A serious question: Who is "him"?

Originally posted by lucifershammer

In the example you gave, I could assert:

a OPERATOR b = b OPERATOR a
or
a OPERATOR (b OPERATOR c) = (a OPERATOR b) OPERATOR c

for any three real numbers a, b, c.

Both of the claims above are true.

It is also the case that both of these are false, which is the crux of my reductio demonstration.

3 * 4 is not equal to 4 + 3.

They are only always true if you use OPERATOR univocally, which is to say always requiring it to have the same meaning. Even if you maintain one meaning for all uses in one proposition, and one different meaning in another proposition, a contradiciton can still be derived, as shown in my original example.

Originally posted by lucifershammer
Standard rules of English - the pronoun refers to the immediately preceding relevant noun; here, therefore, it would refer to the Son.

[b]in the former, people who believe in Jesus but not God would have everlasting life.

Huh? How does this follow from the verse?

Moreover, believing in the Son automatically means believing in the Father - it makes no sense to say "I believe Jesus is the Son of God" and not believe in God.[/b]

Given the incredible elasticity of interpretation necessary to make a lot of the Bible consistent, shouldn't one be careful about imposing upon it such strict rules of grammar?

Originally posted by lucifershammer

The reason you obtain a reductio in your example is precisely because you are not using terms analogically, but equivocally.

I explicitly defined OPERATOR in a way that follows directly from your notion of "analogically."

Of course, it is an equivocation, because what you call an analogical use is nothing different than an equivocation.

Originally posted by DoctorScribbles
It is also the case that both of these are false, which is the crux of my reductio demonstration.

3 * 4 is not equal to 4 + 3.

You're doing it again (equivocating on 'OPERATOR'😉.

Within context, the meaning of 'OPERATOR' does not change. So, if the entire context is the following statement

a OPERATOR b = b OPERATOR a

then the term OPERATOR does not change meanings between the LHS and the RHS.

However, OPERATOR is used analogically to either of + or *; so you can substitute them to get either

a + b = b + a

or

a * b = b * a

respectively.

Within the context of each statement, the operator (+ or *) retains its own meaning, but has a property (commutativity, in this case) that can be "translated" to another operator in a different context. Hence, the commutativity of addition is analogical to the commutativity of multiplication. This analogical relationship is what we signify when we say

a OPERATOR b = b OPERATOR a

when OPERATOR is used to signify either of + or *.

Originally posted by DoctorScribbles
I explicitly defined OPERATOR in a way that follows directly from your notion of "analogically."

Of course, it is an equivocation, because what you can an analogical use is nothing different than an equivocation.

I explicitly defined OPERATOR in a way that follows directly from your notion of "analogically."

And all you've done is show that analogical usage is not the same as univocal usage.

What I've done is to show that analogical usage is not the same as equivocal usage.

Put simply, analogy is not an instance of equivocal-ness.

Originally posted by lucifershammer
You're doing it again (equivocating on 'OPERATOR'😉.

Within context, the meaning of 'OPERATOR' does not change. So, if the entire context is the following statement

a OPERATOR b = b OPERATOR a

then the term OPERATOR does not change meanings between the LHS and the RHS.

However, OPERATOR is used analogically to either of + or *; ...[text shortened]... when we say

a OPERATOR b = b OPERATOR a

when OPERATOR is used to signify either of + or *.

They are only always true if you use OPERATOR univocally, which is to say always requiring it to have the same meaning. Even if you maintain one meaning for all uses in one proposition, and one different meaning in another proposition, a contradiciton can still be derived, as shown in my original example.


For another example,
-a OPERATOR b = a OPERATOR -b
for all a and b

is both true and false.

Within context[/i], the meaning of 'OPERATOR' does not change.

Any term whose meaning does not change within context -- within the universe of discourse -- is univocal. In the preceding example, either OPERATOR is univocal and there is no contradiction, or it is not and I can repeat the proposition and one will be true and the other will be false.

Originally posted by lucifershammer
[b]You fail to understand that if terms are not used univocally in a universe of discourse, then any proposition that contains them is not well formed and thus has no truth value.

This is demonstrably false. Even when terms are used analogically, it is perfectly possible to have true propositions.

In the example you gave, I could assert:

...[text shortened]... your example is precisely because you are not using terms analogically, but equivocally.[/b]

Perhaps you think it's obvious, but I don't see how see your statement is true for any operator on the reals.

Let the operator, T:R-->R, be T(x)=x^2
and let a=2,b=3,c=4.

