# What term is most appropriate when describing the infinite space of possibilities created through inductive reasoning?

In arguments contrasting the differences between deductive reasoning and inductive reasoning, it is often pointed out that deductive reasoning is, by definition, bounded by the terms described in the problem through narrowing application of boolean logic. This contrasts with inductive reasoning, which is by definition unbounded through widening application of probabilistic analysis and inclusion of emergent properties.

In describing the infinite nature of the solution space provided by inductive reasoning, I have generalized this into the phrase "inductive space." However, according to Google, this phrasing is pure jargon and suffers overlap into other knowledge domains that may cause the listener severe confusion.

I am leery to ask this question on other StackExchange sites (especially http://math.stackexchange.com), because this is actually a question of language instead of a mathematical problem and because I would greatly prefer a term applicable to a wider audience than mathematicians. So, I will ask here. To prevent confusion and maximize the odds that the correct definition is understood, what English term or phrase would be most appropriate here?

• Despite your qualms, it'd still probably be better at math.SE because you are looking for a domain specific term, which they would be expected to have more experience with. Oct 7, 2011 at 19:31
• @Mitch I agree, insofar as mathematicians on math.SE are more likely to suggest terms applicable by and understood by other mathematicians. In this case, I'm looking for a term more accessible by the general population, which asking on another StackExchange site would not easily provide. Oct 7, 2011 at 19:34
• Also, it is not clear what concept you want to have a name for. Is it the space of solutions to an experimenal inference as opposed to a logical inference? Oct 7, 2011 at 19:35
• If you are really looking for “a term more accessible by the general population,” then that criteria should appear in the question. The current question contains no clue that you are looking for anything other than a mathematical term. Oct 7, 2011 at 19:36
• From what you describe it may be too much to ask for a term that the general population understand because they'd have to understand your underlaying theory to understand the term. Probability spaces or sets of possible worlds are not common concepts. So it might be more reasonable to try to come up with a term that makes sense given your theory, i.e. one that is easy to remember and comprehend given that one knows something of your theory or similar theories.
– N.N.
Oct 7, 2011 at 19:45

It might not be possible to come up with a term that is accessible by the general population simply because what the term is supposed to describe is unknown to the general population.

Either someone reading your text is someone from the field in question, a professional, or they are a layperson. If they are a professional they'd prefer a term that makes sense given your theory and the field in question, so it doesn't matter if it's technical or ambiguous in other contexts. If the person reading your text is a layperson they would not benefit from one term being more accessible as long as your whole theory is not as accessible.

Thus, I'd suggest that you come up with a term that makes sense within your theory and field. What you seem to speak of is possibilities given premises. These can be construed through concepts such as solution spaces, probability spaces or sets of possible worlds. It's important that the term you choose is consistent with how you speak of possibility in any other place in your theory, e.g. if you speak of possibilities as sets of possible worlds you should only speak of possibility that way to avoid confusion. Even if you use technical terms they can be more or less self-explanatory, so choose them carefully. For instance if you speak of sets of possible world you could say that the set of possible worlds expressed by a deduction is a subset of the set of possible worlds expressed by the premises, but the set of possible worlds expressed by the conclusion of an induction can be a superset of the set of possible worlds expressed by the premises. By comparing cardinality of sets of possible world it might also be possible to effectively communicate their size and infinity (I'm just guessing here, dunno what you want to say).

If you still want a term that a layperson understand you might want to speak of possibilities so that keep close to common talk of possibility, i.e. how possibility is conceived of and discussed in everyday situations. For example you could say that given some conditions there is greater or wider possibility than given some other conditions.

Finally, in both cases examples are powerful tools to illustrate terms you want to define. A good example can make a theory easier to understand and remember.

• +1 for cogency. Like you, I'm not sure exactly what OP wants to say, but your guess looks as good as any - probably better than most. Personally I can't see anything wrong with unbounded. OP used it himself, it chimes with his "infinite", and it seems reasonably accessible (to me at least, and I'm certainly only a layman in this context). Oct 8, 2011 at 0:20
• @FumbleFingers +1. I hadn't actually considered using the term unbounded on its own, which does elegantly and pithily describe the space. Thank you for responding, despite your difficulties with my phrasing of the problem. Oct 9, 2011 at 20:03

Both your suggestions solution space and induction space are appropriate for different reasons.

Solution space works because it is very specific and your concept seems to be about solutions to a problem that come from a given set.

Induction space does seem to be use in widely different ways in your google link, but that's because it is very non-specific and so can be used locally and disambiguated with the context (and your own explicit definition).

Both of these answers artfully and elegantly answer this question and are equally-deserving of the accepted answer:

• This will become the accepted answer in two days, when the expiry for self-accept expires. Because of UI hints and the political ramifications of accepting one's own answer, I've opened a Meta discussion here: meta.stackexchange.com/questions/108729/… Oct 7, 2011 at 22:07

Range of induction. Range of deduction.

Range of function is a well known term in mathematics. as bonus we get Image of induction and Image of deduction

with a deductive map, taking an object from the range of deduction to image of deduction.

Using this terminology we can only ponder what would it mean for a deductive map to act between a inductive range to inductive/deductive image.

In maths or statistical mechanics it would be called "phase space". Perhaps you could adopt it for your needs.

https://en.wikipedia.org/wiki/Phase_space