Locke's views on the syllogism are nuanced. out of four possibilities he selects two roles that it can fulful. Both are inferential :
He does not totally reject the deductive mode of reasoning. In fact, such a rejection would have been inconsistent with his recommendation of mathematics as the appropriate model for scientific inquiry.
But in Chapter 17 of Book IV, entitled "Of Reason," he does discredit the
syllogism, the Aristotelian paradigm of deductive reasoning.
His attack on the syllogism is grounded on his notion of the four degrees
of reasoning: "the first and highest is the discovering and finding out of
proofs; the second, the regular and methodical disposition of them and laying
them in a clear and fit order to make their connexion and force be plainly
and easily perceived; the third is the perceiving their connexion; and the
fourth, the making a right conclusion" (IV, xvii, 3). Fundamentally,
he contends that the syllogism applies only to the third and fourth of these
degrees and that even there, the syllogism was not so much a means of establishing the connections between propositions as a device for testing the connections. Those who are interested in a more detailed summary of Locke's
attack on the syllogism can consult pp. 285-289 of Wilbur Samuel Howell's
Eighteenth-Century British Logic and Rhetoric. (Edward P. J. Corbett, 'John Locke's Contributions to Rhetoric', College Composition and Communication, Vol. 32, No. 4 (Dec., 1981), pp. 423-433 : 428.)
If inference is reasoning from premises to conclusion ('To infer is nothing but by virtue of one Proposition laid down as true, to draw in another as true, i.e. to see or suppose such a connexion of the two Ideas, of the inferr'd Proposition' : Locke, An Essay concerning Human Understanding, IV.xvii.4), then there appears to be nothing in Locke's text, quoted here, that rules out 'the perceiving of their connexion' and 'the making a right conclusion' as inferential.
John Locke, An Essay Concerning Human Understanding, ed. P. Nidditch, ISBN 10: 0198245955 / ISBN 13: 9780198245957
Published by Oxford University Press, USA, 1979.
Edward P. J. Corbett, 'John Locke's Contributions to Rhetoric', College Composition and Communication, Vol. 32, No. 4 (Dec., 1981), pp. 423-433 : 428.
Wilbur Samuel Howell,Eighteenth-Century British Logic and Rhetoric, ISBN 10: 069106203X / ISBN 13: 9780691062037
Published by Princeton University Press, 1971.