2*(3^2) = 3*(2^2)
18 = 12

or

2*(3*(4^2))^2 = (2*(3^2))*(4^2)
2*48*48 = 18*16
48*3 = 9
48 = 3

When you say operator do you only mean multiplication and addition?
Help me out because I'm confused.

Originally posted by lucifershammer
You're doing it again (equivocating on 'OPERATOR'😉.

Within context, the meaning of 'OPERATOR' does not change. So, if the entire context is the following statement

a OPERATOR b = b OPERATOR a

then the term OPERATOR does not change meanings between the LHS and the RHS.

However, OPERATOR is used analogically to either of + or *; ...[text shortened]... when we say

a OPERATOR b = b OPERATOR a

when OPERATOR is used to signify either of + or *.

Oh this explains things. Thanks.

Originally posted by telerion
Perhaps you think it's obvious, but I don't see how see your statement is true for any operator on the reals.

Let the operator, T:R-->R, be T(x)=x^2
and let a=2,b=3,c=4.

2*(3^2) = 3*(2^2)
18 = 12

or

2*(3*(4^2))^2 = (2*(3^2))*(4^2)
2*48*48 = 18*16
48*3 = 9
48 = 3

When you say operator do you only mean multiplication and addition?
Help me out because I'm confused.

OPERATOR can denote raising to a power, under LH's notion of analogical terms, because it is similar to and not wholly unrelated to multiplication.

That's the beauty, or ugliness, of analogical terms, depending on your point of view. One term can denote just about anything.

Originally posted by DoctorScribbles
OPERATOR can denote raising to a power, under LH's notion of analogical terms, because it is similar to and not wholly unrelated to multiplication.

That's the beauty, or ugliness, of analogical terms, depending on your point of view. One term can denote just about anything.

I didn't bother reading most of the past pages in this thread so I'm probably not understanding your two's discussion, but shouldn't his statement include "for some OPERATOR"?

Originally posted by telerion
I didn't bother reading most of the past pages in this thread so I'm probably not understanding your two's discussion, but shouldn't his statement include "for some OPERATOR"?

If he wanted it to mean anything that can be analyzed for truth, yes.

He has invented this notion of "analogical" terms, which get all the benefits but none of the responsibilities of univocal terms. I have been unable to convince him that this is their nature.

Originally posted by DoctorScribbles
They are only always true if you use OPERATOR univocally, which is to say always requiring it to have the same meaning. Even if you maintain one meaning for all uses in one proposition, and one different meaning in another proposition, a contradiciton can still be derived, as shown in my original example.


For another example,
-a OPERATOR b = a ...[text shortened]... or it is not and I can repeat the proposition and one will be true and the other will be false.

The point of analogical usage is not that all propositions true with one meaning will be true with another (if they did, then the terms are being used univocally). What it tells you is that a certain class of propositions (which depend on analogical properties) will be true within context when you switch meanings.

Going back to my crane (bird/machine) example, most propositions true of cranes (birds) will not be true of cranes (machines):

"Cranes are living creatures"
"Cranes fly"
"Cranes have beaks"
etc.†

With + and *, however, many non-trivial non-metaphysical propositions (e.g. those whose truth depends on commutativity and associativity, for instance) are going to be true in both contexts.

---
† There will still be some metaphysical propositions that would still be true (e.g. "Cranes are material beings"😉 under both contexts. But we are talking of more specific propositions than those that involve material being qua being.

Originally posted by lucifershammer
The point of analogical usage is not that all propositions true with one meaning will be true with another (if they did, then the terms are being used univocally). What it tells you is that a certain class of propositions (which depend on analogical properties) will be true within context when you switch meanings.

Then why not just pick a new univocal term to denote the analogical property? Why insist on overloading terms that already have univocal meanings?

Originally posted by lucifershammer
The point of analogical usage is not that all propositions true with one meaning will be true with another (if they did, then the terms are being used univocally). What it tells you is that a certain class of propositions (which depend on analogical properties) will be true within context when you switch meanings.

I just caught up with this thread, and you've been doing a wonderful job with your position that the term "father" might be best considered analogically rather than univocally or equivocally. In fact, I believe that this is often true when reading literature (or almost any written word that is in the slightest bit abstract).
Analogy is a worthy tool not uncommon in any aspect of our lives. Why should it not exist in the Bible?

Originally posted by echecero

Analogy is a worthy tool not uncommon in any aspect of our lives. Why should it not exist in the Bible?

So, are you content to accept that Jesus is God the Father's son only in an analogous sense?