12,080
edits
Changes
MyWikiBiz, Author Your Legacy — Monday November 25, 2024
Jump to navigationJump to searchredo figure style, fix quotation marks and italics
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.
{| align="center" cellpadding="8" style="text-align:center; width:90%"
{| align="center" cellpadding="8" style="text-align:center"
|
|
<pre>
<pre>
The converging operation of all three reasonings is shown in Figure 2.
The converging operation of all three reasonings is shown in Figure 2.
{| align="center" cellpadding="8" style="text-align:center; width:90%"
{| align="center" cellpadding="8" style="text-align:center"
|
|
<pre>
<pre>
The common proposition that concludes each argument is AC. Introducing the symbol "⇒" to denote the relation of logical implication, the proposition AC can be written as C ⇒ A, and read as "C implies A". Adopting the parenthetical form of Peirce's alpha graphs, in their ''existential interpretation'', AC can be written as (C (A)), and most easily comprehended as "not C without A". In the context of the present example, all of these forms are equally good ways of expressing the same concrete proposition, namely, "contributing to charity is wise".
The common proposition that concludes each argument is AC. Introducing the symbol "⇒" to denote the relation of logical implication, the proposition AC can be written as C ⇒ A, and read as "C implies A". Adopting the parenthetical form of Peirce's alpha graphs, in their ''existential interpretation'', AC can be written as (C (A)), and most easily comprehended as "not C without A". In the context of the present example, all of these forms are equally good ways of expressing the same concrete proposition, namely, "contributing to charity is wise".
:* Deduction could have obtained the Fact AC from the Rule AB, 'benevolence is wisdom', along with the Case BC, 'contributing to charity is benevolent'.
:* Deduction could have obtained the Fact AC from the Rule AB, "benevolence is wisdom", along with the Case BC, "contributing to charity is benevolent".
:* Induction could have gathered the Rule AC, after a manner of saying that 'contributing to charity is exemplary of wisdom', from the Fact AE, 'the act of earlier today is wise', along with the Case CE, 'the act of earlier today was an instance of contributing to charity'.
:* Induction could have gathered the Rule AC, after a manner of saying that "contributing to charity is exemplary of wisdom", from the Fact AE, "the act of earlier today is wise", along with the Case CE, "the act of earlier today was an instance of contributing to charity".
:* Abduction could have guessed the Case AC, in a style of expression stating that 'contributing to charity is explained by wisdom', from the Fact DC, 'contributing to charity is done by this wise man', and the Rule DA, 'everything that is wise is done by this wise man'. Thus, a wise man, who happens to do all of the wise things that there are to do, may nevertheless contribute to charity for no good reason, and even be known to be charitable to a fault. But all of this notwithstanding, on seeing the wise man contribute to charity we may find it natural to conjecture, in effect, to consider it as a possibility worth examining further, that charity is indeed a mark of his wisdom, and not just the accidental trait or the immaterial peculiarity of his character — in essence, that wisdom is the 'cause' of his contribution or the 'reason' for his charity.
:* Abduction could have guessed the Case AC, in a style of expression stating that "contributing to charity is explained by wisdom", from the Fact DC, "contributing to charity is done by this wise man", and the Rule DA, "everything that is wise is done by this wise man". Thus, a wise man, who happens to do all of the wise things that there are to do, may nevertheless contribute to charity for no good reason, and even be known to be charitable to a fault. But all of this notwithstanding, on seeing the wise man contribute to charity we may find it natural to conjecture, in effect, to consider it as a possibility worth examining further, that charity is indeed a mark of his wisdom, and not just the accidental trait or the immaterial peculiarity of his character — in essence, that wisdom is the ''cause'' of his contribution or the ''reason'' for his charity.
As a general rule, and despite many obvious exceptions, an English word that ends in '-ion' denotes equivocally either a process or its result. In our present application, this means that each of the words 'abduction', 'deduction', 'induction' can be used to denote either the process of inference or the product of that inference, that is, the proposition to which the inference in question leads.
