Nathan Salmon in Frege's Puzzle on the distinction between intension and extension:
"The intension of a singular term, sentence, or predicate is a function that assigns to any possible world w the extension the singular term, sentence, or predicates takes on with respect to w. The extension of a singular term (with respect to a possible world w) is simply its referent (with respect to w), i.e., the object or individual to which the term refers (with respect to w). The extension of a sentence (with resp3ect to w) is its truth value (with respect to w)--either truth or falsehood. The extension of an n-place predicate (with respect to w) is the predicate's semantic characteristic function (with respect to w), i.e., the function that assigns either truth or falsehood to an n-tuple of individuals, according as the predicate or its negation applies (with respect to w) to the n-tuple. Assuming bivalence, the extension of an n-place predicate may be identified instead with the class or n-tuples to which the predicate applies." p.14
Wednesday, January 28, 2009
Monday, January 26, 2009
Frege's Puzzle--Introduction
Some definitions:
Purely general proposition: a composite purely intensional entity made up solely of further intensional entities such as attributes and concepts, employing purely conceptual representations of the individuals whom the proposition is about in place of the individuals and times themselves. (Fregean view of content)
Purely general proposition: a composite purely intensional entity made up solely of further intensional entities such as attributes and concepts, employing purely conceptual representations of the individuals whom the proposition is about in place of the individuals and times themselves. (Fregean view of content)
Wednesday, October 22, 2008
Bach's Dilemma
(1) If a referring expression functions referringly in some contexts and not in others and that fact is semantically significant, then the expression's semantic contribution to the sentence in which it occurs would have to depend on its sentential context.
(2) But this suggests that its very meaning, which presumably determines its semantic contribution, depends on its sentential context.
(3) The only way to concede that, and this is one horn of the dilemma, would be to abandon the Principle of Compositionality.
(4) The other horn of the dilemma is to accept the dubious implication that referring expressions are systematically ambiguous.
Since the only way to keep (1) is to reject (3) or (4) it seems that we must then reject (1). Bach's claim is that expressions don't refer, rather speaker's refer. So, if it is expressions themselves that refer and they need a context in which to refer from, then it seems that (3) or (4) is true.
(2) But this suggests that its very meaning, which presumably determines its semantic contribution, depends on its sentential context.
(3) The only way to concede that, and this is one horn of the dilemma, would be to abandon the Principle of Compositionality.
(4) The other horn of the dilemma is to accept the dubious implication that referring expressions are systematically ambiguous.
Since the only way to keep (1) is to reject (3) or (4) it seems that we must then reject (1). Bach's claim is that expressions don't refer, rather speaker's refer. So, if it is expressions themselves that refer and they need a context in which to refer from, then it seems that (3) or (4) is true.
Wednesday, July 16, 2008
On Sense and Reference -- Frege
I have here understood any designation representing a proper name, which thus has as its reference a definite object (this word taken in the widest range), but not a concept or a relation, which shall be discussed further in another article. The designation of a single object can also consist of several words or other signs. For brevity, let every such designation be called a proper name.
The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs; but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge we never attain.
(Sense & Reference, p. 57-8)
The reference and sense of a sign are to be distinguished from the associated idea. If the reference of a sign is an object perceivable by the sense, my idea of it is an internal image, arising from memories of sense impression s which I have had and acts, both internal and external, which I have performed. Such an idea is often saturated with feeling; the clarity of its separate parts varies and oscillates. The same sense is not always connected, even in the same man, with the same idea. The idea is subjective: one man’s idea is not that of another. There result, as a matter of course, a variety of differences in the ideas associated with the same sense. A painter, a horseman, and a zoologist will probably connect different ideas with the name ‘Bucephalus.’ This constitutes and essential distinction between the idea and the sign’s sense, which may be the common property of many and therefore is not a part or a mode of the individual mind. For one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another. (Sense & Reference p.59)
The sense of a proper name is grasped by everybody who is sufficiently familiar with the language or totality of designations to which it belongs; but this serves to illuminate only a single aspect of the reference, supposing it to have one. Comprehensive knowledge of the reference would require us to be able to say immediately whether any given sense belongs to it. To such knowledge we never attain.
(Sense & Reference, p. 57-8)
The reference and sense of a sign are to be distinguished from the associated idea. If the reference of a sign is an object perceivable by the sense, my idea of it is an internal image, arising from memories of sense impression s which I have had and acts, both internal and external, which I have performed. Such an idea is often saturated with feeling; the clarity of its separate parts varies and oscillates. The same sense is not always connected, even in the same man, with the same idea. The idea is subjective: one man’s idea is not that of another. There result, as a matter of course, a variety of differences in the ideas associated with the same sense. A painter, a horseman, and a zoologist will probably connect different ideas with the name ‘Bucephalus.’ This constitutes and essential distinction between the idea and the sign’s sense, which may be the common property of many and therefore is not a part or a mode of the individual mind. For one can hardly deny that mankind has a common store of thoughts which is transmitted from one generation to another. (Sense & Reference p.59)
Friday, July 11, 2008
'God' - necessary, a posteriori
I believe that 'God' refers to the divine substance. Furthermore, the divine substance = The Triune God. However, the divine substance = the Triune God is a necessary statement. Yet, OT followers of God were not aware of this meaning of God, therefore the divine substance = the Triune God is an a posteriori statement.
