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Directory:Jon Awbrey/Papers/Functional Logic : Inquiry and Analogy (view source)
Revision as of 05:04, 14 December 2010
, 05:04, 14 December 2010→1.4. Aristotle's “Apagogy” : Abductive Reasoning as Problem Reduction: re-format display
A couple of notes on the reading may be helpful. The Greek text seems to imply a geometric diagram, in which directed line segments ''AB'', ''BC'', ''AC'' are used to indicate logical relations between pairs of the terms in ''A'', ''B'', ''C''. We have two options for reading these line labels, either as implications or as subsumptions, as in the following two paradigms for interpretation.
A couple of notes on the reading may be helpful. The Greek text seems to imply a geometric diagram, in which directed line segments ''AB'', ''BC'', ''AC'' are used to indicate logical relations between pairs of the terms in ''A'', ''B'', ''C''. We have two options for reading these line labels, either as implications or as subsumptions, as in the following two paradigms for interpretation.
{|
{| align="center" width="90%"
| width=36 | || Read as Implications:
| colspan="3" | Read as Implications:
|}
|-
| width="8%" | ''AB''
| width=36 | || "''AB''" || = || "''A'' <= ''B''",
| width="6%" | =
| width="86%" | ''A'' ⇐ ''B'',
|-
|-
| || "''BC''" || = || "''B'' <= ''C''",
| ''BC''
| =
| ''B'' ⇐ ''C'',
|-
|-
| || "''AC''" || = || "''A'' <= ''C''".
| ''AC''
| =
| ''A'' ⇐ ''C''.
|}
|}
{|
{| align="center" width="90%"
| width=36 | || Read as Subsumptions:
| colspan="3" | Read as Subsumptions:
|}
|-
| width="8%" | ''AB''
| width=36 | || "''AB''" || = || "''A'' subsumes ''B''",
| width="6%" | =
| width="86%" | ''A'' subsumes ''B'',
|-
|-
| || "''BC''" || = || "''B'' subsumes ''C''",
| ''BC''
| =
| ''B'' subsumes ''C'',
|-
|-
| || "''AC''" || = || "''A'' subsumes ''C''".
| ''AC''
| =
| ''A'' subsumes ''C''.
|}
|}
Here, "''X'' subsumes ''Y''" means that "''X'' applies to all ''Y''", or that "''X'' is predicated of all of ''Y''". When there is no danger of confusion, we may write this as "''X'' >= ''Y''".
Here, "''X'' subsumes ''Y''" means that "''X'' applies to all ''Y''", or that "''X'' is predicated of all of ''Y''". When there is no danger of confusion, we may write this as "''X'' >= ''Y''".