Propositional Logic Symposia - [4] ? Translating English into Logic

@VideCorSpoon,

If you wanted to just translate the second part on its own, I would do it as J -> ~H.

@Pangloss,

Pangloss wrote:

Nice thread, but just had to comment on this. "But" usually would be translated into an AND operator, not a conditional. Now maybe if it were worded something like "A but for B", it could be translated differently, though it seems that standard practice is usually to take AND from "but".

Now that you've got this posted we just need a follow-up on using truth tables to check validity of arguments. That would come in useful around here. :cool:

My bad, you are right! "but" does indeed translate into conjunction. Thanks!

As to the truth tables, there is a thread on that here; http://www.philosophyforum.com/forum/philosophy-forums/branches-philosophy/logic/1449-propositional-logic-symposia-2-truth-funct-logic-truth-tables-conjunctions.html

I dont think I put complex truth tables in there though, just basic truth tables. I'll have to add something in.

@VideCorSpoon,

Nevermind, I found your other threads where you go into truth tables and determining validity of an argument. You've done a great job with these, it should be required reading for everyone joining this forum. Studying logic is a good way to practice thinking rationally, and that will make us all more productive on this forum and elsewhere.

@Pangloss,

Thank you VideCorSpoon. I am really obliged. Smile

@Arif phil,

Arif;78955 wrote:

Thank you VideCorSpoon. I am really obliged.

Absolutely no problem at all. If you have any questions or anything like that about the propositional logic symposia, I'm happy to help out if I can.

@VideCorSpoon,

VideCorSpoon;15175 wrote:

Take this sentence; "It is not the case that John is funny and Mary is funny."

1.First way, isolate the simple sentences; "It is not the case that John is funny and Mary is funny."
2.Translate with the main connective; J & M
Now you can interpret the sentence again this way? please hang in there with me.
3."It is not the case that John is funny, but Mary is funny"
Translating the sentence again this way makes it easier for you to translate.
4.Isolate the simple sentences; "It is not the case that John is funny, but Mary is funny"
5.Isolate the connective; but.
Here's the thing, in so many words, "but" is equivocal with "and." Just remember that.
6.Translate as; J & M
7.Incorporate the negation, "It is not the case that?" as ~.
8.Translate the whole sentence as; ~J & M.

I'm confused here, because the use of the word "and" seems to allow for two separate meanings. It could be ~J & M, but if you took it to mean "It is not the case that (John is funny and Mary is funny)." Then it could mean that the negation is applying to just the conjuction of J and M, making it ~(J & M)

@Kroni,

Kroni;101340 wrote:

I'm confused here, because the use of the word "and" seems to allow for two separate meanings. It could be ~J & M, but if you took it to mean "It is not the case that (John is funny and Mary is funny)." Then it could mean that the negation is applying to just the conjuction of J and M, making it ~(J & M)

You are concerned for a good reason. There are multiple different meanings of "and" in english. (See N. Swartz, R. Bradley, 1979 for a short survey of these.) I usually distinguish between the logical "and" and the grammatical "and". The grammatical "and"'s function is also to save time by not stating the same predicate twice. Consider this example:

[INDENT]1. John and Mary are not alive.

[/INDENT](1) can be interpreted as:

[INDENT]a. ?Aj∧?Am
b. Aj∧?Am

[/INDENT]The first is the most common interpretation. The function of "and" there is both that of logical conjunction and that of saving time writing. The predicate "is not alive" is intended to be applied to both particulars (John and Mary). Another way of writing (1) is:

[INDENT]2. John is not alive and Mary is not alive.

[/INDENT]This is structurally/syntactically closer to interpretation (a).

A very literal reading of (1) would yield interpretation (b).

---

Also, it is sometimes not clear whether the negation (which is a kind of predicate) applies to only the first conjunct as in ?J∧M, or the whole conjunction as in ?(J∧M) (or equivalently ?J∧?). I usually use parentheses, even in plain english to remove this ambiguity.

@Kroni,

Kroni;101340 wrote:

I'm confused here, because the use of the word "and" seems to allow for two separate meanings. It could be ~J & M, but if you took it to mean "It is not the case that (John is funny and Mary is funny)." Then it could mean that the negation is applying to just the conjuction of J and M, making it ~(J & M)

I think it is clear that the negation operator has the wide scope and that it ranges over the whole statement, and not over just the individual statements.That is, I think it should be formulated as, ~(J & M).
It would be clearer to us the word "both", so the difference would be between:
1.Both John and Mary are not funny. And,
2.John and Mary are not both funny.

1. is, ~(J & M)
2. is, (~J & ~M)

But not, ~J & M.

@VideCorSpoon,

So is there any formal rule saying that the negation applies to the entire statement? If there is no precedent to assign the ~ to the entire conjunction, then it is still open for interpretation.

@Kroni,

Kroni;101353 wrote:

So is there any formal rule saying that the negation applies to the entire statement? If there is no precedent to assign the ~ to the entire conjunction, then it is still open for interpretation.

Of course. But some interpretations are better than others.

Joe and Mary did not both go up the hill.

