100% certainty is often Illogical

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Well, that is a matter of terminology and preciseness than of subjectivity. The bricklayers and aerospace industry people all basically agree on the measurements, there is standardization. Now, knowledge on the details of the world is somewhat imperfect and there are measurements that are not worth all of the details, however, I would not call this a reduction to subjectivity but rather a trade-off. Subjective relates more to mental distortion, imperfect information relates more to things that are beyond the tools/effort used to find that information.

But in most cases people aren't aware of the concept of tolerances, and so their understanding is limited by the context in which they've used the measurement in question, previously. Doesn't that make it subjective? I don't believe this is true:


Having worked extensively with measurements of various kinds, I can assure you that people frequently do not agree on them, and so I didn't think you'd used a very good example. That people do not agree may be due to ignorance, but it can create a perception that people are being untruthful that is relevant to the original post in this thread, I think:


Belief in truth, or certainty, in this sense is generally due to ignorance. The same reason people may not agree over measurements, and assert that figures given are inaccurate, false, untrue etc.

Furthermore, putting aside the subjective, measurements are based on standards that have changed through history. Take for example the foot (there being various systems used), that is currently defined as a fraction of a metre (I think), the metre having been redefined several times during the twentieth century using different criteria.

Anyway, that's my offering, and it's maybe not what you're after as you're more into the deeper philosophical meaning of truth that's beyond my ken.

Indeed, on the last point, but only as a mental construct, 'twould seem.
So, UNDER the system that we normal utilize (which is backed by axioms)
2 + 2 = 4, but WHY we should use that system is more doubtful,
which is why I keep bringing individuation into the issue. If I hand
you a pair of apples, are they really 2? Or just all part of the 1?
See, we really can't be so certain, especially when it's clear that
atoms join and leave what we think of as objects.

No, it means that there is imperfect information found in this issue. The actual measurement is standardized, now, if there is an argument about whether or not the measurement is correct and voices argue based upon pure opinion then that might very well be subjective, however, measurement is by its nature an appeal to the intersubjective.
That does not mean that there isn't an objective standard by which to compare these things to and that is what I speak of on agreement. When people see an objective measure for a measurement then agreement is often found. At the bare minimum people do not tend to disagree on matters of counting, which is another measurement. In sciences though, proper measuring is important enough where the subjective would be discounted.

I would not deny that, it hardly matters for my argument.

If it is a pair of apples then it is 2 apples. You already defined it as 2 apples because pair means 2. If we make arbitrary distinctions and define them then we can absolutely know the numbers. Really though, can you disprove any of the axioms used? I would consider our axioms true by the nature of their definition.

cal.: you say "only" as mental constructs. i say, as ideal entities (ideal as opposed to real) and, as such, much more convenient (because they are on par with logic basics - absolute in their conclusiveness to the extent that you can not but agree) and more evident.
what you describe with the apples as fixed entities versus a random label applied to a constant flux is one of the problems that arises out of the different nature of ideal and real things. i find it interesting that this thought spans from antique philosophers to modern philosophy, by the way. we superimpose an absolute entity (two - exactly and absolutely two - the old guys would have said eternal like the celestial bodies as opposed to matter in decay and change, and they were not so wrong) upon something that is not absolute but merely relative. we do this all day long, however, to make the world work. we superimpose the constant "horse" to all horses in existence, although every new generation horse is removed a bit in its horseness from its parents and these are one generation removed from their parents... horseness is a flux, yet what our great-grandfathers rode on were as much horses as what we have today. the concept of horse is ideal, all the entities it is applied on are real.

as for science (awesomelyglorious, i believe):
an objective world would need to be world-for-itself, not world-through-our-senses. what we do in science is nothing else than what we do all day: we plaster what we want in the world upon it. we even want to have a world, and therefore interpret all the data rushing in as being caused by a world outside us. thats one of the axioms of science, so how could science prove anything, let alone the existence of an outside world? the number one activity in science is to interpret things as causes and effects - as soon as you say that you are doing science, you also asy that you will interpret things as causes and effects. this activity then never can make absolute statements concerning the existence of such relationships, as its the activities method, not its subject.
what people do these days was put best by old edmund husserl: "to take for true being what is bare method"
also, in saying that science employs logic, and thereby claim the absoluteness of logic for science, one overlooks one thing:
science in practise is computed by using logics (maths) - to make it work intersubjectifically.
sciences basic method (its apriori, if you want), however is the following: observe a given number of single events, find patterns, call the patterns cause and effect.
stating universal rules based on random singular events is no hard evidence and certainly not logic.

This is along the lines of cogito ergo sum. The use
of words proves the point? No. Taking the neo-platonist
view, they are merely extensions of The Universal Apple.



Don't be silly. An axiomatic system that is not
consistent is normally viewed as pointless. I'm
NOT convinced that this has to be the case,
but one can only 'disprove' them by assuming
some contradictory axiom.



Ok. So, what say you about the Group wherein there
is only the number 1, and addition and multiplication
are the identity function? Axiomatic. May be MORE
true as a representation of reality, as we are beginning to
understand it. But, clearly at odds with the so called,
natural algebra.

I uphold cogito ergo sum. Yes, it really does. By using the words the way we did, we defined our topic, by defining what we spoke of we can prove its nature. Your statement pair meant that our system was pre-defined as having 2 apples, a neo-platonist would use different terminology and thus define apple differently, but our definitions are arbitrary, the issue is consistency.


