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I don't understand the concept of “Information content of a sentenceâ€
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I came across this concept in my course literature. Here's a snippet from that chapter:
"An essential component in logical reasoning is how much information a sentence contains. If S is a sentence, the number of 1's in the truth table for S can be seen as a measure of the information content in the sentence. The more 1's a sentence has the less information the sentence contains"
Thanks for your help.
logic
asked 5 hours ago
Mogul Khan
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up vote
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I came across this concept in my course literature. Here's a snippet from that chapter:
"An essential component in logical reasoning is how much information a sentence contains. If S is a sentence, the number of 1's in the truth table for S can be seen as a measure of the information content in the sentence. The more 1's a sentence has the less information the sentence contains"
Thanks for your help.
logic
asked 5 hours ago
Mogul Khan
262
New contributor
Mogul Khan 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 |Â
up vote
4
down vote
favorite
up vote
4
down vote
favorite
I came across this concept in my course literature. Here's a snippet from that chapter:
"An essential component in logical reasoning is how much information a sentence contains. If S is a sentence, the number of 1's in the truth table for S can be seen as a measure of the information content in the sentence. The more 1's a sentence has the less information the sentence contains"
Thanks for your help.
logic
asked 5 hours ago
Mogul Khan
262
New contributor
Mogul Khan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I came across this concept in my course literature. Here's a snippet from that chapter:
"An essential component in logical reasoning is how much information a sentence contains. If S is a sentence, the number of 1's in the truth table for S can be seen as a measure of the information content in the sentence. The more 1's a sentence has the less information the sentence contains"
Thanks for your help.
logic
logic
asked 5 hours ago
Mogul Khan
262
New contributor
Mogul Khan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Mogul Khan
262
New contributor
Mogul Khan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Mogul Khan
262
New contributor
Mogul Khan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 5 hours ago
Mogul Khan
262
asked 5 hours ago
Mogul Khan
262
262
New contributor
Mogul Khan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Mogul Khan is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Mogul Khan 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 |Â
add a comment |Â
2 Answers
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up vote
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I assume you are asking for an intuitive explanation.
Imagine the police are looking for a killer, and there are only 20 remaining suspects, one of which is missing an arm. There are several witnesses. One says:
The killer had 2 arms.
This sentence is not very informative, right? Why not? It's because it is true for 19 of 20 suspects (it has $19$ ones in the truth table).
On the other hand, if the witness says
The killer was a man
and half the suspects are male, then that is a more informative sentene (it has $10$ ones in its truth table), and if a witness says
The killer was 180cm tall, red haired, wore glasses and a ring on his right hand
then it's quite likely that there is only one one in the truth table of that sentence, which is therefore very informative.
answered 5 hours ago
5xum
82.8k383147
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See Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921) :
4.46 Among the possible groups of truth-conditions [i.e. lines in the truth table] there are two extreme cases.
In one of these cases the proposition is true for all the
truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.
In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory.
In the first case we call the proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say: tautologies and contradictions show that they say nothing.
A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense [i.e. they convey no "information"].
[...] (For example, I know nothing about the weather when I know that it is either raining or not raining.)
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
add a comment |Â
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
6
down vote
accepted
I assume you are asking for an intuitive explanation.
Imagine the police are looking for a killer, and there are only 20 remaining suspects, one of which is missing an arm. There are several witnesses. One says:
The killer had 2 arms.
This sentence is not very informative, right? Why not? It's because it is true for 19 of 20 suspects (it has $19$ ones in the truth table).
On the other hand, if the witness says
The killer was a man
and half the suspects are male, then that is a more informative sentene (it has $10$ ones in its truth table), and if a witness says
The killer was 180cm tall, red haired, wore glasses and a ring on his right hand
then it's quite likely that there is only one one in the truth table of that sentence, which is therefore very informative.
answered 5 hours ago
5xum
82.8k383147
add a comment |Â
up vote
6
down vote
accepted
I assume you are asking for an intuitive explanation.
Imagine the police are looking for a killer, and there are only 20 remaining suspects, one of which is missing an arm. There are several witnesses. One says:
The killer had 2 arms.
This sentence is not very informative, right? Why not? It's because it is true for 19 of 20 suspects (it has $19$ ones in the truth table).
