Changes

For ease of reference, Figure 1 and the Legend beneath it summarize the classical terminology for the three types of inference and the relationships among them.

For ease of reference, Figure 1 and the Legend beneath it summarize the classical terminology for the three types of inference and the relationships among them.

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Figure 1.  Elementary Structure and Terminology

Figure 1.  Elementary Structure and Terminology

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In its original usage a statement of Fact has to do with a deed done or a record made, that is, a type of event that is openly observable and not riddled with speculation as to its very occurrence.  In contrast, a statement of Case may refer to a hidden or a hypothetical cause, that is, a type of event that is not immediately observable to all concerned. Obviously, the distinction is a rough one and the question of which mode applies can depend on the points of view that different observers adopt over time.  Finally, a statement of a Rule is called that because it states a regularity or a regulation that governs a whole class of situations, and not because of its syntactic form.  So far in this discussion, all three types of constraint are expressed in the form of conditional propositions, but this is not a fixed requirement. In practice, these modes of statement are distinguished by the roles that they play within an argument, not by their style of expression.  When the time comes to branch out from the syllogistic framework, we will find that propositional constraints can be discovered and represented in arbitrary syntactic forms.

In its original usage a statement of Fact has to do with a deed done or a record made, that is, a type of event that is openly observable and not riddled with speculation as to its very occurrence.  In contrast, a statement of Case may refer to a hidden or a hypothetical cause, that is, a type of event that is not immediately observable to all concerned. Obviously, the distinction is a rough one and the question of which mode applies can depend on the points of view that different observers adopt over time.  Finally, a statement of a Rule is called that because it states a regularity or a regulation that governs a whole class of situations, and not because of its syntactic form.  So far in this discussion, all three types of constraint are expressed in the form of conditional propositions, but this is not a fixed requirement. In practice, these modes of statement are distinguished by the roles that they play within an argument, not by their style of expression.  When the time comes to branch out from the syllogistic framework, we will find that propositional constraints can be discovered and represented in arbitrary syntactic forms.

The converging operation of all three reasonings is shown in Figure 2.

The converging operation of all three reasonings is shown in Figure 2.

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Figure 2.  A Thrice Wise Act

Figure 2.  A Thrice Wise Act

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One of the styles of syntax that Aristotle uses for syllogistic propositions suggests the composite symbols that geometers have long used for labeling line intervals in a geometric figure, and it comports quite nicely with the Figure that we have just drawn.  Specifically, the proposition that predicates X of the subject Y is represented by the digram 'XY' and associated with the line interval XY that descends from the point X to the point Y in the corresponding lattice diagram.  In this wise we make the following observations:

One of the styles of syntax that Aristotle uses for syllogistic propositions suggests the composite symbols that geometers have long used for labeling line intervals in a geometric figure, and it comports quite nicely with the Figure that we have just drawn.  Specifically, the proposition that predicates X of the subject Y is represented by the digram 'XY' and associated with the line interval XY that descends from the point X to the point Y in the corresponding lattice diagram.  In this wise we make the following observations:

====Abduction====

====Abduction====

: ''Main article : [[Abductive reasoning]]''

: ''Main article : [[Abductive reasoning]]''

Figure 3 gives a graphical illustration of Aristotle's example of 'Example', that is, the form of reasoning that proceeds by Analogy or according to a Paradigm.

Figure 3 gives a graphical illustration of Aristotle's example of 'Example', that is, the form of reasoning that proceeds by Analogy or according to a Paradigm.

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Figure 3.  Aristotle's 'War Against Neighbors' Example

Figure 3.  Aristotle's 'War Against Neighbors' Example

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In this analysis of reasoning by Analogy, it is a complex or a mixed form of inference that can be seen as taking place in two steps:

In this analysis of reasoning by Analogy, it is a complex or a mixed form of inference that can be seen as taking place in two steps:

Figure 4 gives a graphical illustration of Dewey's example of inquiry, isolating for the purposes of the present analysis the first two steps in the more extended proceedings that go to make up the whole inquiry.

Figure 4 gives a graphical illustration of Dewey's example of inquiry, isolating for the purposes of the present analysis the first two steps in the more extended proceedings that go to make up the whole inquiry.

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Figure 4.  Dewey's 'Rainy Day' Inquiry

Figure 4.  Dewey's "Rainy Day" Inquiry

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In this analysis of the first steps of Inquiry, we have a complex or a mixed form of inference that can be seen as taking place in two steps:

In this analysis of the first steps of Inquiry, we have a complex or a mixed form of inference that can be seen as taking place in two steps:

Figure 5 schematizes this way of viewing the 'analogy of experience'.

Figure 5 schematizes this way of viewing the 'analogy of experience'.

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Figure 5.  Analogy of Experience

Figure 5.  Analogy of Experience

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In these terms, the ''analogy of experience'' proceeds by inducing a Rule about the validity of a current knowledge base and then deducing a Fact, its applicability to a current experience, as in the following sequence:

In these terms, the ''analogy of experience'' proceeds by inducing a Rule about the validity of a current knowledge base and then deducing a Fact, its applicability to a current experience, as in the following sequence: