Implicit statements

[Samadhi]

My "Logic and Critical Thinking" teacher has introduced a definition of implicit that I disagree with.

I've always thought of it as something implied, but not stated. Like if I hire an advocate to speak for me, it's implicit that I lack the the knowledge, skill, ability, or standing to speak for myself. (Not a very good example, but you know what I mean...or if you don't you probably can't help me anyway )

Anyway, his definition primarily is as follows:

Take the sentence "Tom is big and strong."
In this sentence, "Tom is big" is explicit, and "Tom is strong" is implicit.

When I asked in class about it he said it's because "Tom is big and strong" is really "Tom is big and Tom is strong" The 'Tom is' is implied.

I have difficulty agreeing with this definition for two reasons:
1. In typical logic formulas (or whatever you would call it), "A is B and C" is equivalent to "A is C and B." Since they're equivalent, they should both either be explicit or implicit.
2. I think it lessens the importance of recognizing actual implicit propositions.

Anyone have some insight on this? Is the definition actually that broad?
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[extropalopakettle]

You're right, he's wrong.

"Tom is big and strong" is quite explicit that Tom is big and that Tom is strong.

Implicit means something that is implied, or that is assumed to be understood. I.e., in an argument, it might be implied from some assumptions, OR, it might be implied that it IS an assumption (hopefully not a contentious one) by some conclusion drawn that would require the assumption. It's something not stated.

Maybe someone could come up with a better example, but off the top of my head, a "prime number" may be, and often is, defined as a positive integer that is only evenly divisible by 1 and itself. Then one may go on to prove that every positive integer has a unique factorization as a product of prime numbers. Somewhere along the way in that proof, one would realize (or not, because one already implicitly understood it) that implicit in the definition of "prime number" is the implicit exclusion of the integer 1. I.e., explicitly, a prime number is a positive integer greater than 1 which is only divisible by 1 and itself.

We have someone in linguistics here who can explain more throughly (with transformational grammar, parse trees, ...), but "Tom is big and strong" is equivalent to (it says the same thing as) "Tom is big and Tom is strong" or "Tom is big. Tom is strong". There are rules for transforming one to another without changing what they mean (what they say). Maybe it could be said - but I think it's a stretch in the context you seem to be talking about - that "Tom is strong" is implicit, but this is not how the word is generally used. In a course on transformational syntax, maybe. We (normally) understand what sentences say without analyzing them. Implicit is about what no sentence said.

[Mr Stoofer]

I agree. Tom being strong and Tom being big are both explicitly stated in the sentence "Tom is big and strong".

[extropalopakettle]

[wordcross]

From a grammatical point of view, i might see where he's coming from. Grammatically, an implicit statement is usually one that leaves off an implied subject, though it can at times be an implied subject/verb pair.

I hesitate, however, to fully agree with the instuctor, even from this point of view. While it is implied that the "and" is inclusive in the description, it's such an obvious implication that it might be classified as explicit.

maybe Hitchhiker might know better.

Either way, what the hell is a logic teacher doing trying to use grammar to teach logic?
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[extropalopakettle]

WHAT IS AN IMPLICIT ASSUMPTION?

[Samadhi]

[Courk]

I could make a post repeating every point that's already been made, or I can just nod in agreement.

[Samadhi]

Even worse today.

The three propositions of "Tom, Dick* and Harry are cool dudes" are all implicit because you have to change "are," but none of the propositions in "Tom kicked the dog, Harry kicked the cat and he kicked the bucket" are because even though the pronoun is ambiguous it doesn't need to be changed.

Meh.

^{*He insists on not using a comma before "and" in a list.}
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[austinap]

At least I'm not the only one with an idiotic logic professor. My current one is a complete idiot. God I hate generals.

[Dan]

[Samadhi]

One thing I mentioned when briefly arguing with him (briefly because I don't want to take up too much time in the class) was the possibility that the second proposition is, for lack of a better word, sneakier. If you look at it in a formulaic manner then everything is equal, but that's not how the mind works. I don't know the particular fallacy, but there is a fallacy where you try to sneak in one false proposition with a true one by conflation.

He either didn't know what I was talking about or he ignored it out of hand. Either way, whatever.
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Jack_Ian]

Perhaps he was trying to say that it is implied that Tom is strong because he is big and that the phrase "big and strong" was used based purely on the observation that Tom was big.

[Samadhi]

I asked that, it wasn't the reason.
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Doc Borodog]

He's an idiot.

[Dan]

What "Typical logical formulas" are you talking about? Are you talking about biconditionals (equivalaence?).

If so, "A is B and C" does not mean what you want it to mean. If you are talking about a biconditional, the sentence would be formed like this "A<->B and C", or to finish the job "A<->B^C". But to say A has the equivalent truth value as "B and C" doesn't make sense.

Perhaps we should use predicate logic. Let Bx mean "x is big" and Sx mean "x is Strong". So the sentence can be represented as "Ba and Sa" ("Ba^Sa").

This would translate "literally" to "A is big and A is strong", which unfortunately supports your teacher's position. In logic it would be represented this way (I can't think of another way, at least not right now), but in English it is not so "explicit". In English we drop the second mention of A because it is implicit that we are still talking about the same subject.
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Rokk. uuddlrlrbastart

[Antrax]

What's wrong with A<->(B^C)?
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After years of disappointment with get rich quick schemes, I know I'm gonna get rich with this scheme. And quick!