On the other hand, if the witness says
The killer was a man
and half the suspects are male, then that is a more informative sentene (it has $10$ ones in its truth table), and if a witness says
The killer was 180cm tall, red haired, wore glasses and a ring on his right hand
then it's quite likely that there is only one one in the truth table of that sentence, which is therefore very informative.
answered 5 hours ago
5xum
82.8k383147
add a comment |Â
up vote
6
down vote
accepted
up vote
6
down vote
accepted
I assume you are asking for an intuitive explanation.
Imagine the police are looking for a killer, and there are only 20 remaining suspects, one of which is missing an arm. There are several witnesses. One says:
The killer had 2 arms.
This sentence is not very informative, right? Why not? It's because it is true for 19 of 20 suspects (it has $19$ ones in the truth table).
On the other hand, if the witness says
The killer was a man
and half the suspects are male, then that is a more informative sentene (it has $10$ ones in its truth table), and if a witness says
The killer was 180cm tall, red haired, wore glasses and a ring on his right hand
then it's quite likely that there is only one one in the truth table of that sentence, which is therefore very informative.
answered 5 hours ago
5xum
82.8k383147
I assume you are asking for an intuitive explanation.
Imagine the police are looking for a killer, and there are only 20 remaining suspects, one of which is missing an arm. There are several witnesses. One says:
The killer had 2 arms.
This sentence is not very informative, right? Why not? It's because it is true for 19 of 20 suspects (it has $19$ ones in the truth table).
On the other hand, if the witness says
The killer was a man
and half the suspects are male, then that is a more informative sentene (it has $10$ ones in its truth table), and if a witness says
The killer was 180cm tall, red haired, wore glasses and a ring on his right hand
then it's quite likely that there is only one one in the truth table of that sentence, which is therefore very informative.
answered 5 hours ago
5xum
82.8k383147
answered 5 hours ago
5xum
82.8k383147
answered 5 hours ago
5xum
82.8k383147
answered 5 hours ago
5xum
82.8k383147
82.8k383147
add a comment |Â
add a comment |Â
up vote
0
down vote
See Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921) :
4.46 Among the possible groups of truth-conditions [i.e. lines in the truth table] there are two extreme cases.
In one of these cases the proposition is true for all the
truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.
In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory.
In the first case we call the proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say: tautologies and contradictions show that they say nothing.
A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense [i.e. they convey no "information"].
[...] (For example, I know nothing about the weather when I know that it is either raining or not raining.)
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
add a comment |Â
up vote
0
down vote
See Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921) :
4.46 Among the possible groups of truth-conditions [i.e. lines in the truth table] there are two extreme cases.
In one of these cases the proposition is true for all the
truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.
In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory.
In the first case we call the proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say: tautologies and contradictions show that they say nothing.
A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense [i.e. they convey no "information"].
[...] (For example, I know nothing about the weather when I know that it is either raining or not raining.)
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
add a comment |Â
up vote
0
down vote
up vote
0
down vote
See Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921) :
4.46 Among the possible groups of truth-conditions [i.e. lines in the truth table] there are two extreme cases.
In one of these cases the proposition is true for all the
truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.
In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory.
In the first case we call the proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say: tautologies and contradictions show that they say nothing.
A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense [i.e. they convey no "information"].
[...] (For example, I know nothing about the weather when I know that it is either raining or not raining.)
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
See Ludwig Wittgenstein's Tractatus Logico-Philosophicus (1921) :
4.46 Among the possible groups of truth-conditions [i.e. lines in the truth table] there are two extreme cases.
In one of these cases the proposition is true for all the
truth-possibilities of the elementary propositions. We say that the truth-conditions are tautological.
In the second case the proposition is false for all the truth-possibilities: the truth-conditions are contradictory.
In the first case we call the proposition a tautology; in the second, a contradiction.
4.461 Propositions show what they say: tautologies and contradictions show that they say nothing.
A tautology has no truth-conditions, since it is unconditionally true: and a contradiction is true on no condition.
Tautologies and contradictions lack sense [i.e. they convey no "information"].
[...] (For example, I know nothing about the weather when I know that it is either raining or not raining.)
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
answered 35 mins ago
Mauro ALLEGRANZA
61.3k446105
61.3k446105
add a comment |Â
add a comment |Â
Mogul Khan is a new contributor. Be nice, and check out our Code of Conduct.
Mogul Khan is a new contributor. Be nice, and check out our Code of Conduct.
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