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This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice.

In logic, one often draws a distinction between a name (symbol) and the thing it represents (referent) the relationship between the two being called the thought (reference) as per Ogden and Richard's The Meaning of Meaning though the same ideas are found in ancient Greece. And this is a useful distinction if one presumes a sharp distinction between the outside world and the inside mind like in substance dualism.

In your example, note that you are attempting to apply a property to the propositions that does not hold. A-->C, and B-->C and NB that A-/->B and B-/->A. As such, the transitive property ((A-->B, B-->C)--> (A->C)) does not apply!

This is why it is important to examine not just the symbols in an argument, but the content (of the referents) too, because meaning can be found not only in a proposition, but in the relationship between propositions. Particularly important is recognizing that equality is a bidirectional implication, and that questions and answers aren't related the same way two identical quantities with different labels are.

EDIT

NB: A=B, B=C -> A=C is defined as (A<-->B, B<-->C) --> (A<-->C) because (A-->B, B-->C)-->(A-->C) and (C-->B,B-->A)-->(C-->A) where <--> is defined as --> and <-- true over two symbols.

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice.

In logic, one often draws a distinction between a name (symbol) and the thing it represents (referent) the relationship between the two being called the thought (reference) as per Ogden and Richard's The Meaning of Meaning though the same ideas are found in ancient Greece. And this is a useful distinction if one presumes a sharp distinction between the outside world and the inside mind like in substance dualism.

In your example, note that you are attempting to apply a property to the propositions that does not hold. A-->C, and B-->C and NB that A-/->B and B-/->A. As such, the transitive property ((A-->B, B-->C)--> (A->C)) does not apply!

This is why it is important to examine not just the symbols in an argument, but the content (of the referents) too, because meaning can be found not only in a proposition, but in the relationship between propositions. Particularly important is recognizing that equality is a bidirectional implication, and that questions and answers aren't related the same way two identical quantities with different labels are.

EDIT

NB: A=B, B=C -> A=C is defined as (A<-->B, B<-->C) --> (A<-->C) because (A-->B, B-->C)-->(A-->C) and (C-->B,B-->A)-->(C-->A) where <--> is defined as --> and <-- true over two symbols.

To address comments below, let's not get caught in a deepity. The questions with the same answer can be seen essentially as two propositions:

1. Birds are animals with feathers that can fly.
2. Birds are the subject of Audubon.

Yes, birds are a common subject, so insofar as these two propositions have the same subject, they have a common attribute. But because they have different predicates, they have other attributes not the same, so the propositions themselves are different. A is not equal to B. In FOPC, A := Fx : x:=b and B := Sx : x:=b and clearly Fb ≠ Sb despite D: of Fb ∩ D: of Sb = b at a minimum.

What is more interesting is having the same proposition in different statements which highlights the difference between syntax and semantics:

1. Birds are animals with feathers that can fly.
2. Animals of flight adorned with feathers are birds.

The difference in statements (syntax) is obvious, and would likely confuse a computer (see Turing Test), and yet most natural language speakers would have little problem in seeing these as equivalent propositions (semantics), that is they really mean the same thing. In FOPC, A := Fx : x:=b and B := Ax : x:=b and clearly Fb = Sb, and thusly A = B.

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice.

In logic, one often draws a distinction between a name (symbol) and the thing it represents (referent) the relationship between the two being called the thought (reference) as per Ogden and Richard's The Meaning of Meaning though the same ideas are found in ancient Greece. And this is a useful distinction if one presumes a sharp distinction between the outside world and the inside mind like in substance dualism.

In your example, note that you are attempting to apply a property to the propositions that does not hold. A-->C, and B-->C and NB that A-/->B and B-/->A. As such, the transitive property ((A-->B, B-->C)--> (A->C)) does not apply!

This is why it is important to examine not just the symbols in an argument, but the content (of the referents) too, because meaning can be found not only in a proposition, but in the relationship between propositions. Particularly important is recognizing that equality is a bidirectional implication, and that questions and answers aren't related the same way two identical quantities are.

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice.

In logic, one often draws a distinction between a name (symbol) and the thing it represents (referent) the relationship between the two being called the thought (reference) as per Ogden and Richard's The Meaning of Meaning though the same ideas are found in ancient Greece. And this is a useful distinction if one presumes a sharp distinction between the outside world and the inside mind like in substance dualism.

In your example, note that you are attempting to apply a property to the propositions that does not hold. A-->C, and B-->C and NB that A-/->B and B-/->A. As such, the transitive property ((A-->B, B-->C)--> (A->C)) does not apply!

This is why it is important to examine not just the symbols in an argument, but the content (of the referents) too, because meaning can be found not only in a proposition, but in the relationship between propositions. Particularly important is recognizing that equality is a bidirectional implication, and that questions and answers aren't related the same way two identical quantities with different labels are.

EDIT

NB: A=B, B=C -> A=C is defined as (A<-->B, B<-->C) --> (A<-->C) because (A-->B, B-->C)-->(A-->C) and (C-->B,B-->A)-->(C-->A) where <--> is defined as --> and <-- true over two symbols.

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice.

In logic, one often draws a distinction between a name (symbol) and the thing it represents (referent) the relationship between the two being called the thought (reference) as per Ogden and Richard's The Meaning of Meaning though the same ideas are found in ancient Greece. And this is a useful distinction if one presumes a sharp distinction between the outside world and the inside mind like in substance dualism.

In your example, note that you are attempting to apply a property to the propositions that does not hold. A-->C, and B-->C such that A-/->B. As such, the transitive property ((A-->B, B-->C)--> (A->C)) does not apply!

This is why it is important to examine not just the symbols in an argument, but the content (of the referents) too, because meaning can be found not only in a proposition, but in the relationship between propositions.

This is a question in philosophy that deals with the metaphysics of identity. A classic problem in philosophy is the Ship of Theseus and goes back to the pre-Socratics, particularly Heraclitus and his proposition that one cannot stand in the same river twice.

In logic, one often draws a distinction between a name (symbol) and the thing it represents (referent) the relationship between the two being called the thought (reference) as per Ogden and Richard's The Meaning of Meaning though the same ideas are found in ancient Greece. And this is a useful distinction if one presumes a sharp distinction between the outside world and the inside mind like in substance dualism.

In your example, note that you are attempting to apply a property to the propositions that does not hold. A-->C, and B-->C and NB that A-/->B and B-/->A. As such, the transitive property ((A-->B, B-->C)--> (A->C)) does not apply!

This is why it is important to examine not just the symbols in an argument, but the content (of the referents) too, because meaning can be found not only in a proposition, but in the relationship between propositions. Particularly important is recognizing that equality is a bidirectional implication, and that questions and answers aren't related the same way two identical quantities are.