Alfred Ernest Mander (1894-1985) may have been Jewish. He had a mixed background; however I've learned to deeply distrust online biographies. This book was published by Watts & Co, at least in Britain, number 57 in the Thinker's Library. This series (related to South Place Ethical Society) published books by Wells, Haeckel, Bradlaugh, Darwin, Joseph McCabe and others, on similar principles to George Allen & Unwin's paperbacks after WW2. They had a definite, but very muted, secret Jewish bias—in line with all broadcasting, publishing, education, and religion.

The first publication date, 1936, suggests competition with Jepson, but I don't know the story, if any. But I'd guess, from the rather large typeface and the use of capitals, and thickish paper, that Mander's book was a rushed job. It seems to me to be bitty and fragmented.

Mander has a practical attitude to thinking, which looks very different from Jepson's, though the outcomes aren't very different, since neither is radical in the true sense. Mander might produce trade union speakers, and Jepson's Tory types, but neither would get to the roots.
      Mander starts ‘Thinking is skilled work. It is not true that we are naturally endowed with the ability to think clearly and logically—without learning how, or without practising. It is ridiculous to suppose that any less skill is required for thinking than for carpentering, or for playing tennis, golf, or bridge, or for playing some musical instrument. ... as a people, we are so much less efficient in this respect than we are in our sports. ...’
      Mander is keen not just on thinking, but outputting thoughts to his audiences: Most speakers and writers use far too many words. They obscure their thought with great masses of verbiage. Usually it is possible to re-write a passage—expressing every essential point with clarity and precision—in one-half, one-third or one-quarter of the number of words. Mander gives a 9-point suggested process to work through any passage to check the "facts" and the reasoning. He has a section VII THEORIES where he starts from "It's all right in theory [not OK, back then!} but it doesn't work out in practice", ridicules that form of words, and goes on to discuss testing of theories—including 'general' and 'special' theories. Mander has a section on the RECOGNIZED EXPERT AUTHORITIES which resembles the 'peer group' idea in modern academia, though Mander has doubts which seem correct: he wants actual name(s), recognition as an expert authority, preferably alive, and unbiassed. if there is AGREEMENT among most of the expert authorities, then we may assume that their various interests and prejudices cancel out ... Um, well. The book is unindexed, and has an Appendix on Determinacy and cause; it has the concept of probability, but not probability distributions.

Mander, in a section entitled 'Evolution': ‘During the last few generations, man has made a discovery the importance of which it is difficult to over-estimate. It is this: that nothing can be fully understood except by reference to its context. .. all things are largely unintelligible—if we consider only the facts at any given instant of time. .. like going into a cinema in the middle of a picture.. glancing.. and coming out. What we should see would be unintelligible. Perhaps a horseman.. with one foot in the stirrup,.. looking.. at a square black box on the ground; .. a policeman, his clothes dripping water, rushes from a house.. carrying a dead goose.. Similarly.. to understand the present, we must know something of the past out of which it has grown. This truth.. though it now seems obvious, is really quite new to man .. But already it has revolutionized the whole thought of educated, civilized people. To-day we try to see almost everything in the light of its history.. in its new sense of one thing leading to another. ..'
      H G Wells credited Marx with having this conception; — in New Worlds for Old he says Marx invented it. Possibly The Outline of History would not have existed unless Wells believed something like that. Or perhaps not!
      I can think of at least two 'important discoveries'—the discovery of suspended judgment, and the discovery of the idea of evolution. Mander doesn't really explain how such discoveries could be tested.

'Children, savages, and the majority of persons.. are content to take things as they find them. ... The desire to understand.. things.. is not a desire that comes early in the development of either the individual or the race. It is remarkable how incurious primitive savages are. About as incurious as is the average lady motorist about what is under the bonnet of her car! Or the average man about what is going on under his own hat!'
      Primitive man's beliefs were permitted by lack of knowledge:] ‘[found it].. not.. incredible that a stick might become a snake; the the Nile might rise in answer to prayers..; that a donkey might begin speaking Hebrew; that the sun might "go out" at the bidding of.. Christopher Columbus..; that mountains in New Zealand might quarrel..; that Buddha might be begotten in his mother by a ray of moonlight..’

Mander is refreshing, but shies away from serious discussions on wars, law, industry, raw materials. So his book turns out to be rather limited. Perhaps he added 'Logic for Everyman' to his title as an acknowledgement of this limitation.