I would humbly submit that the sentence
Anthropomorphism is inevitable if the question of the how of predication of the attribute is raised in the expectation of an answer similar to that analyzing the relation of the predicate to the subject in the empirical world.
be taken out and shot. That is a sterling example of how not to write English, and I am very sorry your life circumstances have put you in a situation where understanding it is necessary or desirable.
Without knowing what on earth the author is actually going on about, here is my best crack at what can be discerned.
The author is arguing that there is a certain circumstance in which a person's mind is effectively forced to anthropomorphize. (Whether the author is speaking of anthropomorphizing in general, or anthropomorphizing one particular thing is ambiguous in this passage.) That circumstance (the author explains) is one in which the thinker in question attempts to analyze something "transcendent" in the same way he attempts to analyze empirical things in the every-day world. In particular, when the thinker attempts to think about this transcendent thing (or things) in an similar way to "analyzing the relation of the predicate to the subject". (I have no idea what that means here.)
The author goes on to explain that this happens because "the question itself is invalid". It seems the author believes this effect (the anthropomorphizing) in the mind of the thinker happens because of a sort of divide-by-zero or typecasting error in humans, when they attempt to reason in this way about a transcendent "subject and predicate" (whatever "transcendent", "subject" and "predicate" mean here.)
The author argues that the mechanism of this is that the failure of the analytic method which had served the thinker in the empirical realm, provokes the thinker to be open to alternatives to the empirical, to being willing to think in a "new modality" other than the empirical. However, there is, according to the author, no such thing: the author argues that the mind of the thinker attempts something impossible because "no new modality is possible". When that happens (according to the author), that is when the mind of the thinker is caught between the impossibility of both ordinary reasoning and a "new modality", the thinker's imagination is forced to step in and make one up on the spot.
And when that happens, "an intuition of transcendence is obtained", by which I think the author means, "the thinker experiences a felt sense of 'transcendence'", since he says it's like what happens when one contemplates infinity. (I am entirely unfamiliar with the "sensory inexpressibility engendered by the arabesque". I have no sense of what "the arabesque" is in this context.)
The author does not in this paragraph get back to the connection to anthropomorphization. I'm guessing that that's what the author is contending the imagination does in this circumstance: imagine the transcendent thing being reasoned about as a person or other entity with agency. But that is not made explicit in this paragraph.
Upshot: According to this author, when you try to reason normally about "transcendent" things, your mind hiccups and your imagination makes stuff up that feels "transcendent".