Muslims, God, & the law of non-contradiction
So to review some of the previous discussion, I will explain how 'God' can refer to the divine substance that is the Triune Godhead.
Assuming that we hold to the following three statements:
(1) The Father is God.
(2) Jesus is God.
(3) The Holy Spirit is God.
I'm arguing that 'God' is not a proper name, because it doesn't semantically function like a proper name. An objection was presented to my view that sometimes 'God' is used to refer to the Father in the Bible and that was a problem for my view. In (1)-(3) 'God' occurs in the predicate position, however God cannot be identical to any one person of the Trinity for the following reason, there are properties that God has that any one member of the Trinity lacks. For instance, Jesus died on the cross, however the Father didn't die on the cross. Therefore, God died on the cross, but if we claim that God = the Father, then we commit the heresy of patripassionism (that the Father was crucified).
Here is an analogy to help better explain my view that 'God' refers to the divine substance.
(4) The Atlantic Ocean is water.
(5) The Pacific Ocean is water.
(6) The Indian Ocean is water.
(7) The Artic Ocean is water.
So we can speak about and refer to the Pacific Ocean as water, because it is water, however, the Pacific Ocean isn't identical to water, because the Pacific Ocean isn't identical to the Atlantic Ocean. So just as we can speak of God as Jesus or God as the Father, 'God' is not the name of Jesus or the name of the Father, though it can be used to refer to the Father or to the Son, but this is pragmatic reference and not an issue of semantics (or it may even be what is said).
Muslims affirm that there is one God, Allah. I take this to be a rejection of the Trinity, or to state this in a positive manner, this is an affirmation of a belief in a non-Triune God. Now, if 'God' refers to the divine substance and this divine substance means the Triune God, then clearly Muslims wouldn't refer to the same God that Christians refer to. In other words, 'God' must mean something different for Muslims than it does for Christians. We don't want to attribute any contradictory beliefs to Muslims, especially since they claim that they worship a non-Triune God, then it seems uncharitable to claim that they do worship a Triune God.
However, there is a problem for the Christian theist who claims that Muslims and Christians worship different Gods, since Muslims claim to worship the God of the OT. Yet, Muslims ignore what the NT teaches us about God and which is that God is a Triune God. So by explicitly rejecting a Triune God Muslims have broken the causal chain of reference. Since Israel, didn't explicitly reject a Triune God, then when they uttered the word 'God' they referred to God, although without knowing that God was a Triune God.
Assuming that we hold to the following three statements:
(1) The Father is God.
(2) Jesus is God.
(3) The Holy Spirit is God.
I'm arguing that 'God' is not a proper name, because it doesn't semantically function like a proper name. An objection was presented to my view that sometimes 'God' is used to refer to the Father in the Bible and that was a problem for my view. In (1)-(3) 'God' occurs in the predicate position, however God cannot be identical to any one person of the Trinity for the following reason, there are properties that God has that any one member of the Trinity lacks. For instance, Jesus died on the cross, however the Father didn't die on the cross. Therefore, God died on the cross, but if we claim that God = the Father, then we commit the heresy of patripassionism (that the Father was crucified).
Here is an analogy to help better explain my view that 'God' refers to the divine substance.
(4) The Atlantic Ocean is water.
(5) The Pacific Ocean is water.
(6) The Indian Ocean is water.
(7) The Artic Ocean is water.
So we can speak about and refer to the Pacific Ocean as water, because it is water, however, the Pacific Ocean isn't identical to water, because the Pacific Ocean isn't identical to the Atlantic Ocean. So just as we can speak of God as Jesus or God as the Father, 'God' is not the name of Jesus or the name of the Father, though it can be used to refer to the Father or to the Son, but this is pragmatic reference and not an issue of semantics (or it may even be what is said).
Muslims affirm that there is one God, Allah. I take this to be a rejection of the Trinity, or to state this in a positive manner, this is an affirmation of a belief in a non-Triune God. Now, if 'God' refers to the divine substance and this divine substance means the Triune God, then clearly Muslims wouldn't refer to the same God that Christians refer to. In other words, 'God' must mean something different for Muslims than it does for Christians. We don't want to attribute any contradictory beliefs to Muslims, especially since they claim that they worship a non-Triune God, then it seems uncharitable to claim that they do worship a Triune God.
However, there is a problem for the Christian theist who claims that Muslims and Christians worship different Gods, since Muslims claim to worship the God of the OT. Yet, Muslims ignore what the NT teaches us about God and which is that God is a Triune God. So by explicitly rejecting a Triune God Muslims have broken the causal chain of reference. Since Israel, didn't explicitly reject a Triune God, then when they uttered the word 'God' they referred to God, although without knowing that God was a Triune God.
