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I have been reading Florian Steinberger's dissertation (Harmony and logical inferentialism) and I come across the following on p60:

...two fundamental assumptions (the other one being the principle of autonomy) that underpin not only the inferentialist approach to logicality but also the logical inferentialist's view more generally.

The principle of innocence: logic alone should not be a source of new information. That is, it should not be possible, solely by engaging in deductive reasoning, to discover hitherto unknown (atomic) truths about the world that we would have been incapable of discovering (at least in principle) independently of logic.

And Steinberger remarks at the footnote:

The principle of innocence has a well-known flipside: if logic really does not deliver any new knowledge, then how are we to explain its usefulness?

This strucks me as a very interesting point: indeed, if one believes in the principle of innocence, it seems that we shouldn't be able to derive new knowledge, e.g. mathematical truths, by deductive reasoning.

So my question is as follows: Is there a particular name given to this debate? And could anyone suggest any further reading (would be best if they are an overview article on the debate in general) please?

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    This issue is well understood now, the new knowledge discovered in deductions is of a different sort than what Steinberger is talking about, see What is the difference between depth and surface information?
    – Conifold
    Mar 11, 2019 at 23:22
  • @Conifold Thank you; this is exactly what I need
    – Constantly confused
    Mar 11, 2019 at 23:30
  • That seems like a very silly debate. Imagine logic as being a machine. The machine has one input funnel and one output conveyor belt. "If the machine can't output new fact without us putting new facts in, then why is the machine useful?" It's like saying if you don't put any gasoline into a car, the car goes nowhere. Therefore, the car is useless. Logic is useful for the same reason that if you had gasoline, but no car, you would go nowhere. If you have some old facts, but no logic machine to put then into, cranking out new facts will be rather difficult.
    – Toothpick Anemone
    Mar 3, 2020 at 22:53

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If you were blindfolded, and taken to a city you have never been to or seen on any map, and then taken to inside a building with no windows, un-blindfolded, and asked to draw a map of the city you were in - you'd fail. Logic would not enable you to construct a map of the city from scratch.

However, if you grew up in a city, but had never seen a map of it, you could still try to draw a map of it, based on what you knew. The easiest way to map a city, is obviously looking at it, and drawing what you see. But logic (or other ways of processing information better) may allow one to to discover the implications of what you already know, without having to wait for the data to hit you over the head with it.

On your first visit to a large city you may observe power lines or water. Or, today, without going there you may deduce (or make an educated guess) that they have power lines and water based on things like the population, what country it is in, its precise geographic location, and other such things. (Likewise, without going back in time to when the dinosaurs lived, you may deduce that there where no power lines anywhere back then, but there was water in a lot of places back then.)

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