When Logic Equates to Knowledge

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hue-man
 
Reply Tue 23 Feb, 2010 08:25 pm
Does logic only equate to knowledge in analytic propositions? Can synthetic propositions be verified with logical decidability if there's only one logical conclusion?
 
Reconstructo
 
Reply Tue 23 Feb, 2010 08:30 pm
@hue-man,
hue-man;131687 wrote:
Does logic only equate to knowledge in analytic propositions?


I think imperfect but useful knowledge extends beyond analytic propositions.

---------- Post added 02-23-2010 at 09:34 PM ----------

hue-man;131687 wrote:
Can synthetic propositions be verified with logical decidability if there's only one logical conclusion?


If by "logical decidability" you mean tautological certainty, I would say no.
 
Pyrrho
 
Reply Thu 25 Feb, 2010 10:51 am
@hue-man,
hue-man;131687 wrote:
Does logic only equate to knowledge in analytic propositions? Can synthetic propositions be verified with logical decidability if there's only one logical conclusion?


Your question is a bit unclear, so I am unsure whether the following will address your concerns or not. If I know that a particular man is Roman, and if I know that all Romans are Italians, then I could deduce that that particular man is Italian. But that, of course, is dependent upon me knowing the premises, which would need to be known from something other than just pure logic.
 
kennethamy
 
Reply Thu 25 Feb, 2010 11:16 am
@hue-man,
hue-man;131687 wrote:
Does logic only equate to knowledge in analytic propositions? Can synthetic propositions be verified with logical decidability if there's only one logical conclusion?


A logical conclusion from what? What is desperately needed here are some examples of what you are thinking of. That will concentrate your mind, and ours too. I don't think your question is specific enough to be answerable. I don't know what you have in mind. To repeat, what is needed is an example or two.
 
hue-man
 
Reply Thu 25 Feb, 2010 12:04 pm
@Pyrrho,
Pyrrho;132331 wrote:
Your question is a bit unclear, so I am unsure whether the following will address your concerns or not. If I know that a particular man is Roman, and if I know that all Romans are Italians, then I could deduce that that particular man is Italian. But that, of course, is dependent upon me knowing the premises, which would need to be known from something other than just pure logic.


That's an analytic proposition. All Romans are Italian by definition.
 
kennethamy
 
Reply Thu 25 Feb, 2010 12:09 pm
@hue-man,
hue-man;132365 wrote:
That's an analytic proposition. All Romans are Italian by definition.


I doubt that. It certainly was not true when Italy was not a country. And it is certainly possible that some Romans are not citizens of Italy. As I am told is about Berliners and Germany.
 
hue-man
 
Reply Thu 25 Feb, 2010 12:34 pm
@kennethamy,
kennethamy;132368 wrote:
I doubt that. It certainly was not true when Italy was not a country. And it is certainly possible that some Romans are not citizens of Italy. As I am told is about Berliners and Germany.


If we're speaking about the present era then every Roman is an Italian by definition. Also, wasn't Rome always a part of the land mass named Italia? Wouldn't that make all Romans Italian by geographical association? Weren't all Spartans Greek before the unification of the city-states?

How can a modern Roman not be a citizen of Italy if they were born in Rome?
 
Pyrrho
 
Reply Thu 25 Feb, 2010 12:38 pm
@hue-man,
hue-man;132365 wrote:
That's an analytic proposition. All Romans are Italian by definition.


No, it is a contingent proposition. If another country, say France (in order to give us a name to make our lives easier), had taken over Italy 200 years ago and still had it to this day, or just the part of Italy that includes Rome, then being a Roman would make one French, not Italian.

We can see this sort of thing clearly when thinking about people who are French, and not part of the Roman Empire (and therefore not Roman in another sense of that word), simply due to historical facts.

Being Roman (in the sense it was intended in my original example), means being from the city of Rome. And that is regardless of whether or not Italy has possession of it, so being also Italian is not a part of the definition of being a Roman at all.
 
kennethamy
 
Reply Thu 25 Feb, 2010 12:45 pm
@hue-man,
hue-man;132382 wrote:


How can a modern Roman not be a citizen of Italy if they were born in Rome?


They can't legally speaking (I suppose). But that doesn't mean it is true by definition. It is not part of the meaning of the term "Roman" or "Italian" that all Romans are Italians. A person who spoke perfect English, but who knew nothing about politics, or of geography, would not know that all Romans are Italians. That proposition (if true) is a legal and geographical (or ethnic) truth. It is not a definitional truth. (Quick. Are all citizens of Ascuncion citizens of Bolivia?).
 
hue-man
 
Reply Thu 25 Feb, 2010 09:00 pm
@kennethamy,
kennethamy;132391 wrote:
They can't legally speaking (I suppose). But that doesn't mean it is true by definition. It is not part of the meaning of the term "Roman" or "Italian" that all Romans are Italians. A person who spoke perfect English, but who knew nothing about politics, or of geography, would not know that all Romans are Italians. That proposition (if true) is a legal and geographical (or ethnic) truth. It is not a definitional truth. (Quick. Are all citizens of Ascuncion citizens of Bolivia?).


