I am currently reading Edmund Husserls "Ding und Raum". The book is a complete lecture series about how spatiality and things are constituted. It is heavily descriptive. Husserl used for his analysis the most basic operations I can imagine (e.g. the operation of identity and the operation of distiction) . The level of primitivness seems to me the like of mathematics.

But first we have to clearify, what we want to compare? I see 2 different understandings here: (1) A discipline can be prior to another in regards to its methodological approach. Here Husserl demonstrates that phenomenology operates on an equal level of primitivness. (2) On the other hand a discipline can be seen prior in regards to the nature of its epistemical interests and outcomes. Philosophy loves to ask "why is stuff the way it is?" This kind of questioning and the corresponding anwers can be seen as fundamental.

I think Marc's second conflicting argument entails the second understanding as a hidden component. To say "... phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one." is in fact a consequence of phenomenological insights. But, we have to be careful here: The validity of this argument derives from what it wants to point out.

II think Louis Brassard is right. Mathematics reached a point of high abstraction long before any human started to reflect about whats going on in our mind and why all this stuff is even possible. Now Phenomenology reinvents the wheel again. But this time with an interest into the nature and the origin of transcendental principiles.

So yes. Mathematics is prior to philosophy. This is true only because philosophy is more than just phenomenology. But in some cases philosophy can be as "prior" as mathematics.

Dear Marc,

Mathematics is based on many axioms, on numbers and their operations, and so many others basic ideas that are built-in into axioms. All of this is an epuration/abstraction of very acients accounting , measurement and building practices developed in the first civilisations and which thousand of years later were abstract away and separated from them in pure abstactions. These abstractions although declared axiomatically as independent of the real world are initially imported from it. So mathematics is a formal quantitative epuration of these practices , a kind of phenomenology of these practices. It developed mostly by adding new level of abstraction unifying this basic phenomenology. Pierce is right but is wrong to think mathematic is not a phenomenology. These humans practices abstract away in formalized in mathematics have been possible because human used the abstraction of their senses, especially vision so we re-invent some version of what is already built-in in our sensory-motor system interface. So against mathematic is a phenomenology, a phenomenology that does not know it is one.

Regards,

- Louis

well, let’s try to drive some stakes into the ground:

first,

concerning C.S. Peirce [henceforth CSP] from his description of maths and his description of φανερόν, on whether he were self contradicting with respect to the ‘presuppositionless status of mathematics‘ :

CSP on ‚the essence of math‘ (CP IV, 189-203)

“‚…Mathematics is the study of what is true of hypothetical states of things. That is its essence and definition. Everything in it, therefore, beyond the first precepts for the construction of the hypotheses, has to be of the nature of apodictive inference. …“

and

CSP on appearances ( phenomena) (CP I, 284 … )

„PHANEROSCOPY [or Phenomenology] is the description of the phaneron; and by the phaneron I mean the collective total of all that is in any way or in any sense present to the mind, quite regardless of whether it corresponds to any real thing or not. …“

secondly,

conclusions thereof:

consider, that “imagining an instance in which the premises are true and observing by contemplation of the image that the conclusion is true“ is far from committing to the truth of the premises;

and Marc’s conclusion

‘In fact, I find considerations about the inevitability of appearing in mathematics to be decisive‘

might very well be CSP’s own view;

and if we take for granted, that - according to CSP – mathematics is prior to philosophy ( including phenomenology ) with respect to being presupposition-free, nevertheless (again, according to CSP) we may need phenomenology to describe the essence of mathematical reasoning.

I am currently reading Edmund Husserls "Ding und Raum". The book is a complete lecture series about how spatiality and things are constituted. It is heavily descriptive. Husserl used for his analysis the most basic operations I can imagine (e.g. the operation of identity and the operation of distiction) . The level of primitivness seems to me the like of mathematics.

But first we have to clearify, what we want to compare? I see 2 different understandings here: (1) A discipline can be prior to another in regards to its methodological approach. Here Husserl demonstrates that phenomenology operates on an equal level of primitivness. (2) On the other hand a discipline can be seen prior in regards to the nature of its epistemical interests and outcomes. Philosophy loves to ask "why is stuff the way it is?" This kind of questioning and the corresponding anwers can be seen as fundamental.

I think Marc's second conflicting argument entails the second understanding as a hidden component. To say "... phenomenology is prior to mathematics because whatever happens during mathematical inquiry must perforce appear before (some)one." is in fact a consequence of phenomenological insights. But, we have to be careful here: The validity of this argument derives from what it wants to point out.

II think Louis Brassard is right. Mathematics reached a point of high abstraction long before any human started to reflect about whats going on in our mind and why all this stuff is even possible. Now Phenomenology reinvents the wheel again. But this time with an interest into the nature and the origin of transcendental principiles.

So yes. Mathematics is prior to philosophy. This is true only because philosophy is more than just phenomenology. But in some cases philosophy can be as "prior" as mathematics.

I don't understand the relationship of "is prior to" to ideas. Do you mean which idea came first to a human being? Or which idea has fewer presuppositions? Or which idea does not depend on the other? If that is the case, is your question a false either-or assertion, as can't two ideas be co-dependent, like chicken and egg?

Presuppositions are by definition taken for granted for the sake of getting any form of conceptual system off the ground. However, presuppositions can shake off their presuppositional nature if they end up becoming self-confirmed in some way - either trivially upon presupposing them or afterwards via a technical method (think Cartesian doubt). Axiomatic laws of logic - identity, non-contradiction, etc. - are another example, and how they're confirmed, and whether their truths are merely analytic or in some sense non-analytically a priori, are issues that are still being debated within the literature.

My problem with mathematics and any claims of an absence of presuppositions is simple to explain. I will accept that in theory one hydrogen atom plus one hydrogen atom equals two hydrogen atoms, hydrogen atoms being fungible. In this case one need only presuppose the existence of hydrogen atoms with the consistent properties they are declared to have along with the intellectual concept of class or set by which they may be gathered and described while disregarding spacetime/quantum differences in order for them to conform to the strictures assigned by mathematics and to be identical.

1+1=2 is quite another thing. For a start it presupposes the constants and variables in adstract to denote something in reality, eventually. Since two stones on the ground are different the application of the 1+1=2 rule presupposes some purpose for the stones which makes them practically (strictly and identically) the same. Mathematics attempts to overlay a template of perfection on reality, (consider the concept of zero which is said to have been invented sometime well after humans conceived the idea of being without, of possessing nothing).

When we begin counting presuppositions I think we need to use as our point of departure first consciousness. By that I mean the individual becoming aware of the world and of oneself the first time. What is not to be presupposed beyond awareness be it any phenomenon one may care to study? First I must acquire a pre-constructed human body of knowledge in order to observe the phenomenological world and to count it. This I suggest applied to Husserl and Pierce as well as it applies to the rest of us.

I have no general problem with such well considered leaps of faith as speculated by these great thinkers. It is what we do in making our world picture.

Why is Peirce so much en vogue today? He tried to explain scietific thought before Popper came along, and others whose thought and language are much clearer and less meta-physical. . ???

Peter Thomas Byrne Gregory

You wrote: „Since two stones on the ground are different the application of the 1+1=2 rule presupposes some purpose for the stones which makes them practically (strictly and identically) the same.“

Even if that is so, the employed notion of „practically (strictly and identically) the same“ is so weak that it is almost trivial: Namely, it follows from the truth of the statement „this is a stone and that is another stone“. No further „identity“ or „sameness“ is required except that both things are stones. If each is „1 stone“, then both together are „2 stones“. And in order for two things to be stones, they need not be „(strictly and identically) the same“ in any more substantial sense.

Notice that we could say the same already about „things“: here is a thing and there is a thing, hence, these are two things. Nothing is presupposed here but that there are (at least) two different things. And, as you may notice, this difference is the first thing you uncontroversially presupposed above.

Point 1:

1 + 1 = 2

+ =

Note that +, = are symbols, so the above can be restated as:

Now revisit and replace symbols with numbers and operators.

1 + 1 = 2

Easy peasy, but what is the difference between 1 + 1 = 2 and 1 + 1 = 1?

Point 2:

one hydrogen atom plus one hydrogen atom equals two hydrogen atoms

but one hydrogen atom plus two oxygen atoms equals water,

Can you explain water using logic?

1+1=1.

That notation reflects a remarkable fact of my reality. In my mind I am able to create new ideas from old ones. Ideas which have never existed before; that make objects which have never existed before. This phenomenon, this fact of genuine novelty in emergent reifying acts makes the role of mathematics historiographic. What is inevitable about mathematics, in its decisiveness, is ex post facto. It predicts nothing new but what could be probable, roughly speaking, and not what is to be. The boundary between present and future is not breached by mathematics.

What is the difference between logic and imagination? Logic must follow a consistent set of rules, while with imagination one can pick and choose, if one so chooses.

1 + 1 = 1 is true, if "+" is the boolean "OR" operator and the digit is binary. using boolean "AND", 1 + 1 = 0, with a carry, if one is intending to create mathematical logic - in this I wonder if Russell had been a little less clever and a little more practical, he might have discovered the Principia of digital circuits ahead of Shannon.

New question, considering Russell and Peirce, what are Champagne's follower's beliefs about paradoxes? Present one or two paragraphs, no more, in this thread by this coming Monday. Have a good weekend, all.

There is an intrinsic difference between language as we use it day-to-day and the language of mathematics.

1 + 1 = 1, however, makes sense in mathematics if we were to exchange the "plus" operator for the logical "and" operator. Note that "+" is a symbol, and as such, could be interpreted as anything. But then, so is the symbol "1." And so we are reduced to silence on the interpretation, and Wittgenstein would have approved, for a while anyway, until he changed his mind.

I'm not sure how to interpret "Wittgenstein offers a pragmatic approach" whether "pragmatic" is his approach to language or to mathematics. I find Wittgenstein to be extremely insular, that only Wittgenstein could really understand what Wittgenstein meant.