Necessary Synthetic Truths: Part 2

This argument is similar to the one I gave in a previous post, but it may be easier to understand, and so here is the second version of my argument for necessary synthetic truths:

Now what is a synthetic truth?

Philosophers have divided truths into two kinds of truths, analytic truths and synthetic truths. Analytic truths are basically the relationships between ideas. The definitions of words are analytic truths. Other analytic truths include 1+1=2, all bachelors are unmarried, and all triangles have three sides. Those truths simply tell you about how ideas are related. Once you understand what a bachelor is, you realize that a bachelor is by definition an unmarried male.

Synthetic truths are truths that deal with the way reality is. They are about matters of fact The mass of the Eiffel Tower, what clothes you are wearing, the number of books on your bookshelf, the length of a movie, are all synthetic truths.

One common objection I often see regarding the Ontological Argument is that the existence of a being is a synthetic truth, and therefore cannot be a necessary truth. I intend to put this to bed once and for all.

To say that "there are no necessary synthetic truths" if true would either be an analytic truth or a synthetic truth. If it were a synthetic truth, then the statement "there are no necessary synthetic truths" would itself be a necessary synthetic truth! Therefore, if true, it would have to be an analytic truth. If so, then the term is merely a sterile definition of a word, having no applicability to which ways reality could or could not be configured. The statement would be trivial and irrelevant to the debate.

To then say that there are no necessary truths about how reality is configured is again, to claim a synthetic truth. If any statement is about the configuration of reality, and not merely about the relation of ideas, the statement "there are no necessary truths about how reality is configured" is. If true, it would be a necessary synthetic truth, and therefore self-refuting.

Any statement about what matters of fact could or could not be the case is by definition a statement about matters of fact, not relations of ideas. Any statement about what could or could not be the case is by definition a modal statement (concerning possibility and necessity). Hence, any assertion that there are no necessary synthetic truths is either self-refuting, or twists its vocabulary to the point that it is no longer talking about necessary synthetic truths.