Saturday, July 05, 2008
Water = H20
If water is identical with H20, then necessarily, water is identical with H20. Analogously, if Christianity is true, then God is identical with the Triune God. Therefore, Necessarily, God is identical with the Triune God. So, although 'God' is a natural kind, 'God' means the Triune God. In other words, the only God that exists, is the Triune God, all other Gods are fictional objects, since there is only one divine substance and no other individual Gods other than the Triune God.
Tuesday, July 01, 2008
'God' as a Natural Kind
Most people assume that 'God' is a proper name. If this is the case then we ought to apply the semantics to 'God' that apply to other proper names. However, it if isn't a proper name, and instead 'God' is a general term, then the semantics that apply to general terms apply to 'God'. Perhaps the first question we should ask is whether 'God' functions as a proper name. So let's use an example of a proper name:
(1) Bruce Wayne is Batman.
(2) The Dark Knight is Batman.
(3) The Detective is Batman.
The reason why I claim that the 'is' in (1)-(3) is the 'is' of identity is because the predicate term functions as a name. We can apply transivity of identity to (1)-(3) as follows:
(4) Bruce Wayne = The Dark Knight
(5) The Dark Knight = The Detective
Since, (1)-(3) showed that all the names in (4) and (5) were identical to 'Batman' we can assume that 'Batman' is a proper name. So if 'God' is a proper name, then it should function in a similar manner as the examples in (4)and (5)
(6) Jesus is God.
(7) The Father is God.
(8) The Holy Spirit is God.
However, orthodox Christians would reject the following assertions:
(9) Jesus = The Father
(10) The Father - The Holy Spirit
Yet, (6)-(8) shows that the terms in (9) and (10) are identical to God. It seems that the best explanation for the 'is' in (6)-(8) is that all the subject terms are consubstantial with God, that is, the subject terms all share the same substance. So it seems the best way to understand 'God' that 'God' functions as a general term. This is due to the fact that God is a substance. So when we use the word 'God' we refer to a divine substance.
(1) Bruce Wayne is Batman.
(2) The Dark Knight is Batman.
(3) The Detective is Batman.
The reason why I claim that the 'is' in (1)-(3) is the 'is' of identity is because the predicate term functions as a name. We can apply transivity of identity to (1)-(3) as follows:
(4) Bruce Wayne = The Dark Knight
(5) The Dark Knight = The Detective
Since, (1)-(3) showed that all the names in (4) and (5) were identical to 'Batman' we can assume that 'Batman' is a proper name. So if 'God' is a proper name, then it should function in a similar manner as the examples in (4)and (5)
(6) Jesus is God.
(7) The Father is God.
(8) The Holy Spirit is God.
However, orthodox Christians would reject the following assertions:
(9) Jesus = The Father
(10) The Father - The Holy Spirit
Yet, (6)-(8) shows that the terms in (9) and (10) are identical to God. It seems that the best explanation for the 'is' in (6)-(8) is that all the subject terms are consubstantial with God, that is, the subject terms all share the same substance. So it seems the best way to understand 'God' that 'God' functions as a general term. This is due to the fact that God is a substance. So when we use the word 'God' we refer to a divine substance.
Scooby-Doo, General Terms, & God
According to Nathan Salmon, natural kinds refer to a species or a genus. Natural kinds don't refer to classes because there must be at least one member in a class in a world, w, in order for that class to exist. However, it seems that even in a world that dogs don't exist, 'dog' still refers to the species canine. With this in mind I present the following puzzle:
(1) Scooby-Doo is a dog.
(2) Dog refers to the species canine.
(3) If Daphne kisses Scooby-Doo, then she kisses a canine.
(4) Scooby-Doo isn't a dog, rather Scooby-Doo is a cartoon drawing of a dog, i.e. Scooby-Doo is a fictional object.
(5) The word 'dog' in (1) is ambiguous.
Let's take the following example:
(6) The Greeks worshiped Zeus.
(7) Zeus is a god.
(8) Gods are a species of divine beings.
(9) Therefore, the Greeks worshiped a species of divine beings.
However, (9) is false, once again Zeus is a fictional object, so the intentionality of the Greeks was directed at a fictional object.
Furthermore, if Christianity is true, then God is a divine substance, consisting of three persons (who are all consubstantial). So if this is the case, then 'God' refers to a divine substance. So let's assume that any occurrence of God that doesn't refer to the divine substance refers to a fictional object.
(1) Scooby-Doo is a dog.
(2) Dog refers to the species canine.
(3) If Daphne kisses Scooby-Doo, then she kisses a canine.
(4) Scooby-Doo isn't a dog, rather Scooby-Doo is a cartoon drawing of a dog, i.e. Scooby-Doo is a fictional object.
(5) The word 'dog' in (1) is ambiguous.
Let's take the following example:
(6) The Greeks worshiped Zeus.
(7) Zeus is a god.
(8) Gods are a species of divine beings.
(9) Therefore, the Greeks worshiped a species of divine beings.
However, (9) is false, once again Zeus is a fictional object, so the intentionality of the Greeks was directed at a fictional object.
Furthermore, if Christianity is true, then God is a divine substance, consisting of three persons (who are all consubstantial). So if this is the case, then 'God' refers to a divine substance. So let's assume that any occurrence of God that doesn't refer to the divine substance refers to a fictional object.
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