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I am having a hard time to understand what a definition does. Is it an abbreviation we use instead of using too many words? But then why mathematicians define mathematical objects? Does it mean they "create" a new abstract object or the object already exists and they give it a name? Are the objects (abstract or concrete) that come first or the definitions? I apologise if the question is silly.

ado sar
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  • Definitions are not absolute as you think they are. Definitions serve MULTIPLE PURPOSES--not just one. There are even distinct types of definitions --not just one type. Some definitions apply to reality while others don't. Some definitions simply swap & substitute with the word. In this way we can use shorter sentences by using a word instead of the literal attributes that word refers to in reality. So I could just use the term Rhetoric instead of writing ". . . The faculty of observing all of the available means of persuasion." One word as opposed to many right? Just 1 example for you. – Logikal May 21 '20 at 19:10
  • There are different types of definitions, the ones that are just abbreviations are called stipulative, mathematical definitions within an axiomatic theory are of this sort. It is implicit "definitions" of the theory itself (through axioms) that do more than just abbreviate. But whether mathematicians thereby "create" new objects or "discover" them in a pre-existing "landscape" (or, perhaps, a mixture of both) is a perennial question that depends on one's metaphysics, and the answer makes no difference to the substance of mathematics. – Conifold May 21 '20 at 19:12
  • Some definitions are conceptual & not sense verifiable. I can combine ideas that are true & not reality: I have an idea of a man; I also have an idea of a horse distinctly. If I combine them I can define a Cenataur which is not true in reality. 2 true ideas brought forth an idea not verifiable in science for instance.some terms have no legit definition such as human being. A dictionary will report a person. What is a person? You get told a human being. Circular reasoning in the dictionary. So the dictionary is NOT AN AUTHORITY. You as a human being should know words are used in a context. – Logikal May 21 '20 at 19:18
  • Context express definitions not the dictionary entries. The dictionary is a guide not something you should be pointing to & say "the dictionary says . . . " This means no literal reading of every sentence you read. Some sentences are ironic, analogous satire, rhetorical etc.Context defines what idea is being brought forward to others . You can read the Stanford entry or other philosophical sources about definitions: plato.stanford.edu/entries/definitions. You will find that philosophy materials go into rules of definition as well. We can't just do what we like with words! Well we OUGHT NOT. – Logikal May 21 '20 at 19:24
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    You may have a look at " Theory Of Definition " in Suppes, Introduction to Logic http://web.mit.edu/gleitz/www/Introduction%20to%20Logic%20-%20P.%20Suppes%20(1957)%20WW.pdf –  May 22 '20 at 14:20
  • Your question is too broad. Consider if the attribute concrete is possible outside of a mind; if not, the difference with the attribute abstract is absolutely subjective. Such thought experiment will help you focus the idea. – RodolfoAP May 25 '20 at 17:54
  • @Logikal For example in we can define functions, matrices etc without actually show that indeed inside the system (I don't care if they exist in platonic or whatever view) there are such objects that we give them that name. It is like I give a definition that doesn't correspond to any object in reality. If math do the same then there is a problem. Suppose I define "fc=flying crocodiles". I make the statement "All flying crocodiles are green". The problem is that this sentence fails to refer as much as the sentece "All functions are even" if there are no functions at all. – ado sar Jul 30 '20 at 10:48
  • @ado sor, IN MATHEMATICAL LOGIC the term proposition is not used correctly usually. In philosophy the term proposition is NOT A SENTENCE. So there are issues already. The issue has a name in Mathematical logic: existential import. This means that some propositions can fail to refer in a sense verification way. That is, you can't apply out famous 5 senses to it. This is a problem for you because you don't know what propositions are. Existential import is irrelevant if a set has members. That is if there are real world members you could apply at least one of the famous 5 senses to the member. – Logikal Jul 30 '20 at 12:48

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