Hume and Mathematic 'certainty'...

Hi there.
I enjoy philosophy for pleasure but have not studied it formally so apologies if this question sounds a little simplistic or has been discoursed-to-death!

I’m currently reading through Hume’s Treatise and I’m trying to grapple with one aspect in particular -

I understand the proposition that we do not come to an appreciation of cause and effect through RATIONAL REASONING but from us percieving the repetition of instances leading us to the assumption that the sun will rise in the morning or predicting the behaviour of a billiard ball when struck by another. So this leaves relation of cause and effect impenetrable to human understanding.

Is our understanding of Mathematics subject to the same repetitive animalistic presumption or do we truly penetrate into mathematical relations like addition and subtraction?

Does this make any sense? Again apologies if this is a stupid question

Hi Rick, welcome! It’s certainly not a stupid question, the status of mathematics is in important and interesting philosophical subject. I’m moving this post to the Hall of Questions, as that’s the place to go for, well, questions. :slight_smile:

Hume saw mathematics, like logic, as a language to describe the relations of ideas. It’s therefore principally a deductive practice - there’s no need to infer anything from ones impressions about the world, or experience, and mathematics doesn’t tell one anything about the world besides its relations.

As I see it: he wasn’t against deductive thought per se, he just wanted to define its limitations (in the context of Rationalist claims like those of Spinoza and Descartes). Causation isn’t something we can deduce, but take as axiomatic solely due to our repeated experiences; Pythagoras’ Theorem is something we can deduce.

Wasn’t it Popper who was challenged to prove absolutely that 2+2=4; so Popper went and picked up two apples, then two more apples, then counted 4 apples, and shrugged his shoulders with that typical incredulous look he got when the over-analytic crowd tried to include him as “one of them”, which he denied til his death?

Si non e vero, e ben trovato :slight_smile:

It sounds apocryphal, given that he did proper philosophy of mathematics, and his falsifiability criterion for scientific knowledge needed to allow mathematical truths to be applied to scientific facts. But he could have looked to Moore’s proof of an external world for inspiration.

Thanks for the clarification. I stand corrected. Per Popper, the proposition 2 apples + 2 apples is falsifiable; but 2+2 is logically true and not falsifiable unless it is applied to the real world, like apples. Lucky he didn’t work with rabbits, eh? :-"

This is becoming a little clearer, thanks guys. But I still can’t help but think the relations in mathematics are impentrable. To run through my position - take cause and effect. A causes B. I understand that we cannot infer effect B by merely observing cause A (there is nothing in the apple itself that says it will fall to the ground when released) and it is the repetition of the instances A cause B that leads us to causation. (Old ground,I know, sorry). Now I take A+A=AA, super basic (for my my basic mind!). I can see that we can infer AA from A in itself IF the addative is included in the observation. But isn’t the addative relationship something that we can only fathom from expereince, the same way we can only understand causation from expereince. I hate to use a religious reference, but would Adam if plucked from the garden of eden straight after his creation with no experience ofthe world was asked by God ‘Look at this apple, now look at this apple. Now choose form these piles (a pile of 1 apple, a pile of 2 apples and a pile of 3 apples) which pile best represents the first 2 apples,’ would he even fathom what the relationship was or would he need experience of the world to make that associative mathematical principle? I think he would need expereince. Leading me to believe that the base mathematical principles are understood through a comprehension of the world around us.

As I write this I worry this might sound a little rambling, non sensical and maybe a little stupid!

It doesn’t get more concise than that. Well said O_H, as usual. The way you write has a way of making me feel stupid.

Just a note;
The equation “2+2=4” can actually be proven to be absolutely true beyond merely mathematical standardization.


It doesn’t sound very likely. It don’t prove anything. At best, it demonstrates how mathematics may have been inspired by physical experience. Once the physicality is stripped from the apples and action of collecting/grouping , there are pure symbols left.

I actually saw this just the other day while researching something unrelated–