Do definitions have truth values?

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humy
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Do definitions have truth values?

Post by humy » Thu Feb 04, 2016 7:39 pm

I always thought all non-contradictory definitions are 'true by definition' (or at least providing people are in general agreement of that definition) i.e. they are simply 'true'.
But then a friend made me unsure because he insisted they don't. He says all non-contradictory definitions have no truth value i.e. they are neither 'true' or false'. I am not sure but I think his reasoning is vaguely along the lines; "because they can be so defined to be whatever you want it to be" and thus there is no 'correct' or incorrect' definition because all definitions are arbitrary and it is subjective which is the 'correct' definition thus, because there isn't such thing as 'correct' or incorrect' definition, there isn't such thing as a definition that is 'true' or 'false' either -or at least I think that is what he means.
Is he right?

I have a bit of a problem with that because, I assume if he is right, if you DEFINE number 4 as being;

2+2=4

Then that is neither true or false because it is a DEFINITION.
BUT, if that is true, you cannot present 2+2=4 as a proposition (or can you?), as opposed to a definition, because all propositions are statements with truth values by definition of proposition.

But then what if you present;

1+1+1+1=4

? Is that a proposition or a definition? Because it seems to me you could present it as either thus, if he is right, It is totally unclear whether that has a truth value. If you say that is a proposition because "2+2=4" is the definition and "1+1+1+1=4" is not the same form as the definition "2+2=4", then, say, what if you change your mind which you prefer as the definition and say the definition of 4 is "1+1+1+1=4" ? Now suddenly you have implicitly decided you where talking nonsense when you said earlier that 1+1+1+1=4 is 'true' but 2+2=4 is neither true or false because it is a definition. I find that a rather eccentric way to think.
Personally I would naturally think all non-contradictory definitions are 'true' at least providing people are in general agreement of that definition.

What do you think?

JSS
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Re: Do definitions have truth values?

Post by JSS » Fri Feb 05, 2016 11:45 pm

humy wrote:I always thought all non-contradictory definitions are 'true by definition' (or at least providing people are in general agreement of that definition) i.e. they are simply 'true'.
But then a friend made me unsure because he insisted they don't. He says all non-contradictory definitions have no truth value i.e. they are neither 'true' or false'. I am not sure but I think his reasoning is vaguely along the lines; "because they can be so defined to be whatever you want it to be" and thus there is no 'correct' or incorrect' definition because all definitions are arbitrary and it is subjective which is the 'correct' definition thus, because there isn't such thing as 'correct' or incorrect' definition, there isn't such thing as a definition that is 'true' or 'false' either -or at least I think that is what he means.
Is he right?
Your friend was wrong. One must understand what "true" means before one can make such claims concerning it.

Using his reasoning, if he defines "true" and proclaims that it means merely whatever he wants it to mean at the time (because he is free to define it), then anything he says about being true, is a bit irrelevant, isn't it? He is, in effect, "caught up in his own petard". By disqualifying definitions, one disqualifies anything he has to say .. including the disqualifying of definitions.
humy wrote:2+2=4

Then that is neither true or false because it is a DEFINITION.
That isn't the definition. The definition is:
4 ≡ 1+1+1+1
2 ≡ 1+1
therefore
4 = 2+2
therefore
2+2 = 4

There is a difference in a definition (≡) and an equivalence (=). Logic determines the equivalence. Language determines the definition. Words that are not defined, are meaningless distractions to confuse and obfuscate a victim.

If one is not going to agree on the language being used, he is attempting, intentionally or not, to distort truth. Truth has three qualifiers, but is more about language being consistent than anything else. A language without definitions, is a mind killer .. right there along side fear.

Obvious Leo
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Re: Do definitions have truth values?

Post by Obvious Leo » Fri Feb 05, 2016 11:58 pm

JSS wrote: Words that are not defined, are meaningless distractions to confuse and obfuscate a victim.
The word "god" has always been a perennial favourite in this category. Since all the punters have always been free to define it for themselves much mayhem and bloodshed has ensued. Luckily more prosaic questions such as the definition of 4 have generally been resolved in a more gentlemanly fashion, although not always to everybody's satisfaction.

JSS
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Re: Do definitions have truth values?

Post by JSS » Sat Feb 06, 2016 12:04 am

Obvious Leo wrote:
JSS wrote: Words that are not defined, are meaningless distractions to confuse and obfuscate a victim.
The word "god" has always been a perennial favourite in this category. Since all the punters have always been free to define it for themselves much mayhem and bloodshed has ensued. Luckily more prosaic questions such as the definition of 4 have generally been resolved in a more gentlemanly fashion, although not always to everybody's satisfaction.
True and as you say, "satisfaction" is really the issue. People have to agree on the language definitions, else there isn't much use in having a language. That is why definitions ended up being the purpose of dictionaries. Originally a dictionary was strictly for the purpose of maintaining pronunciation ("diction"). It took a while for the silly twits to realize that definitions were far more relevant.

Obvious Leo
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Re: Do definitions have truth values?

Post by Obvious Leo » Sat Feb 06, 2016 12:30 am

JSS wrote: People have to agree on the language definitions, else there isn't much use in having a language
As a habitual contributor to various philosophy forums over a considerable span of years I can certainly attest to the truth of this statement. I wouldn't mind a dollar for every conversation I've witnessed where the parties are at loggerheads with each other and all the while they weren't even arguing about the same bloody question because they hadn't agreed on a common definition of terms in the first place. And yet the central thrust of the entire philosophical discourse revolves around the assumption that such a common ground must be established a priori.

JSS
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Re: Do definitions have truth values?

Post by JSS » Sat Feb 06, 2016 6:36 am

If the scriptures had come with a lexicon, the entire world of Man would be a different place.

