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Definition

The existence is definitional.
In a scientific field definitions of terms must be bijective. If we apply this criterion we’ll see that physics is not a science but scholastic casuistry and a consistent system of equivocations.
«Unless you respect the sanctity of your definitions no formal logic can save you from scholastic sophistry.»
Existence is definitional. Everything that exist exists because it is defined.
Football leagues are definitions. They are legal entities based on consensus.
Stopping at red lights is a definition. It is a contract. A social contract. Contract is definition anyway.
These letters and words are all definitions.
The world will not exist without definition. Human society will not exist. But nature too is definitional.
And then there imaginary definitional links. Conventions that everyone believes to be true. Even family ties. What are they?

Would it be correct to say that “mathematical definition does not ascribe meaning”?

It depends on what you mean by “meaning” and how you are using the term “mathematical definition.” Here’s a breakdown:

If by “meaning” you refer to real-world interpretation or application, then yes, a mathematical definition itself does not directly ascribe meaning in that sense. A definition simply establishes a precise framework for a concept within mathematics, without concern for its external significance.

Example: The definition of a group in abstract algebra describes a set with a binary operation satisfying specific properties (closure, associativity, identity, and inverses). This definition doesn’t tell you what the group means in the real world (e.g., symmetry operations or transformations); it only defines its mathematical structure.
If by “meaning” you refer to internal consistency or conceptual clarity, then no, mathematical definitions do carry meaning within the mathematical context. They provide the foundation for reasoning, proofs, and the development of new ideas.

Example: The mathematical definition of a limit in calculus gives a precise meaning to the intuitive idea of approaching a value. This meaning is essential for understanding the concept of continuity or derivatives.

Let me know which perspective you want to emphasize!