1. ~( J & M) ?
2. ~J & ~M ?

@kennethamy,

kennethamy;101359 wrote:

Of course. But some interpretations are better than others.

Joe and Mary did not both go up the hill.

1. ~( J & M) ?
2. ~J & ~M ?

True, but ~(J & M) and ~J & ~M really mean the same thing. The latter is just a less abbreviated notation of the former. But when you say "It is not a fact that John is funny and Mary is funny." This can be interpreted with two different notations that have different meanings. ~J & M would mean that it is not a fact that John is funny and it is a fact that Mary is funny. ~(J & M) would mean that it is not a fact that john is funny and it is NOT a fact that Mary is funny.

@Kroni,

Kroni;101353 wrote:

So is there any formal rule saying that the negation applies to the entire statement? If there is no precedent to assign the ~ to the entire conjunction, then it is still open for interpretation.

There is no formal rule, but there are tendencies in normal languages in general and in english.

---------- Post added 11-03-2009 at 12:53 AM ----------

Kroni;101362 wrote:

True, but ~(J & M) and ~J & ~M really mean the same thing. The latter is just a less abbreviated notation of the former. But when you say "It is not a fact that John is funny and Mary is funny." This can be interpreted with two different notations that have different meanings. ~J & M would mean that it is not a fact that John is funny and it is a fact that Mary is funny. ~(J & M) would mean that it is not a fact that john is funny and it is NOT a fact that Mary is funny.

They do not mean the same, but the propositions that they express are logically equivalent. You seem to be confusing these two.

@Emil,

Emil;101367 wrote:

They do not mean the same, but the propositions that they express are logically equivalent. You seem to be confusing these two.

You're right. I was looking at it wrong but that do have different meanings. I would say in that situation the correct notation would be ~(J & M) because "Joe and Mary did not both go up the hill." Implies that even though they both did not go up the hill, one may still have. Therefore ~J & ~M would be inaccurate because it says that neither of them could have gone up the hill.

@Kroni,

Kroni;101362 wrote:

True, but ~(J & M) and ~J & ~M really mean the same thing. .

\
But they do not. To prove that, place both on a truth table. They have different truth values.

@Emil,

Emil;101343 wrote:

Consider this example:
[INDENT]1. John and Mary are not alive.

[/INDENT](1) can be interpreted as:
[INDENT]a. ?Aj∧?Am
b. Aj∧?Am

[/INDENT]The first is the most common interpretation. The function of "and" there is both that of logical conjunction and that of saving time writing. The predicate "is not alive" is intended to be applied to both particulars (John and Mary). Another way of writing (1) is:
[INDENT]2. John is not alive and Mary is not alive.

[/INDENT]This is structurally/syntactically closer to interpretation (a).

A very literal reading of (1) would yield interpretation (b).

Sorry, but no native english speaker beyond grade school would read statement 1. and interpret it as (b). "Are" here is used as a third-person plural form of "be", and this means that both John and Mary are not alive. Proper grammar does not allow for ambiguity in this statement, though you could certainly come up with many other statements where this can be an issue.

@Pangloss,

Pangloss;101391 wrote:

Sorry, but no native english speaker beyond grade school would read statement 1. and interpret it as (b). "Are" here is used as a third-person plural form of "be", and this means that both John and Mary are not alive. Proper grammar does not allow for ambiguity in this statement, though you could certainly come up with many other statements where this can be an issue.

Yes, consider the statement, Mary sat next to the old men and women. What is the scope of "old" there?

That is why interpolating the word "both" is important. Consider the difference between:

1. John and Mary are not both alive. And,
2. Both John and Mary are not alive.

The difference is between: "not both" and "both not".

@kennethamy,

kennethamy;101373 wrote:

\
But they do not. To prove that, place both on a truth table. They have different truth values.

Yes. I was wrong in stating that they are logically equivalent. They are not of course. I would post the truth table but this board doesn't support tables.

---------- Post added 11-03-2009 at 03:07 PM ----------

Pangloss;101391 wrote:

Sorry, but no native english speaker beyond grade school would read statement 1. and interpret it as (b). "Are" here is used as a third-person plural form of "be", and this means that both John and Mary are not alive. Proper grammar does not allow for ambiguity in this statement, though you could certainly come up with many other statements where this can be an issue.

Yes my example is bad.

@kennethamy,

kennethamy;101406 wrote:

Yes, consider the statement, Mary sat next to the old men and women. What is the scope of "old" there?

That is why interpolating the word "both" is important. Consider the difference between:

1. John and Mary are not both alive. And,
2. Both John and Mary are not alive.

The difference is between: "not both" and "both not".

Yes, your first two examples are indeed ambiguous. Number 2 is equivalent to what emil posted, you can take or leave 'both' in that case, the meaning is the same.

A common logical mistake is the 'misplaced modifier'. Something like, "The young girl was walking the dog in a short skirt." It's funny to read, because people automatically pick up on the ambiguity and logical lapse in such a statement.

Philosophy Forum

Propositional Logic Symposia - [4] ? Translating English into Logic

Quick Links

My Account

able2know