[Dan]

It's not saying what the English sentence is saying.

A<->B^C says something to the effect of "A, if and only if B and C", or "If A then B, and If A then C". Equivalence is a two-way implication and it doesn't say at all what something "is". If you try to apply it to the sentence you get something like:

[Samadhi]

I meant more along the lines A has the properties (B, C)
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[naD]

How would you represent that in logic? Cause I think your teacher probably has the "Ba^Sa" business in mind. How do you represent the idea that A has all the properties in that set {B, C}?

I think my basic question is: How do you logically represent the "having" in your statement "A has the properties (B,C)"? I assume it is either part of the variables B and C (the properties) or part of other type of variable A (the subject), or are you proposing an operator for the verb "to have" (I'm not familiar with any)?

Another idea: B and C are members of the "set of properties of A". But how would this work into your English sentence? The only way I see it working is to say:

(in these formulas let "e" mean "exists in", cause I don't know how to make that symbol here)

B = "big"
S = "strong"
BeP^SeP where P is "the set of properties of the object Tom".

Is "BeP^SeP" the kind of interpretation you intended? "Big is a property that exists in P and Strong is a property that exists in P."

But now we have the same problem. In English, we don't have to say that "Tom has the property B and Tom has the property S". We just simply say "Tom has the properties B and S."

The question is, Is this statement valid?

BeP^SeP -> (B^S)eP

It would seem that this is valid, but I think there's a fallacy (I could just be sleepy). "B" and "S" are individual properties. Is "B^S", a conjunction, also a property? If not, it does not belong in the set of properties P. I would argue that "B^S" is not a property, because it seems odd to me to apply it to many different things.

For instance. To say "big and strong" is equivalent in "Tom is big and strong" and "Jake is big and strong" seems odd to me since the entire phrase "big and strong" is being treated as one property, one adjective, when it is in fact two. There is soemthing going on behind the scenes with the second adjective (in this case "strong"). The subject is being applied to it after the subject was already applied to the first adjective. There is somethign telling it to apply also to the second. This is the implication.

(And don't go saying "big and strong" have been mushed together by language to form one adjective. That may be true, but this has to work for all adjectives. Try treating "electronic and rich" as one adjective.)

P.S. Sorry about the rantage, I'm just legitimately trying to figure out the semantics of the problem. I really should be studying for my logic test. :-p
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[Antrax]

[Bicho the Inhaler]

Dan, you've also got me confused...what are you trying to say?

I think the problem as most people (including me) see it is that Samadhi's professor is treating implicitness as a very superficial syntactic property, as if to trivialize it, while it deserves careful attention. There's nothing logically wrong with it...implicitness and explicitness are sort of blurry concepts, and you can make the distinction at different places. But the way he's doing it is particularly inane.

[MatthewV]

^{*He insists on not using a comma before "and" in a list.}

[Dan]

Please excuse the double post. Or my dear Aunt Sally. Whichever really.
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Rokk. uuddlrlrbastart

[Dan]

[Bicho the Inhaler]

[Samadhi]

[Samadhi]

[Guest]

[Dan]

If I had to pick one thing I didn't like about the new boards...:p
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Rokk. uuddlrlrbastart

[Samadhi]

I have no training with the formulas you're using. When I said "typical" I meant typically what I or any other layman might see, as opposed to the "typical" esoteric usage. Sorry for the ambiguous term.

My main point is that I really don't see how saying "John is big and strong" is explictly saying "John is strong" but only implying that "John is big"
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Dan]

It doesn't. "John is strong and big" does.
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Rokk. uuddlrlrbastart

[Dan]

Ah, I see now that this is where what Bicho was talking about comes in, but I would hardly call this syntactic property "superficial" or "inane". It is a part of our language's deep-structure syntax. Though I could not say off the top of my head if this could be technically called an "implicit" subject, I think it makes sense that it would be called so. But it may just be an "unstated premise" or "assumed/unstated subject". This sort of distinction also depends on who's teaching you linguistics. :p

What class is this for anyway Sam?
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Rokk. uuddlrlrbastart

[Samadhi]

[GH]

[Samadhi]

sheesh. I get no respect.
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Dan]

I was serious though Sam. "John is big and strong" and "John is strong and big" have the same "meaning" (if I were so arrogant as to claim to know what that is). But they obviously are not the same sentence, they have different structure.
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Rokk. uuddlrlrbastart

[Samadhi]

Yes, but I hardly think that qualifies one as exlicit and the other not.
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And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Dan]

The stucture of the sentence dictates which statement is implicit. It's not that one is explicit and the other not. In different positions they are different things.
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Rokk. uuddlrlrbastart

[extro...]

This all seems to be about various meanings of the word "implicit". One is very common usage, and very relevant to a logic and critical thinking course: Something that is left unsaid and unmentioned, but can be understood to be an assumption or an implication. The other is a usage that we're not even sure is real (i.e., is the term really used that way?) - a sort of syntactic thing that describes, in this case, the difference between parts of two sentences with different surface structure, but identical deep structure. This latter notion of an "implicit" statement is something that requires no more critical thinking than what is done automatically by an average five year old.

Actually, you could argue that in the sentence "Tom is big", it is implicit that "Tom" means Tom, "big" means big, and "is" means is. It is implicit. The sentence doesn't explicitly state that the words have their usual meanings. It's about as meaningful an avenue of discussion, IMO.