Beauty
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Re: Do definitions have truth values?

Post by Beauty » Wed Sep 14, 2016 11:04 am

There is a difference in a definition not being contradictory and not being contradicted. If you mean the first, then what is it that you mean to say, because all definitions would be so that they are not contradictory or it would be apparent that they are not true. If not contradicted by someone, it does not mean they have truth value, for truth value should stand absolute, irrespective of any suggestion. So if a definition has truth value that is absolutely right, then it is right. Who decides the right in a definition? Our God in us does, which is how definitions - word/meaning have come up.

creativesoul
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Re: Do definitions have truth values?

Post by creativesoul » Fri Sep 16, 2016 5:51 am

Depends upon what is being defined.

HexHammer
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Re: Do definitions have truth values?

Post by HexHammer » Fri Sep 16, 2016 7:22 am

True truths are nothing but delusions, a carrot on a stick for naive people! We can't with absolute certainty conclude anything, since science books are rewritten, news articles are weekly claimed as faulty, fraud or inconclusive.

For decades eggheads have said that the bumblebee can't fly, that flesh can't burn, that 2+2=4 ..etc, etc.

The bumblebee can indeed fly and only because we can observe the true source, we can conclude that human perception are faulty since it's difficult to take account for all the factors of life. It was found that it's turbulence that sucks the wings up and acts like a spring, thus the energy spend are way less than what anticipated.

Eggheads claims that flesh can't burn, because it consist of 80% water, which is true in itself, but there's this weird concept of 0+0=1, because of the "wig effect" flesh can indeed burn, because there's this tiny amount of fat, and when there's charred flesh it will act like a wig!

2+2=4 are twisted in the realm of relativity, where weird concepts of length contraction and time exist.

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Terrapin Station
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Re: Do definitions have truth values?

Post by Terrapin Station » Wed Sep 21, 2016 5:59 pm

Definitions are stipulations that F will count as x.

The stipulations do not have truth values.

However, it's true that "We've stipulated that 'An article of food consisting of paste baked with something in it or under it' will count as 'pie'" and false that "We've stipulated that 'Not divided by a partition or partitions having septa as a septate pod or shell' will count as 'septate.'"

With something like "2+2=4" it depends on whether one is saying that it's a definition in the same sense of the definitions above, and whether "2+2=4" is true (without it being a statement about conventions or whatever) will depend on one's ontology of mathematics. If one is a mathematical realist/platonist, then one will likely say that "2+2=4" is true. But one can be a mathematical anti-realist or noncognitivist, in which case mathematical statements do not actually have truth values.

Re "true by definition," that should be seen as simply another way of saying that the support for something in an argument is that we've stipulated that x will be defined that way. It's just another way of saying that x=F by definition. You do not need to say true by definition. When we're doing mathematics and logic we typically treat it in a way so it works just as well for realists/cognitivists and anti-realists/noncognitivists. In fact, most mathematics professors will become quite annoyed if you try to broach ontological issues in mathematics class. (Something I know from experience. :D ) The ontological issues do not matter practically for doing math, and so most mathematics profs don't care about ontological issues.

And yeah, we've stipulated that propositions are things with truth values. So if something doesn't have a truth value, then it's not a proposition by that convention.

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Dunce
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Re: Do definitions have truth values?

Post by Dunce » Sat Nov 05, 2016 4:51 pm

"Brexit means Brexit" has truth value, but is not what we might call content-rich.

HexHammer
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Re: Do definitions have truth values?

Post by HexHammer » Sat Nov 05, 2016 6:54 pm

Definitions can have values, like in psychology where they operate with "prevalence", not all people are psychopaths, but a certain %, in war some will get PTSD, not all but some, etc.

Many will naively think that numbers don't lie, but they do. Worked in a newspaper and we had overwhelming success, and the CEO said we are in a strong position when I said we are weak, because he had not so bright people in key positions and they can't help years of crisis, which the newspaper are ended up in, with a huge debt ..etc.

duszek
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Re: Do definitions have truth values?

Post by duszek » Sun Nov 06, 2016 9:37 am

Definitions can have relative truth values perhaps.

If we have a definition of a man (human being of the male sex) and a definition of an unmarried person (someone who has not registered a marriage with another person) then the definition of a bachelor "a man who is not married" is a true one.

This last definition is true as long as the other two definitions are considered to be true.

True in the context of a definition means: the correct use of a word in a specific communicative situation.

Sheepy
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Re: Do definitions have truth values?

Post by Sheepy » Fri Dec 16, 2016 10:59 pm

If I understand correctly, the issue is how a sentence like 2 +2 can be a proposition and a definition at the same time. I don't see the problem with tautological propositions, but maybe you have a different definition of a proposition, like as a possible matter of fact statement.

This makes me think of Quine :D He would say the proposition 2+2 = 4, is not necessarily true by definition because when you really get down to the details there is no difference between matter-of-fact and tautological statements. The fact that "a bachelor is an unmarried man" is a tautology is only because we know from our linguistic expertise that "bachelor" and "unmarried man" are used interchangably. In a way it is empirical too, not a-priori. Also, mathematics apparently cannot be reduced to logic, so mathematical statements are not true by logic, they too are revisable. So 2+2=4 is not fundamentally different from "that wall is green." So, it is more of a proposition and not a definition.

I have no idea what the definition of 4 is, but it seems to me that 1+1+1+1 is just as arbitrary as just 4 itself.

Necromancer
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Re: Do definitions have truth values?

Post by Necromancer » Sat Dec 17, 2016 12:18 am

The way I see it is that definitions need to function and for them to function, they need to relate and in their functioning there is a truth value, definitely! :)

(Tautologies or other.)

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