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ODD NUMBER in Cognitive Linguistics of WILLIAM CROFT and D. ALAN CRUSE
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
Announcing the arrival of Valued Associate #679: Cesar Manara
Unicorn Meta Zoo #1: Why another podcast?What does the term “coercion” mean in the context of Cognitive Linguistics?What does a cognitive linguistics researcher actually do in practice?What kinds of maths to learn for understanding dynamical systems in cognitive linguistics?Short summary of Cognitive LinguisticsDoes understanding free word order require a distinct cognitive process?How does flexible and context-dependent Categorisation not imply fuzzy Category Boundaries?Subject-verb number agreement with complex subjectDefinition of “concept” and "conceptual field in cognitive linguisticsWhat is the view of prototype theory regarding features?Is there any bridge between cognitive linguistics and cognitive psychology, beside knowledge representation?
In the subsection 4.3.4.2 The ‘odd number paradox’ of Cognitive Linguistics by W. Croft & D. A. Cruse
We read:
The ‘odd number paradox’ has also been put forward as a problem for
prototype theory. Armstrong et al. (1983) found that people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features. Their proposed solution, the so-called ‘dual representation’ hypothesis, combines the prototype approach and the classical approach (Smith et al. 1974). The idea is that concepts have two representations, which have different functions. There is a ‘core’ representation, which has basically the form of a classical definition. This representation will govern the logical properties of the concept. The other representation is some sort of prototype system which prioritizes the most typical features, and whose function is to allow rapid categorization of instances encountered. With this set-up, the odd-number effect ceases to be a puzzle. However, this conjunction of two theories inherits most of the problems of both of them: in particular, it reinstates a major problem of the classical theory that prototype theory was intended to solve, namely, the fact that for a great many everyday concepts there is no available core definition.
It is clear for me that they speak about conjecture of the two representations of a concept.
But I is unclear for me what do they mean in this sentence 'people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features.'
cognitive-linguistics prototype-theory
edited Apr 11 at 22:49
curiousdannii
2,97431531
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
In the subsection 4.3.4.2 The ‘odd number paradox’ of Cognitive Linguistics by W. Croft & D. A. Cruse
We read:
The ‘odd number paradox’ has also been put forward as a problem for
prototype theory. Armstrong et al. (1983) found that people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features. Their proposed solution, the so-called ‘dual representation’ hypothesis, combines the prototype approach and the classical approach (Smith et al. 1974). The idea is that concepts have two representations, which have different functions. There is a ‘core’ representation, which has basically the form of a classical definition. This representation will govern the logical properties of the concept. The other representation is some sort of prototype system which prioritizes the most typical features, and whose function is to allow rapid categorization of instances encountered. With this set-up, the odd-number effect ceases to be a puzzle. However, this conjunction of two theories inherits most of the problems of both of them: in particular, it reinstates a major problem of the classical theory that prototype theory was intended to solve, namely, the fact that for a great many everyday concepts there is no available core definition.
It is clear for me that they speak about conjecture of the two representations of a concept.
But I is unclear for me what do they mean in this sentence 'people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features.'
cognitive-linguistics prototype-theory
edited Apr 11 at 22:49
curiousdannii
2,97431531
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
In the subsection 4.3.4.2 The ‘odd number paradox’ of Cognitive Linguistics by W. Croft & D. A. Cruse
We read:
The ‘odd number paradox’ has also been put forward as a problem for
prototype theory. Armstrong et al. (1983) found that people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features. Their proposed solution, the so-called ‘dual representation’ hypothesis, combines the prototype approach and the classical approach (Smith et al. 1974). The idea is that concepts have two representations, which have different functions. There is a ‘core’ representation, which has basically the form of a classical definition. This representation will govern the logical properties of the concept. The other representation is some sort of prototype system which prioritizes the most typical features, and whose function is to allow rapid categorization of instances encountered. With this set-up, the odd-number effect ceases to be a puzzle. However, this conjunction of two theories inherits most of the problems of both of them: in particular, it reinstates a major problem of the classical theory that prototype theory was intended to solve, namely, the fact that for a great many everyday concepts there is no available core definition.
It is clear for me that they speak about conjecture of the two representations of a concept.
But I is unclear for me what do they mean in this sentence 'people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features.'
cognitive-linguistics prototype-theory
edited Apr 11 at 22:49
curiousdannii
2,97431531
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
In the subsection 4.3.4.2 The ‘odd number paradox’ of Cognitive Linguistics by W. Croft & D. A. Cruse
We read:
The ‘odd number paradox’ has also been put forward as a problem for
prototype theory. Armstrong et al. (1983) found that people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features. Their proposed solution, the so-called ‘dual representation’ hypothesis, combines the prototype approach and the classical approach (Smith et al. 1974). The idea is that concepts have two representations, which have different functions. There is a ‘core’ representation, which has basically the form of a classical definition. This representation will govern the logical properties of the concept. The other representation is some sort of prototype system which prioritizes the most typical features, and whose function is to allow rapid categorization of instances encountered. With this set-up, the odd-number effect ceases to be a puzzle. However, this conjunction of two theories inherits most of the problems of both of them: in particular, it reinstates a major problem of the classical theory that prototype theory was intended to solve, namely, the fact that for a great many everyday concepts there is no available core definition.
