I agree with Wittgenstein that "we seldom learn new propositions piecemeal; rather we acquire propositional knowledge in holistic clusters". When I study math from a textbook, I definitely learn page by page, not entire chapters at once!
But I don't understand Wittgenstein's example on §143 with the mountain. Can you please explain like I'm 13? I never studied philosophy.
And I don't grok John Henry McDowell's example that the "natural metaphor for the learning of a first language is "Light dawns"." What? How? You can't learn a language (e.g. Korean) by learning word by word, or grammatical rule by rule. You must know a holistic cluster of vocabulary and of grammatical rules before native speakers of Korean can understand you!
In his posthumously published On Certainty Wittgenstein discusses, amongst other things, the nature of knowledge, belief and certainty.
He stresses the holistic nature of beliefs, saying at section 141, for example, "That when we first believe anything, what we believe is not a single proposition, it is a whole system of propositions. (Light dawns gradually over the whole.)"
Relatedly, despite appearances, we seldom learn new propositions piecemeal; rather we acquire propositional knowledge in holistic clusters. And Wittgenstein illustrates this with the following example at section 143: "I am told, for example, that someone once climbed this mountain many years ago. Do I always enquire into the reliabiliy of the teller of the story, and whether the mountain did exist years ago? A child learns there are reliable and unreliable informants much later than it learns facts which are told it. It doesn't learn at all that that mountain has existed for a long time: that is, the question whether it is so doesn't arise at all. It swallows this consequence down, so to speak, together with what it learns."
The natural metaphor for the learning of a first language is "Light dawns". For light to dawn is for one's dealings with language to cease to be blind responses to stimuli: one comes to hear utterances as expressive of thoughts, and to make one's own utterances as ex- pressive of thoughts. This seems indistinguishable from coming to have something to say, and to conceive others are having something to say; as opposed to merely making and reacting to sounds in a way one has been drilled to feel comfortable with. And light does not dawn piecemeal over particular sentences: "Light dawns gradually over the whole"44—a more or less coherent totality, that is, of sen- tences that one has been drilled into simply accepting. A difficulty in saying anything satisfying about the phenomenology of understand- ing is thus that working one's way into language—or better, being cajoled into it—is, simultaneously, working one's way into a concep- tion of the world, including a conception of oneself as a person among others.45 This idea would be enormously hard to elaborate further; but we cannot even recognize the difficulty—a real problem of description with which we are presented by the phenomenology of understanding—if we accept the assumption that learning a language leaves the content of our perceptions unaltered.
44Wittgenstein, On Certainty §141.
Meaning, Knowledge, and Reality by John Henry McDowell, p 333. Emboldening's mine.
Light is used in a different sense in the quotation from Wittgenstein (1969): "Light dawns gradually over the whole." Light and fire appear as key images of cre- ation and creativity in the Bible, in Blake's poetry, in Shelley's—but the sense of each metaphor must be worked out in each case, from its place in a system of beliefs and feelings.
Creativity, Psychology and the History of Science edited by H.E. Gruber, Katja Bödeker. p 279.