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Can someone explain this logical statement?

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2

1

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced mathematics.

Taken from the book "A Short Introduction to Logic":

"Suppose we think of the relevant domain of objects as causes and effects, and write "x is caused by y" as xCy:

1). ∀x ∃y xCy
2).∃y ∀x xCy

Can someone rewrite this in plain English? I'm not sure what's happening here. Where do I plug in words like "and," "or," "true," "if," etc.? What does this sentence mean step by step?

I know that it is very simple, but I'm lost without the other logical symbols.

logic

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asked 9 hours ago

SermoSermo

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2

1

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced mathematics.

Taken from the book "A Short Introduction to Logic":

"Suppose we think of the relevant domain of objects as causes and effects, and write "x is caused by y" as xCy:

1). ∀x ∃y xCy
2).∃y ∀x xCy

Can someone rewrite this in plain English? I'm not sure what's happening here. Where do I plug in words like "and," "or," "true," "if," etc.? What does this sentence mean step by step?

I know that it is very simple, but I'm lost without the other logical symbols.

logic

share|improve this question

asked 9 hours ago

SermoSermo

43722 silver badges77 bronze badges

add a comment | 

I have been trying to teach myself philosophical logic, but my mind is completely stuck. I cannot seem to understand the abstractions, which is unusual for me given that I have taken very advanced mathematics.

Taken from the book "A Short Introduction to Logic":

"Suppose we think of the relevant domain of objects as causes and effects, and write "x is caused by y" as xCy:

1). ∀x ∃y xCy
2).∃y ∀x xCy

Can someone rewrite this in plain English? I'm not sure what's happening here. Where do I plug in words like "and," "or," "true," "if," etc.? What does this sentence mean step by step?

I know that it is very simple, but I'm lost without the other logical symbols.

logic

share|improve this question

asked 9 hours ago

SermoSermo

43722 silver badges77 bronze badges

share|improve this question

asked 9 hours ago

SermoSermo

43722 silver badges77 bronze badges

share|improve this question

asked 9 hours ago

SermoSermo

43722 silver badges77 bronze badges

asked 9 hours ago

SermoSermo

43722 silver badges77 bronze badges

asked 9 hours ago

SermoSermo

43722 silver badges77 bronze badges

2 Answers
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1). ∀x ∃y xCy 

Literally: for every x, there exists some y such that x is caused by y. This means that every object x has at least one object y that causes it.

2).∃y ∀x xCy

Literally: there exists some y such that every x is caused by y. This means that there is some object y that is the cause of every object x.

I'm not sure what your text is asking for here. Does it want you to explain these phrases in natural language? Does it want you to evaluate them? Does it want you to combine them somehow, or prove a result? Evaluation would lead you to true/false conditions; combining them would involve 'and,' 'or,' and other logical connectors; trying to prove some result from these premises would likely involve both. What does the text want?

share|improve this answer

edited 9 hours ago

answered 9 hours ago

Ted WrigleyTed Wrigley

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Ted Wrigley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Whoops, misread it. easy enough to fix, though...
  
  – Ted Wrigley
  9 hours ago
  

  
  
  
  

add a comment | 

0

This is a formal description of causality.

The text specifies a "domain of discourse" or Universe (U).

U = {The set of causes and effects}

This isn't explicitly written but then the universe is basically divided into two sets of objects.

X = {the set of causes}

Y = {the set of effects}

Note: the difference in case is important.

x = an arbitrary element of X

y = an arbitrary element of Y

Then it defines a relationship between those sets.

C ≔ "causes"

In plain English, the statements mean that for any arbitrary cause, there is a corresponding effect and visa versa.

Conditionals or Boolean operators not required.

share|improve this answer

edited 6 hours ago

answered 6 hours ago

user40358user40358

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2

1). ∀x ∃y xCy 

Literally: for every x, there exists some y such that x is caused by y. This means that every object x has at least one object y that causes it.

2).∃y ∀x xCy

Literally: there exists some y such that every x is caused by y. This means that there is some object y that is the cause of every object x.

I'm not sure what your text is asking for here. Does it want you to explain these phrases in natural language? Does it want you to evaluate them? Does it want you to combine them somehow, or prove a result? Evaluation would lead you to true/false conditions; combining them would involve 'and,' 'or,' and other logical connectors; trying to prove some result from these premises would likely involve both. What does the text want?

share|improve this answer

edited 9 hours ago

answered 9 hours ago

Ted WrigleyTed Wrigley

26933 bronze badges

New contributor

Ted Wrigley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Whoops, misread it. easy enough to fix, though...
  