I like being silly


We can define systems where more than one object exists, therefore the idea that there is only the number 1 does not seem perfectly descriptive, especially given that multiple objects are more useful. Addition would be meaningless in that system if used as we define addition because it would lead to falsehood. Can a person look at the universe as being just 1? Certainly, but such a view would gloss over all of the distinction that we know exists.

There is no known world other than the world that we see through our senses.
No, it is fundamentally different, what we do all day is completely subjective, science is highly intersubjective, the idea is that the common things we see in reality are real whereas distortions are the subjective elements.
We undoubtedly have a world as we have data. The nature of this world as shared hallucination, complete self-deception, etc, is outside of science but nobody here denies the existence of sensory data nor can they.

Science is not meant to prove the existence of an outside world, it is meant to find truth in aspects of our shared reality.
Well, the ways of the world cannot be understood outside of cause and effect relationships and no human being can act without them. Now, technically, science is only constrained by epistemological limitations, not a failure of objective knowledge here.

Well, that is why scientists state these matters as theories which can be disproven if the patterns found do not hold. It is inductive logic to do what scientists do, and induction is reasonably valid given that human beings do it all of the time. Now, it is correct that scientists can never absolutely find truth, but they have a better pursuit of truth than the rest of us do given our even less supported inductions and even less rigorous use of logic.

I would suppose then, that you must accept
the proof that St. Anselm gave for the existence
of God, as well.



We can (and generally do) define systems where
there is no 'highest number' though that too doesn't
seem to describe reality. Indeed, the natural numbers
that we used are defined in JUST such a manner, yet
the prevalent thinking is that there is indeed a limit
on the size of the universe.



I was simply describing a different algebra.
and giving addition and multiplication operators
as that is the convention. Hence {1}
with 1 + 1 = 1
and 1 x 1 = 1

Perfectly meaningful. AND seems more likely
to represent reality.



I'm not at all convinced that there is any distinction.

No, I don't because his proof sucks.

Do we need to create a limitation if we are dealing with extremely large numbers at times.

You are describing a different system. Addition is clearly defined differently. Actually, it does not because we can create divisions according to our whims, even if these divisions are arbitrary. The fact of the matter is that in this discussion the participants > 1.


By simply acting you are convinced. A universe of only 1 cannot carry information as there is only information in greater complexity and hence more numbers. You act based upon information to convey information, therefore, you recognize the existence of multiple entities.

Seemed your style. Words spoken force it.
Indeed, 'tis irrefutable, more so than Cogito
ergo sum.


Makes NO sense to have numbers
larger than the size of existence.
.
Uhm...yeah.




Not meaningfully.



Sorry. Instincts and all.



1 is terribly complex.



Only if I BUY into your conception.

More irrefutable than Cogito ergo sum??? That is ridiculous, cogito ergo sum is plain and straightforward, Anselm's proof of God is ridiculous, "I imagine a perfect being therefore God exists"?? it almost seems that he proves God by assuming God at the end of his argument rather than maintaining God as an abstract.
We haven't counted all of the numbers in existence, and there are a lot of them, especially if we change our arbitrary divisions. Because of that, an infinite number of numbers is acceptable as through redefining our divisions we can reach whatever number we want.

Within your system it would be meaningless, however, it still ends up having to be a different mathematical operation then it was previously.

No, conscious action. Your instincts are not such that you must get onto internet forums and type out philosophical arguments, that extends beyond the power ascribed to pure instinct.

No, it isn't. If 1 can be different than 1 must have more to it than 1. 1 is terribly simple


No, only if my conception is correct. My conception is a statement that yours lacks necessary features that you already acknowledge as truly existing, that being the existence of multiple entities. I would assert that you do and must acknowledge my assumption as you see pie as distinct from gasoline and treat them different and the same as treating the 'a' key as different from the 'f'.

Ok - we agree that science can change over time. I guess my point is that while we sometimes do junk certain ideas and completely throw them out, the good science gets expanded but not necessarily discarded ... because it was true to start with. The new version adds another variable to the equation, or explains what happens on the other side of the universe.

Its all semantics? Yes - but not just words - its words and meanings.

Just my $0.02. Obviously, mathematics has a rather different ontological and epistemological status than the other exact sciences. I won't go into these differences, because they give rise to very difficult questions which cannot be answered - if at all - without very laborious and subtle thought.

I just wanted to say that to me mathematical assertions aren't in any meaningful way more certain than the assertions of, say, particle physics. This is because to me certainty requires at the very least consistency with the commonly accepted rules of plain logic - in particular the rule of non-contradiction. But Goedel's Incompleteness Theorems (look them up at Wikipedia if you want) completely and utterly shatter the hope of *proving* (using a particularly simple kind of logic: first-order logic, which to me is the only acceptable one) that any formal mathematical system, sophisticated enough to formulate ordinary arithmetic or number theory in, is free from contradictions. So perhaps the ZFC formulation of set theory, on which almost all of modern mathematics rests, is infested with contradictions, and even if there are none, we shall never have any acceptable way (i.e., acceptable to my mind) of knowing that for sure! So, if someone posits 2+2=4, to me that means either a precept of experience, or some abstract statement in a system whose consistency cannot be proved. Either interpretation, to my mind, falls short of absolute certainty.

dddhgg: at least when i refer to the often-quoted 2+2=4 example, i am in no way talking about any science but the apodictic evidence in the judgemental act of thinking 2+2 (or any other correct statement using ideal entities. any science can at best reach assertoric evidence, and is therefore, formally not able to make statements about truth, being or anything related to these.

if you want to talk about truth, stop thinking scioence but start thinking science theory and see why thinking science wont lead to statements regarding truth.