Deep suspicion of any line?

Does "deep suspicion of any line" mean "deep suspicion on/about any line"?

Background info:

The real question is: Is there anything we can think of which, by the mere fact that we can think of it, is shown to exist outside our thought? Every philosopher would like to say yes, because a philosopher's job is to find out things about the world by thinking rather than observing.
If yes is the right answer, there is a bridge from pure thought to things. If not, not.

My own feeling, to the contrary, would have been an automatic, deep suspicion of any line of reasoning that reached such a significant conclusion without feeding in a single piece of data from the real world. Perhaps that indicates no more than that I am a scientist rather than a philosopher. Philosophers down the centuries have indeed taken the ontological argument seriously, both for and
against. The atheist philosopher J. L. Mackie gives a particularly

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