A syllogism can relate to anything if it's constructed as an argument in which X is Y; Y is Z; therefore, X is Z. This kind of reasoning is called deductive; two premises support a logical conclusion.
Does the word syllogism have something to do with biology?
Here's an example of a syllogism:
Only someone with proper training should fly airplanes.
Charles Lindbergh has the proper training.
Therefore, Charles Lindbergh should be allowed to fly an airplane.
References to syllogisms surface in literature. In The Mill on the Floss, George Eliot writes,
"And so the poor child, with her soul's hunger and her illusions of self-flattery, began to nibble at this thick-rinded fruit of the tree of knowledge, filling her vacant hours with Latin, geometry, and the forms of the syllogism, and feeling a gleam of triumph now and then that her understanding was quite equal to these peculiarly masculine studies."
In Far from the Madding Crowd, Thomas Hardy notes,
"Many of her thoughts were perfect syllogisms; unluckily they always remained thoughts. Only a few were irrational assumptions; but, unfortunately, they were the ones which most frequently grew into deeds."
The same author says in his 19th-century novel Tess of the d'Urbervilles,
"She reflected; and with her acute memory for the letter of Angel Clare's remarks, even when she did not comprehend their spirit, she recalled a merciless polemical syllogism that she had heard him use when, as it occasionally happened, he indulged in a species of thinking aloud with her at his side."
And, in case you were wondering, polemical refers to a controversial argument.