  – Ted Wrigley
  9 hours ago
  

  
  
  
  

add a comment | 

2

1). ∀x ∃y xCy 

Literally: for every x, there exists some y such that x is caused by y. This means that every object x has at least one object y that causes it.

2).∃y ∀x xCy

Literally: there exists some y such that every x is caused by y. This means that there is some object y that is the cause of every object x.

I'm not sure what your text is asking for here. Does it want you to explain these phrases in natural language? Does it want you to evaluate them? Does it want you to combine them somehow, or prove a result? Evaluation would lead you to true/false conditions; combining them would involve 'and,' 'or,' and other logical connectors; trying to prove some result from these premises would likely involve both. What does the text want?

share|improve this answer

edited 9 hours ago

answered 9 hours ago

Ted WrigleyTed Wrigley

26933 bronze badges

New contributor

Ted Wrigley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  
  Whoops, misread it. easy enough to fix, though...
  
  – Ted Wrigley
  9 hours ago
  

  
  
  
  

add a comment | 

1). ∀x ∃y xCy 

Literally: for every x, there exists some y such that x is caused by y. This means that every object x has at least one object y that causes it.

2).∃y ∀x xCy

Literally: there exists some y such that every x is caused by y. This means that there is some object y that is the cause of every object x.

I'm not sure what your text is asking for here. Does it want you to explain these phrases in natural language? Does it want you to evaluate them? Does it want you to combine them somehow, or prove a result? Evaluation would lead you to true/false conditions; combining them would involve 'and,' 'or,' and other logical connectors; trying to prove some result from these premises would likely involve both. What does the text want?

share|improve this answer

edited 9 hours ago

answered 9 hours ago

Ted WrigleyTed Wrigley

26933 bronze badges

New contributor

Ted Wrigley is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

1). ∀x ∃y xCy 

2).∃y ∀x xCy

share|improve this answer

edited 9 hours ago

answered 9 hours ago

Ted WrigleyTed Wrigley

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answered 9 hours ago

Ted WrigleyTed Wrigley

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answered 9 hours ago

Ted WrigleyTed Wrigley

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0

This is a formal description of causality.

The text specifies a "domain of discourse" or Universe (U).

U = {The set of causes and effects}

This isn't explicitly written but then the universe is basically divided into two sets of objects.

X = {the set of causes}

Y = {the set of effects}

Note: the difference in case is important.

x = an arbitrary element of X

y = an arbitrary element of Y

Then it defines a relationship between those sets.

C ≔ "causes"

In plain English, the statements mean that for any arbitrary cause, there is a corresponding effect and visa versa.

Conditionals or Boolean operators not required.

share|improve this answer

edited 6 hours ago

answered 6 hours ago

user40358user40358

111 bronze badge

New contributor

user40358 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 | 

0

This is a formal description of causality.

The text specifies a "domain of discourse" or Universe (U).

U = {The set of causes and effects}

This isn't explicitly written but then the universe is basically divided into two sets of objects.

X = {the set of causes}

Y = {the set of effects}

Note: the difference in case is important.

x = an arbitrary element of X

y = an arbitrary element of Y

Then it defines a relationship between those sets.

C ≔ "causes"

In plain English, the statements mean that for any arbitrary cause, there is a corresponding effect and visa versa.

Conditionals or Boolean operators not required.

share|improve this answer

edited 6 hours ago

answered 6 hours ago

user40358user40358

111 bronze badge

New contributor

user40358 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 | 

This is a formal description of causality.

The text specifies a "domain of discourse" or Universe (U).

U = {The set of causes and effects}

This isn't explicitly written but then the universe is basically divided into two sets of objects.

X = {the set of causes}

Y = {the set of effects}

Note: the difference in case is important.

x = an arbitrary element of X

y = an arbitrary element of Y

Then it defines a relationship between those sets.

C ≔ "causes"

In plain English, the statements mean that for any arbitrary cause, there is a corresponding effect and visa versa.

Conditionals or Boolean operators not required.

share|improve this answer

edited 6 hours ago

answered 6 hours ago

user40358user40358

111 bronze badge

New contributor

user40358 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

U = {The set of causes and effects}

X = {the set of causes}

Y = {the set of effects}

x = an arbitrary element of X

y = an arbitrary element of Y

C ≔ "causes"

share|improve this answer

edited 6 hours ago

answered 6 hours ago

user40358user40358

111 bronze badge

New contributor

user40358 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 6 hours ago

user40358user40358

111 bronze badge

New contributor

user40358 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

answered 6 hours ago

user40358user40358

111 bronze badge