A Roman is citizen of Rome. Rome is a city in the country of Italy, therefore every Roman is an Italian. Is that not true by definition?
 
Reconstructo
 
Reply Thu 25 Feb, 2010 09:07 pm
@hue-man,
hue-man;132382 wrote:
If we're speaking about the present era then every Roman is an Italian by definition.


I agree. I think your meaning was clear to begin with. But I suppose it becomes more clear and less disputable when you clarify the time element.
 
Pyrrho
 
Reply Thu 25 Feb, 2010 10:05 pm
@hue-man,
hue-man;132632 wrote:
A Roman is citizen of Rome. Rome is a city in the country of Italy, therefore every Roman is an Italian. Is that not true by definition?


No, that is wrong. The statement: "Rome is a city in the country of Italy" is a contingent truth, not a definitional truth. Therefore, any conclusion requiring that premise cannot be merely a definitional truth.
 
Reconstructo
 
Reply Thu 25 Feb, 2010 10:23 pm
@hue-man,
Pyrrho raises a good issue. How do we treat proper names? I agree that the system of names is more complicated and less intuitional than A = A. If we press this difficulty, we are moving into linguistic philosophy, away from logic. As far as a geographical system of names is mutual, "Rome is in Italy" is analytic, in my opinion.

A skeptic could make a case even against "A = A." How? Because the meaning of these signs is also contingent. The meaning of "=" is contingent upon one's education. Even "A" as an iterable/stable sign is contingent. It's learned in the context of social practice.

It seems to me that anlalytic propositions depend on the understanding of a contigent language but are otherwise intuition-grounded tautologies.

http://en.wikipedia.org/wiki/Intuitionism
 
kennethamy
 
Reply Fri 26 Feb, 2010 12:44 am
@hue-man,
hue-man;132632 wrote:
A Roman is citizen of Rome. Rome is a city in the country of Italy, therefore every Roman is an Italian. Is that not true by definition?


No. Since it is not part of the meaning of Roman that all Romans are Italians. The test is whether some Romans are not Italians is a contradiction. Suppose Rome seceded from Italy. Then it would be possible for a Roman not to be an Italian. It is would be possible for a Roman not to be an Italian, then some Romans are not Italians is a contradiction. But it is not a contradiction, then all Romans are Italians is not analytic. QED. Remember, an analytic proposition is a proposition whose negation is a contradiction.

By the way, with regard to your example, a proposition is not analytic simply because it follows necessarily from other propositions. It that were true, then the conclusions of all valid arguments would be analytic. And that, of course, is false.

---------- Post added 02-26-2010 at 01:53 AM ----------

Reconstructo;132649 wrote:
Pyrrho raises a good issue. How do we treat proper names? I agree that the system of names is more complicated and less intuitional than A = A. If we press this difficulty, we are moving into linguistic philosophy, away from logic. As far as a geographical system of names is mutual, "Rome is in Italy" is analytic, in my opinion.

A skeptic could make a case even against "A = A." How? Because the meaning of these signs is also contingent. The meaning of "=" is contingent upon one's education. Even "A" as an iterable/stable sign is contingent. It's learned in the context of social practice.

It seems to me that anlalytic propositions depend on the understanding of a contigent language but are otherwise intuition-grounded tautologies.

Intuitionism - Wikipedia, the free encyclopedia


It does not follow from the premise that a case can be made for some proposition, that a good case, or even a plausible case can be made for that proposition. I suppose a case could be made for the proposition that the world is triangular in shape. So what?
 
Reconstructo
 
Reply Fri 26 Feb, 2010 01:00 am
@hue-man,
It's pretty obvious, in my opinion, what the difference is between an analytic and a synthetic proposition. But philosophers have argued the finer points. Here's a point of view I can agree with:

Quote:

Thus the logical positivists drew a new distinction, and, inheriting the terms from Kant, named it the "analytic/synthetic distinction." They provided many different definitions, such as the following:

  1. analytic proposition: a proposition whose truth depends solely on the meaning of its terms
  2. analytic proposition: a proposition that is true (or false) by definition
  3. analytic proposition: a proposition that is made true (or false) solely by the conventions of language

(While the logical positivists believed that the only necessarily true propositions were analytic, they did not define "analytic proposition" as "necessarily true proposition" or "proposition that is true in all possible worlds.")
Synthetic propositions were then defined as:

  • synthetic proposition: a proposition that is not analytic

These definitions applied to all propositions, regardless of whether they were of subject-predicate form. Thus under these definitions, the proposition "It is raining or it is not raining," was classified as analytic, while under Kant's definitions it was neither analytic nor synthetic. And the proposition "7 + 5 = 12" was classified as analytic, while under Kant's definitions it was synthetic.
 
HexHammer
 
Reply Fri 26 Feb, 2010 06:53 am
@hue-man,
hue-man;131687 wrote:
Does logic only equate to knowledge in analytic propositions? Can synthetic propositions be verified with logical decidability if there's only one logical conclusion?
No, you only make logically assumptions based on knowledge. If it's the other way around we get to world is flat, witches flow ..innocent sink.

