is called the '''predicate'''. In our example, the subject of the first premise, ''No heroes are cowards'' would be the category of ''heroes''. The second category ''cowards'', would be the "predicate".		We can first break down propositions by looking at their '''subject''' and '''predicate''': the first category in a proposition is called the '''subject''' and the second category is called the '''predicate'''. In our example, the subject of the first premise, ''No heroes are cowards'' would be the category of ''heroes''. The second category ''cowards'', would be the "predicate".

-	Now, in order to figure out which proposition is '''major term''' and which is the '''minor term''', we look at the conclusion of the argument. The category referred to in the predicate of the conclusion is called the major term. So the major term in this argument is ''cowards'' It appears in the first proposition, so we will call this premise the '''major premise'''.	+	Now, in order to figure out which proposition is '''major term''' and which is the '''minor term''', we look at the conclusion of the argument. The category referred to in the predicate of the conclusion is called the major term. So the major term in this argument is ''cowards'' It appears in the first proposition, so we will call this premise the '''major premise'''. The classical approach to syllogisms is to list the major premise first, but this need not be the case. Major premises always do make a generalization about some category, however.

	The subject of the conclusion contains the minor term. In our example, the category of "heroes" would be the minor term. The second proposition of the categorical syllogism contains this term, so we will call it the '''minor premise''.		The subject of the conclusion contains the minor term. In our example, the category of "heroes" would be the minor term. The second proposition of the categorical syllogism contains this term, so we will call it the '''minor premise''.

Hannibal: /* Nicknames for the Valid Forms */

Hannibal — Tue, 19 Aug 2008 21:05:52 GMT

Nicknames for the Valid Forms

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	===Nicknames for the Valid Forms===		===Nicknames for the Valid Forms===

-	This leaves us with 15 valid ~~syllogism~~. Classical logicians gave each of these 15 valid syllogisms a name.	+	This leaves us with 15 valid syllogisms. Classical logicians gave each of these 15 valid syllogisms a name.

	In figure 1, in which the middle term is the subject of the major premise and the predicate of the minor premise: AAA-1, '''Barbara''', EAE-1 '''Celarent''', AII-1 '''Darii''', and EIO-1, '''Ferio'''.		In figure 1, in which the middle term is the subject of the major premise and the predicate of the minor premise: AAA-1, '''Barbara''', EAE-1 '''Celarent''', AII-1 '''Darii''', and EIO-1, '''Ferio'''.

Hannibal: /* Major, Minor and Middle Terms */

Hannibal — Wed, 20 Jun 2007 17:07:58 GMT

Major, Minor and Middle Terms

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	In order to grasp the workings of a syllogism, we must introduce some new terms: The '''Major Term''', The '''Minor Term''' and the '''Middle Term'''. Let's make matters simple by using this example:		In order to grasp the workings of a syllogism, we must introduce some new terms: The '''Major Term''', The '''Minor Term''' and the '''Middle Term'''. Let's make matters simple by using this example:

-	Premise 1: No heroes are cowards - (This is an E proposition - No S are P)	+	Premise 1: No heroes are cowards - (This is an E proposition - No S are P)
-	Premise 2: Some soldiers are cowards (This is an I proposition - Some S are P )	+	Premise 2: Some soldiers are cowards (This is an I proposition - Some S are P )
-	Conclusion: Therefore, some heroes are not cowards (This is an O proposition, Some S are not P)	+	Conclusion: Therefore, some heroes are not cowards (This is an O proposition, Some S are not P)

	We can first break down propositions by looking at their '''subject''' and '''predicate''': the first category in a proposition is called the '''subject''' and the second category is called the '''predicate'''. In our example, the subject of the first premise, ''No heroes are cowards'' would be the category of ''heroes''. The second category ''cowards'', would be the "predicate".		We can first break down propositions by looking at their '''subject''' and '''predicate''': the first category in a proposition is called the '''subject''' and the second category is called the '''predicate'''. In our example, the subject of the first premise, ''No heroes are cowards'' would be the category of ''heroes''. The second category ''cowards'', would be the "predicate".

