What is the best English title for chapter 3?
DAS DENKEN IM DIENSTE DER WELTAUFFASSUNG
DENKEN: thought, thinking DIENSTE: service
WELTAUFFASSUNG: world-view---  WELT: world AUFFASSUNG: perception, conception, view, understanding

Chapter 3 mainly compares thinking and thought to other things and concludes it is special. 3-1 "But thought, as an object of observation, differs essentially from all other things." It establishes that thinking is always correct in itself but may not always be correctly applied or may not even tell us anything of the world. Later chapters will cover this. 3-12 "I can understand someone doubting whether we can determine anything about the world by means of thinking, but I find it incomprehensible that anyone can doubt the correctness of thinking in itself." If this chapter ends with not being sure we can understand anything about the world with thinking, how can you give it the title; Thinking in the service of Understanding the World? Our thinking may be correct but we may have the wrong concepts, 3-5 I know immediately, from the content of the two concepts, why my thinking connects the concept of thunder with the concept lightning. This, of course, does not depend at all on whether I have the right concepts of lightning and thunder.

How does thinking serve the world in this chapter; world-understanding, world-knowledge, world-comprehension, world-apprehension, or world-view?
In this chapter we have doubts whether

it gives us world-knowledge. But we have no doubt we have knowledge of our own thinking. 3-10 We can grasp thought through itself. The only question is whether we can, with thinking, grasp anything else other than thought. Should the title be; Thinking in the Service of Knowing Itself?

It translates as Thinking in the Service of World-View. If chapter 2 describes the basic world-views such as Materialism, Spiritism, and Idealism then in this context you could see thinking as a service to these world-views. Knowledge of our own thinking would be knowledge of our world-view so you could justify the title: Thinking in the Service of Knowing World-View. Thinking in the Service of World-View would mean that thinking serves our way of thinking, using the proper world-view for the situation, 3-11 I find it very strange that philosophers should be accused of troubling themselves, first and foremost, with the correctness of their principles instead of turning straight to the objects which they want to understand.

The overall mood of chapter 3 is Mysticism. Mysticism is experiencing something about the world internally, "only in the inner realm does the world unveil its secrets". Thought is revealed in our inner realm and reveals the secrets of the world. So thinking is in the service of understanding, comprehending or apprehending the world. Thinking is only a tool that can be properly used or mis-used in understanding the world. Later chapters will teach how to properly use it.

Chapter 3 explains the tool so it is an "instrument" that can be used justifying; Thinking as the Instrument of Knowledge. Is thinking a service or tool? Thinking is shown to be something we can choose to use or not use, 3-0 I can be content with the observation, and do without any search for concepts if I have no need of them. The chapter explains how to use it.

Understand stresses the full awareness or knowledge arrived at, and comprehend, the process of grasping something mentally. One may comprehend the words in an idiom without understanding at all what is meant. Here is one: Thinking as the Instrument for Understanding the World .

revision: Thinking as the Instrument for Understanding the World (I will make this change and see if it holds up after some time)

Other Translations:
Lipson: Thinking in the service of Understanding the World
Stebbing: Thinking in the service of Understanding the World
Wilson: Thinking in the service of Knowledge
Stebbing?: Thinking in the service of Comprehending the World
Lindeman: Thinking in the service of Apprehending the World
Poppelbaum: Thinking as the Instrument of Knowledge
Hoernle: Thought as the Instrument of Knowledge