Analogy, Explanation, and Proof
People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the exist...
Main Authors: | , , |
---|---|
Format: | Article |
Language: | English |
Published: |
Frontiers Media S.A.
2014-11-01
|
Series: | Frontiers in Human Neuroscience |
Subjects: | |
Online Access: | http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00867/full |
id |
doaj-94c61f883ea14fb4b073eeabf5d64a65 |
---|---|
record_format |
Article |
spelling |
doaj-94c61f883ea14fb4b073eeabf5d64a652020-11-25T02:04:00ZengFrontiers Media S.A.Frontiers in Human Neuroscience1662-51612014-11-01810.3389/fnhum.2014.00867100800Analogy, Explanation, and ProofJohn eHummel0John eLicato1Selmer eBringsjord2Selmer eBringsjord3University of IllinoisRensselaer Polytechnic Institute (RPI)Rensselaer Polytechnic Institute (RPI)Rensselaer Polytechnic Institute (RPI)People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the (inductive) inference that the milk is sour have in common with the (deductive) proof that, say, the square root of two is irrational? Our ability to generate explanations bears striking similarities to our ability to make analogies. Both reflect a capacity to generate inferences and generalizations that go beyond the featural similarities between a novel problem and familiar problems in terms of which the novel problem may be understood. However, a notable difference between analogy-making and explanation-generation is that the former is a process in which a single source situation is used to reason about a single target, whereas the latter often requires the reasoner to integrate multiple sources of knowledge. This small-seeming difference poses a challenge to the task of marshaling our understanding of analogical reasoning in the service of understanding explanation. We describe a model of explanation, derived from a model of analogy, adapted to permit systematic violations of this one-to-one mapping constraint. Simulation results demonstrate that the resulting model can generate explanations for novel explananda and that, like the explanations generated by human reasoners, these explanations vary in their coherence.http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00867/fullmodelinglogicanalogyexplanationLISA |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
John eHummel John eLicato Selmer eBringsjord Selmer eBringsjord |
spellingShingle |
John eHummel John eLicato Selmer eBringsjord Selmer eBringsjord Analogy, Explanation, and Proof Frontiers in Human Neuroscience modeling logic analogy explanation LISA |
author_facet |
John eHummel John eLicato Selmer eBringsjord Selmer eBringsjord |
author_sort |
John eHummel |
title |
Analogy, Explanation, and Proof |
title_short |
Analogy, Explanation, and Proof |
title_full |
Analogy, Explanation, and Proof |
title_fullStr |
Analogy, Explanation, and Proof |
title_full_unstemmed |
Analogy, Explanation, and Proof |
title_sort |
analogy, explanation, and proof |
publisher |
Frontiers Media S.A. |
series |
Frontiers in Human Neuroscience |
issn |
1662-5161 |
publishDate |
2014-11-01 |
description |
People are habitual explanation generators. At its most mundane, our propensity to explain allows us to infer that we should not drink milk that smells sour; at the other extreme, it allows us to establish facts (e.g., theorems in mathematical logic) whose truth was not even known prior to the existence of the explanation (proof). What do the cognitive operations underlying the (inductive) inference that the milk is sour have in common with the (deductive) proof that, say, the square root of two is irrational? Our ability to generate explanations bears striking similarities to our ability to make analogies. Both reflect a capacity to generate inferences and generalizations that go beyond the featural similarities between a novel problem and familiar problems in terms of which the novel problem may be understood. However, a notable difference between analogy-making and explanation-generation is that the former is a process in which a single source situation is used to reason about a single target, whereas the latter often requires the reasoner to integrate multiple sources of knowledge. This small-seeming difference poses a challenge to the task of marshaling our understanding of analogical reasoning in the service of understanding explanation. We describe a model of explanation, derived from a model of analogy, adapted to permit systematic violations of this one-to-one mapping constraint. Simulation results demonstrate that the resulting model can generate explanations for novel explananda and that, like the explanations generated by human reasoners, these explanations vary in their coherence. |
topic |
modeling logic analogy explanation LISA |
url |
http://journal.frontiersin.org/Journal/10.3389/fnhum.2014.00867/full |
work_keys_str_mv |
AT johnehummel analogyexplanationandproof AT johnelicato analogyexplanationandproof AT selmerebringsjord analogyexplanationandproof AT selmerebringsjord analogyexplanationandproof |
_version_ |
1724945304900337664 |