Concepts are certainly unreal. People doubt this but they can prove it to themself if there is direct insight. That is what the development of satipatthana reveals - that it is only ignorance that takes concepts for realities. As the Abhidhammathasangaha says about concepts like human, person, man, chariot that
"
All such different things , though they do not exist in the ultimate sense , become objects of consciousness in the form of shadows of ultimate things [paramattha dhammas]"(
bodhi p.326)
Just to be explicit: the thinking process consists of different cittas and cetasikas (nama) all arising and passing away rapidly. These are paramattha dhammas, ultimate realities. Let us consider a couple of [examples of] thinking.
1. Think of a flying purple elephant. The process of thinking that imagines this, whether a graphic visualisation or your no-frills, idea only version, consists of cittas and cetasikas. The object of this thinking is a concept, not real.
2. Think of your mother or father (whether alive or not). Again same process - the cittas and cetasikas of the thinking process are real but the object, mother and father, is concept- not real.
3. If your mother and father were right in front of you now (talking to you) and you think of them, again the object is concept, not real; but the thinking process is real. The colours are real, the sounds are real, but mother and father is concept.
Obviously example 1 is easily understood. It is number 2 and especially number 3 that in daily life we get confused by.
Satipatthana can only take paramattha dhammas for object, not concepts. Does this mean we should try not to think of concepts? Some would have us do this but this is not the middle way. All the arahants thought of concepts but they could never confuse concept for reality. Panna and sati can understand dhammas directly even during the processes of thinking that take concepts for objects.
Now there is thinking happening that is trying to comprehend what was just read. The process of thinking is real and it might be rooted in lobha (desire) that wants to understand. The lobha is real - is it seen as just a dhamma , not you. There is also feeling; if you liked what was written this will be pleasant feeling - is it seen as just a conditioned dhamma, not you. And if you didn't like it there was unpleasant feeling, (not your feeling). These present objects must be seen wisely otherwise there will always be doubt and one will not gain confidence. Or one will settle for attachment to the Dhamma rather than insight. Or worse become someone whose aim is to look for little flaws thinking that this is proper investigation.