It is clear for me that they speak about conjecture of the two representations of a concept.
But I is unclear for me what do they mean in this sentence 'people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features.'
cognitive-linguistics prototype-theory
cognitive-linguistics prototype-theory
edited Apr 11 at 22:49
curiousdannii
2,97431531
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 11 at 22:49
curiousdannii
2,97431531
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited Apr 11 at 22:49
curiousdannii
2,97431531
edited Apr 11 at 22:49
curiousdannii
2,97431531
edited Apr 11 at 22:49
curiousdannii
2,97431531
2,97431531
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
asked Apr 11 at 18:10
Ana VardosanidzeAna Vardosanidze
183
183
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Ana Vardosanidze is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
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"people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features" means that you can ask people things like "which is a better example of an odd number, 19 or 1001" and at least some of them will answer with one or the other (I'd guess most people will go with 19) rather than rejecting the question by saying something like "they're both odd numbers, since neither is divisible by two, so they're equally good examples". Presumably whatever sources Croft and Cruse cite would have details on the exact nature of the experiments that have been done.
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
4
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
4
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
1
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
1
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
|
show 1 more comment
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1 Answer
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"people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features" means that you can ask people things like "which is a better example of an odd number, 19 or 1001" and at least some of them will answer with one or the other (I'd guess most people will go with 19) rather than rejecting the question by saying something like "they're both odd numbers, since neither is divisible by two, so they're equally good examples". Presumably whatever sources Croft and Cruse cite would have details on the exact nature of the experiments that have been done.
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
4
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
4
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
1
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
1
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
|
show 1 more comment
"people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features" means that you can ask people things like "which is a better example of an odd number, 19 or 1001" and at least some of them will answer with one or the other (I'd guess most people will go with 19) rather than rejecting the question by saying something like "they're both odd numbers, since neither is divisible by two, so they're equally good examples". Presumably whatever sources Croft and Cruse cite would have details on the exact nature of the experiments that have been done.
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
4
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
4
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
1
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
1
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
|
show 1 more comment
"people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features" means that you can ask people things like "which is a better example of an odd number, 19 or 1001" and at least some of them will answer with one or the other (I'd guess most people will go with 19) rather than rejecting the question by saying something like "they're both odd numbers, since neither is divisible by two, so they're equally good examples". Presumably whatever sources Croft and Cruse cite would have details on the exact nature of the experiments that have been done.
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
"people will grade ODD NUMBERS for centrality, even though the category ODD NUMBER has a clear definition in terms of necessary and sufficient features" means that you can ask people things like "which is a better example of an odd number, 19 or 1001" and at least some of them will answer with one or the other (I'd guess most people will go with 19) rather than rejecting the question by saying something like "they're both odd numbers, since neither is divisible by two, so they're equally good examples". Presumably whatever sources Croft and Cruse cite would have details on the exact nature of the experiments that have been done.
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
answered Apr 11 at 18:35
sumelicsumelic
10.2k12156
10.2k12156
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
4
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
4
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
1
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
1
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
|
show 1 more comment
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
4
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
4
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
1
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
1
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
Thank you for your answer, it was very useful one. I have an additional question: Why do they call it paradox? Does the paradox mean choosing one of the odd numbers, when they are both the same type and one is not batter than another?
– Ana Vardosanidze
Apr 11 at 19:25
4
4
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
The paradox is that the definition of odd numbers means that no odd number is more odd-like than another; but people act as if they were. And yet anybody who knows what's an odd number knows the definition. Therefore people seem to act in contradiction to the definition they themselves are using.
– melboiko
Apr 11 at 23:15
4
4
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
Probably people would say that 444 was more even than 716; if we're presented with a forced choice, we'll cope. That doesn't say much about basic representations, though.
– jlawler
Apr 11 at 23:54
1
1
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
With the sight of the eye you can tell that a group of 1, 3, or 5 is odd and 2, 4, or 6 even. Larger numbers are undeterminable by eye-sight and need reference to counting or mathematics. And even then: How often does a counting error occur in manual counting?
– jknappen
Apr 12 at 10:05
1
1
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
@jlawler Indeed, and one way to cope might be to append to the question: "...better example to demonstrate what, to whom?" :)
– Luke Sawczak
Apr 12 at 12:42
|
show 1 more comment
Ana Vardosanidze is a new contributor. Be nice, and check out our Code of Conduct.
Ana Vardosanidze is a new contributor. Be nice, and check out our Code of Conduct.
Ana Vardosanidze is a new contributor. Be nice, and check out our Code of Conduct.
Ana Vardosanidze is a new contributor. Be nice, and check out our Code of Conduct.
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