As a general rule, and despite many obvious exceptions, an English word that ends in ''-ion'' denotes equivocally either a process or its result. In our present application, this means that each of the words ''abduction'', ''deduction'', ''induction'' can be used to denote either the process of inference or the product of that inference, that is, the proposition to which the inference in question leads.
One of the morals of Peirce's illustration can now be drawn. It demonstrates in a very graphic fashion that the three kinds of inference are three kinds of process and not three kinds of proposition, not if one takes the word 'kind' in its literal sense as denoting a ''genus'' of being, essence, or substance. Said another way, it means that being an abductive Case, a deductive Fact, or an inductive Rule is a category of relation, indeed, one that involves at the very least a triadic relation among propositions, and not a category of essence or substance, that is, not a property that inheres in the proposition alone.
One of the morals of Peirce's illustration can now be drawn. It demonstrates in a very graphic fashion that the three kinds of inference are three kinds of process and not three kinds of proposition, not if one takes the word ''kind'' in its literal sense as denoting a ''genus'' of being, essence, or substance. Said another way, it means that being an abductive Case, a deductive Fact, or an inductive Rule is a category of relation, indeed, one that involves at the very least a triadic relation among propositions, and not a category of essence or substance, that is, not a property that inheres in the proposition alone.
This category distinction between the absolute, essential, or monadic predicates and the more properly relative predicates constitutes a very important theme in Peirce's architectonic. There is of course a parallel application of it in the theory of sign relations, or semiotics, where the distinctions among the sign relational roles of Object, Sign, and Interpretant are distinct ways of relating to other things, modes of relation that may vary from moment to moment in the extended trajectory of a sign process, and not distinctions that mark some fixed and eternal essence of the thing in itself.
This category distinction between the absolute, essential, or monadic predicates and the more properly relative predicates constitutes a very important theme in Peirce's architectonic. There is of course a parallel application of it in the theory of sign relations, or semiotics, where the distinctions among the sign relational roles of Object, Sign, and Interpretant are distinct ways of relating to other things, modes of relation that may vary from moment to moment in the extended trajectory of a sign process, and not distinctions that mark some fixed and eternal essence of the thing in itself.
Now let any two of these statements be Givens (their order not mattering), and let the remaining statement be the Conclusion. The result is an ''argument'', of which three kinds are possible:
Now let any two of these statements be Givens (their order not mattering), and let the remaining statement be the Conclusion. The result is an ''argument'', of which three kinds are possible:
{| class=wikitable cellpadding="4"
{| align="center" cellpadding="4"
|-
|-
! !! Deduction !! Induction !! Abduction
! !! Deduction !! Induction !! Abduction
|- style="border-top:1px solid #999;"
|- style="border-top:1px solid #999;"
|-
|-
| ''Given'' || Rule || Case || Rule
| ''Premiss'' || Rule || Case || Rule
|-
|-
| ''Given'' || Case || Result || Result
| ''Premiss'' || Case || Fact || Fact
|-
|-
| ''Conclusion'' || Result || Rule || Case
| ''Conclusion'' || Fact || Rule || Case
|}
|}
====Deduction====
====Deduction====
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.
{| align="center" cellpadding="8" style="text-align:center; width:90%"
{| align="center" cellpadding="8" style="text-align:center"
|
|
<pre>
<pre>
| |
| |
o-----------------------------------------------------------o
o-----------------------------------------------------------o
Figure 3. Aristotle's 'War Against Neighbors' Example
Figure 3. Aristotle's "War Against Neighbors" Example
</pre>
</pre>
|}
|}
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.
{| align="center" cellpadding="8" style="text-align:center; width:90%"
{| align="center" cellpadding="8" style="text-align:center"
|
|
<pre>
<pre>
Figure 5 schematizes this way of viewing the 'analogy of experience'.
Figure 5 schematizes this way of viewing the 'analogy of experience'.
{| align="center" cellpadding="8" style="text-align:center; width:90%"
{| align="center" cellpadding="8" style="text-align:center"
|
|
<pre>
<pre>