It takes a genious to produce anything reasonable from pure assumptions.
 
hue-man
 
Reply Fri 26 Feb, 2010 08:01 am
@kennethamy,
kennethamy;132694 wrote:
No. Since it is not part of the meaning of Roman that all Romans are Italians. The test is whether some Romans are not Italians is a contradiction. Suppose Rome seceded from Italy. Then it would be possible for a Roman not to be an Italian. It is would be possible for a Roman not to be an Italian, then some Romans are not Italians is a contradiction. But it is not a contradiction, then all Romans are Italians is not analytic. QED. Remember, an analytic proposition is a proposition whose negation is a contradiction.

By the way, with regard to your example, a proposition is not analytic simply because it follows necessarily from other propositions. It that were true, then the conclusions of all valid arguments would be analytic. And that, of course, is false.
You keep dealing with the past or the possible future. To say that some Romans are not Italian today would be a contradiction. If we go by the possibility of the definition of words changing, couldn't that apply to every word and definition?

---------- Post added 02-26-2010 at 09:09 AM ----------

Pyrrho;132646 wrote:
No, that is wrong. The statement: "Rome is a city in the country of Italy" is a contingent truth, not a definitional truth. Therefore, any conclusion requiring that premise cannot be merely a definitional truth.


The sentence "Rome is a city in the country of Italy" is indeed a contingent truth. However, if you look up the definition of the word 'Rome' you'll find this:

Rome 1 (rhttp://img.tfd.com/hm/GIF/omacr.gifm)1. The capital and largest city of Italy, in the west-central part of the country on the Tiber River.
 
kennethamy
 
Reply Fri 26 Feb, 2010 08:58 am
@hue-man,
hue-man;132805 wrote:
You keep dealing with the past or the possible future. To say that some Romans are not Italian today would be a contradiction. If we go by the possibility of the definition of words changing, couldn't that apply to every word and definition?

---------- Post added 02-26-2010 at 09:09 AM ----------



The sentence "Rome is a city in the country of Italy" is indeed a contingent truth. However, if you look up the definition of the word 'Rome' you'll find this:

Rome 1 (rhttp://img.tfd.com/hm/GIF/omacr.gifm)1. The capital and largest city of Italy, in the west-central part of the country on the Tiber River.


But what makes you believe that by definition of "Roman" all Romans are Italians. Do you believe that by definition of "Ascunionian" that all Assuncionians are Paraguyans? Insofar as "Roman" has a definition, "Roman" means, "a person who lives in Rome". What do you think the definition of "Roman" is? One problem may be that it is not clear that proper names like, "Rome" have a definition. What is the definition of the name, "Ascuncionian"? I guess, someone who lives in Ascuncion.

---------- Post added 02-26-2010 at 10:17 AM ----------

hue-man;132632 wrote:
A Roman is citizen of Rome. Rome is a city in the country of Italy, therefore every Roman is an Italian. Is that not true by definition?


Is what true "by definition"? That the whole sentence, "A Roman is citizen of Rome. Rome is a city in the country of Italy, therefore every Roman is an Italian" is analytic (if it is) does not mean that the sentence, "All Romans are Italians" is analytic. Just as, that the whole sentence, "All Men are mortal, and Socrates is a man, therefore Socrates is mortal" is analytic (if it is) doesn't make, "Socrates is mortal" analytic. I have been trying to explain that to you. That a sentence is the conclusion of a valid argument doesn't mean that that sentence is analytically true. Otherwise, all conclusions of valid arguments would be true by definition. And that is absurd.
 
Zetherin
 
Reply Fri 26 Feb, 2010 09:21 am
@hue-man,
Quote:

The sentence "Rome is a city in the country of Italy" is indeed a contingent truth. However, if you look up the definition of the word 'Rome' you'll find this:

Rome 1 (r[URL="http://img.tfd.com/hm/GIF/omacr.gif"]http://img.tfd.com/hm/GIF/omacr.gifm)1. The capital and largest city of Italy, in the west-central part of the country on the Tiber River.[/URL]


You're confusing things. Reconstructo posted a good article on the analytic and synthetic distinction.

Here's an easy way, according to Kant, to show you are wrong:

The concept "Italian" is not contained within the concept "Roman". Therefore "Every Roman is an Italian" is a synthetic proposition. Also, not all Italians are Roman (someone could be Sicilian, for instance). Something like, "All bachelors are unmarried men" would be an analytic proposition, true by definition. All unmarried men are bachelors, and all bachelors are unmarried men.
 
jgweed
 
Reply Fri 26 Feb, 2010 09:22 am
@hue-man,
What do we mean when we say that something is true by definition, or that this kind of truth is not contingent?

If we take Rome or Sparta as examples, then the truth of the definition is historically dependent. Sparta may always have been "Hellenic" in opposition to bar-barians, but it was not always a part of Greece (in the sense of a modern state). When Romulus and Remus established Rome (Ab urbe condita, 753 BC), it was as a city-state at most, and it would make no sense at that time to say it was the capital of Italy (the Sabines would have made a very strong protest).

Definitions obviously change with time, so something is true by definition when the definition itself is true, and if the meanings of words are contingent, one presumes that whether or not something is true by definition is equally so.
 
 

 
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