Having been in engineering for most of my life, I have also found the attractions of science to be almost irresistible. There is something neat about it. The scientist begins by making an observation and proceeds to ascertain the causes of it. After many such investigations, and when sufficient data has been accumulated, he then feels confident enough to propose a law which will account for his observations. And, using that law, he then feels able to make some predictions of a more general nature.
Let me say at once that I see nothing wrong with this method. It is, after all, the foundation a good deal of our technology ; and that technology can be seen to work. The weakness of science does not lie in its method but in attitudes towards it. The method has proved so successful that it has seduced many into believing that it is the only valid method of describing the natural world. So successful has it been that many, perhaps the majority, of people pour scorn on any attempt to devise another. This is especially true, I think, of the people of the West. But there are objections to it, and there are many of them, so they will need to be severely summarised.
In the first place, science investigates the causes of natural events ; but there is no mention of purposes. A scientist will perhaps tell us what happens, but is silent on why a thing happens. A scientist will tell us of a natural physical law, but offers no opinion on why the law exists. Also there is the question of what is observed. Out of all the events occurring in an experimental condition, only certain of them are selected for observation. Thus science deals with abstractions, with simplicities ; and by its nature is partial in the data it considers worthy of investigation.
So, all in all, science as it is done now is successful in what it attempts to do ; but its methods are limiting and, therefore, it cannot offer more than an abstract view of the world. Therefore it cannot provide complete knowledge of nature, however hard it tries.
The physicist, AN Whitehead offered this insight : science is the application of commonsense to an idealised world. But the world is not ideal ; it is not a laboratory ; and there is much going on in nature that science knows nothing of.