The phrase "arguments to show" is correct and usable in written English.
It can be used when presenting reasoning or evidence to support a particular point or claim in an argument or discussion.
Example: "In this essay, I will present several arguments to show the importance of renewable energy sources."
Alternatives: "points to demonstrate" or "reasons to illustrate".
Plato's Republic contains one of the earliest systematic arguments to show that sense experience cannot be a source of knowledge.
Then they proceed negatively, deploying various arguments to show that Darwinian mechanisms could not possibly do the trick.
Young used geometrical arguments to show that the superposition of the two waves results in a series of equally spaced bands, or fringes, of high intensity, corresponding to regions of constructive interference, separated by dark regions of complete destructive interference.
Starting from the skeptical doctrines of Socrates, its leaders, Arcesilaus and Carneades, set forth a series of epistemological arguments to show that nothing could be known, challenging primarily what were then the two foremost schools, Stoicism and Epicureanism.
Bishop Basil of Caesarea, in his treatise On the Holy Spirit, defended the same view and then deployed theological arguments to show that the three persons of the Trinity properly received equal praise and adoration in the church's liturgy.
These scientists used mathematical arguments to show, first, that continuous variation (in such characteristics as body size, number of eggs laid, and the like) could be explained by Mendel's laws and, second, that natural selection acting cumulatively on small variations could yield major evolutionary changes in form and function.
His feat is always dragged forth as Exhibit A in the argument to show that mathematics really does seem to have something to do with reality.
Descartes's argument to show that his knowledge extends beyond his own existence depends upon the claim that whatever he perceives "clearly and distinctly" is true.
Harvey devotes a large part of his argument to show how this is done through the close ties of the state and finance.
In a now classic paper published in 1980, "Minds, Brains, and Programs," Searle developed a provocative argument to show that artificial intelligence is indeed artificial.
There is danger in the rhetoric that proclaims wars as just or necessary, the human sacrifice as made in a noble cause, without any honest argument to show that it is so.
