Re: “Since all reasoning is inductive, it would have a little consistency problem.” No: see deductive reasoning.
Re: “Hume’s complaint is that there is uncertainty and doubt in all conclusions”—Hume’s problem of induction is only concerned with induction.
Re: Acceptance of induction among philosophers: Hume’s point was not that induction was common or mistaken—but that it is not rational, it lacks justification that would convince a sceptical rational agent.
Re: “How does a position merit the title “skeptical” when it maintains an infinite certainty of something completely contrary to experience”—the idea that the past cannot predict the future is not contrary to experience. It conflicts with evolutionary biology—but good luck with convincing an inductive sceptic that evolutionary biology is correct—the whole enterprise is founded on induction.
Re: “Since all reasoning is inductive, it would have a little consistency problem.” No: see deductive reasoning. Re: “Hume’s complaint is that there is uncertainty and doubt in all conclusions”—Hume’s problem of induction is only concerned with induction. Re: Acceptance of induction among philosophers: Hume’s point was not that induction was common or mistaken—but that it is not rational, it lacks justification that would convince a sceptical rational agent. Re: “How does a position merit the title “skeptical” when it maintains an infinite certainty of something completely contrary to experience”—the idea that the past cannot predict the future is not contrary to experience. It conflicts with evolutionary biology—but good luck with convincing an inductive sceptic that evolutionary biology is correct—the whole enterprise is founded on induction.