To find found out the reason behind Hume’s phrase (connected to his philosophy) and to express own opinion about it.
Welcome bbbbbbb. Hume did not encourage others to burn his books. In An Enquiry concerning Human Understanding, 1748, XII.3, in a rhetorical flourish he recommended the burning of other people's books if they did not meet the two conditions he had set for properly conducted philosophy:
If we take in our hand any volume of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.
Hume confined the matters with which philosophy should concern itself and with which it is capable of dealing to (1) 'relations of ideas' and (2) 'matters of fact' (IV.1). If a philosopher makes a claim that does not involve conceptual analysis ('relations of ideas' here illustrated rather restrictedly by 'abstract reasoning concerning quantity or number') or that cannot be checked or verified by empirical investigation ('matters of fact' here referred to as 'matter of fact or existence') then there is no way in which the claim can be vindicated or refuted. It is therefore pointless to discuss.
Hume emphasises this pointlessness by his (non-literal) recommendation to consign to the flames any book that fails either or both of his two conditions.
We may (or may not) accept Hume's restriction of philosophy to conceptual analysis and empirical investigation; and we cannot endorse Hume's account of 'relations of ideas' and 'matters of fact' as it stands; our understanding of these things is more refined than Hume's or at least different from it. But Hume's essential objection to the books he would consign to the flames is clear enough.