Hannibal at 06:22, 19 June 2007

Hannibal — Tue, 19 Jun 2007 06:22:51 GMT

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	However, it is actually not necessary to remember this list today. Today, we simply look back at it to understand the beginnings of formal logic, and to appreciate how classical scholars approached the subject.		However, it is actually not necessary to remember this list today. Today, we simply look back at it to understand the beginnings of formal logic, and to appreciate how classical scholars approached the subject.
-
-	~~Those following the [[Course in Logic 101]] should proceed to the next section: [[Disjunctive and Hypothetical Syllogisms]]~~

	==Further Resources==		==Further Resources==

-	If you feel you have mastered this section, test your knowledge here:	+	If you feel you have mastered this section, then first try out this Categorical Syllogism Program
		+
		+	http://www.roninabox.com/venndiagram.html
		+
		+	Then further test your knowledge of syllogisms here:

	http://duniho.com/fergus/sillysyllogisms.html		http://duniho.com/fergus/sillysyllogisms.html
		+
		+
		+	Those following the [[Course in Logic 101]] should proceed to the next section: [[Disjunctive and Hypothetical Syllogisms]]

	----		----

Hannibal at 06:06, 19 June 2007

Hannibal — Tue, 19 Jun 2007 06:06:57 GMT

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	These six rules apply only to standard form categorical propositions. To examine other logical forms and their validity and invalidity, you will need to read the section on [[Propositional Logic]].		These six rules apply only to standard form categorical propositions. To examine other logical forms and their validity and invalidity, you will need to read the section on [[Propositional Logic]].

-	==Exposition of the Valid ~~Syllogism~~==	+	==Exposition of the Valid Syllogistic Forms==

	For now, let's use are knowledge of these rules to uncover why ''there are only 15 valid categorical syllogisms''. The easiest manner to perform this process is to at the four possible figures for an argument, and to see which of the four possible classical propositions: A, E, I or O can be a valid conclusion given the figure.		For now, let's use are knowledge of these rules to uncover why ''there are only 15 valid categorical syllogisms''. The easiest manner to perform this process is to at the four possible figures for an argument, and to see which of the four possible classical propositions: A, E, I or O can be a valid conclusion given the figure.

Hannibal: /* Nicknames for the Valid Forms */

Hannibal — Tue, 19 Jun 2007 00:12:16 GMT

Nicknames for the Valid Forms

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	In figure 4, the middle term is the predicate of the major premise and the subject of the minor premise: AEE-4, '''Camenes''', IAI-4, '''Dimaris''', and EIO-4, '''Fresison'''.		In figure 4, the middle term is the predicate of the major premise and the subject of the minor premise: AEE-4, '''Camenes''', IAI-4, '''Dimaris''', and EIO-4, '''Fresison'''.

-	If you think it's daunting to remember this list, remember that this is the list for the more limited [[~~The Modern Square of Opposition\|~~Modern Square of Opposition]]. classical logicians memorized all the forms that were considered valid under the [[Traditional Square of ~~Oposition~~]]! For many centuries, it was common practice to present formal disputations in classical syllogistic form, and it was considered a sign of being a learned man if you could use the mnenumonic "on the fly". ''Datisi! My form is valid!''	+	If you think it's daunting to remember this list, remember that this is the list for the more limited [[Modern Square of Opposition]]. classical logicians memorized all the forms that were considered valid under the [[Traditional Square of Opposition]]! For many centuries, it was common practice to present formal disputations in classical syllogistic form, and it was considered a sign of being a learned man if you could use the mnenumonic "on the fly". ''Datisi! My form is valid!''

	However, it is actually not necessary to remember this list today. Today, we simply look back at it to understand the beginnings of formal logic, and to appreciate how classical scholars approached the subject.		However, it is actually not necessary to remember this list today. Today, we simply look back at it to understand the beginnings of formal logic, and to appreciate how classical scholars approached the subject.