A colossal accident?

  • Thread starter Thread starter tonyrey
  • Start date Start date
Status
Not open for further replies.
1…where is 2?, I don’t see any 2…1…where is the 2? I still don’t see any 2…still no 2…still no 2…where are you getting this 2? Oh wait! you are adding a quantity of 1 and another quantity of 1…1+1=2. 2!!! knowledge gained.
This demonstration shows why mathematical propositions are axiomatic. In this case, you apply rules of addition to get to the proof.
40.png
james1215:
I searched ‘axiom’ on wikipedia and found that maths has logical axioms and non-logical axioms. So maths can be both axiomatic and tautological, there is no need to oppose these.
Where do you get the notion that either logical or non-logical axioms can also be tautological? Just because you can form a tautological statement using math symbols doesn’t make mathematics tautological. Useful mathematical propositions use axioms (logical or non-logical) and, hence, are axiomatic in orientation.
 
I have asserted a non-contradictory empiricism, and have evidenced it.
Your assertion “physical experience is required for knowledge” is a proposition which makes knowledge dependent on experience and thus is a logical contradiction. As all the historical facts have long demonstrated. Further, you have provided no evidence, you have claimed that unrelated observations concerning the physical world are evidence of a theory of knowledge. I have demonstrated several times that you cannot make the leap from something like “I observe water oxidizes iron” to "Therefore physical experience is required for knowledge. As I pointed out, you are trying to defend the strong empirical statement with the weak empirical argument.
You have not countered it, you just keep asserting it’s not possible right after we actually demonstrate it being done.
You have not countered it, you just keep asserting it’s not possible right after we actually demonstrate it being done.
As such, you are already addressing empiricism as a hypothesis, and are challenging it based on evidence.
Changing the synonyms doesn’t change anything, its always been a theory and now it is a long disproven theory. If you want to say hypothesis feel free, then you can say it’s a long disproven hypothesis. Nor am I using any physical evidence to challenge it.
(Then G-d does not deal with the empirical world)
What does this have to do with anything?
If it is clear to you, then would you provide some evidence?
I just did. What did you think the talk about triangles was?
The universe is describable using numbers, but one can hardly say that it bends itself to mathematical forms.
Yet the universe obeys truths that transcend it. It certainly looks as if the universe bends itself to a platonic reality.
Also, triangles do not exist, whereas the universe does. You cannot have knowledge about triangles, you can only elaborate geometry self-consistently.
triangles certainly exist, and you have no idea if the empirical universe does. You have it backwards.
It has everything to do with epistemology. Pi is not knowable; it is stateable.
Funny but as we aren’t born knowing Pi, it is demonstrably something we come know.
The circumference of the earth is knowable, but pi will not tell you it. You have to first look at the earth and find out (empirically, need I say?) that it is not spherical. As a result, pi will not be accurate. This is the same as saying that euclidean geometry may help you, it may not. One has to be dealing with an empirical arrangement that fits the specific models of maths for those models to assist with knowledge.
Not in the least. As I have pointed out before, we can do math without reference to any empirical reality.
Precisely. There is no overlap. Maths can be true, but does it give knowledge? That is the real question we should turn to.
Sure does, just like Pi.
As I have said before, and as is obvious, being able to verify something does not make that thing false. Even if the principle of verification cannot be verified; other things still can.
Still using a proven contradiction as part of your theory of knowledge I see.
No, deliberately missing the point here I think. Where there is only evidence in favour of a proposition and none against, it is reasonable to assent to the proposition.
There is no evidence for the proposition that you assert and there is a ton of evidence in favor of rationalism, you have even admitted it yourself.
This is the non-problem of the reliability of perception.
In so far as you cannot claim to be experiencing empirical reality. It is a huge problem for the empricist. You cannot claim that knowledge only comes from the physical senses when you have no idea if you actually have physical senses.
I have already told you. If we are to consciously engage in a project of doubt, we have to doubt that we are doubting; therefore if successful we are not certain of anything, and we have nothing about which to gain knowledge. You forget who you are and what you’re doing, you don’t think you exist… If that’s the hallmark of reason (which it isn’t) that’s what you’re throwing at empiricism with dubito.
When you doubt everything, including doubt itself, then you are left with Dubito. The act of doubting doubt proves *Dubito *. Real basic stuff here. The only thing we are certain actually exists is a rational object, not an empirical one.
Reality can be described using numbers, that is all we know. How does the universe depend upon numbers exactly? Or how does the universe follow logic?
Or numbers are describing reality. We don’t know how, the foundations of mathematics have been in crisis for a long time. As each school has flaws it is likely to continue for a very long time.
One might say: ‘Something cannot be in two places at once’, as if that proves the universe is governed by logic.
Something cannot be in two places at the same time. That does seem to indicate that the universe fallows laws that transcend it.
However, things can be in two places at once… Think about subatomic stuff. As Krauss says, we should learn from the universe, not impose our ideas onto it about what it can and cannot do.
Nothing in quantum theory allows something to bilocate.
The non-problem of the reliability of perception.
How do you know you actually have physical senses again? You think by declaring it to be true that it is? Fact is it’s a huge problem for the empiricist who claims that “physical experience is required for knowledge” when he doesn’t even know if physical experience exists.
 
Regarding the discussion I’ve seen here pertaining to math and reality “bending” to it, I disagree with Petey. A statement is “true” in math if it is a definition, logical axiom, mathematical postulate, or a theorem. In other words, everything that is true in math is dependent on its initial assumptions, since the “initial assumptions” are definitions, logical axioms, and postulates and the theorems are defined as those statements that logically follow from the assumptions or other theorems.

That being said, different kinds of math depend on different initial assumptions, and therefore they reach different conclusions. For example, you guys keep tossing around the equation “1+1=2”, but that’s not true in a base 2 number system (in other words, binary). In that case 1+1=10.

And the difference can be more profound that just different sorts of notation. For example, in calculus, the notion of continuity is very important, but continuity doesn’t even exist in discrete mathematics, or so I hear. And you could theoretically invent a sort of math that would serve no practical purpose but nonetheless produce true statements.

The reason we use different kinds of math is because they each serve different purposes. Thus, math is a malleable tool that humans use to explain the world around them. In short, the world isn’t shaped by math; rather, our use of math is inspired by the state of the world.
 
You’re using an appeal to authority. Having a graduate level mathematics skills in no way settles an argument. Regardless, you’ve admitted that mathematics isn’t necessarily tautological, so it’s a step in the right direction. As for the demonstrated arithmetic, it only appears tautological because is not clearly applied from your framework. You can define 1+1=2, but then you still have to determine whether it is equal to 3-1. There isn’t a definition for each mathematical proposition as it would require in infinite number of such propositions. You need a set of logical axioms to demonstrate proofs, hence, mathematics is axiomatic in nature.
No it’s not an appeal to authority (why are you both so adamant about authorities!), it’s intellectual honesty. I’m saying that there are complexities about maths and the philosophy of maths that are way beyond what I’m familiar with. These things are very likely dealt with in graduate level teaching and research. Is that something you’re familiar with?

As such, given that neither of us can apparently grapple with logical and non-logical axioms, I’m not going to address this: ‘You need a set of logical axioms to demonstrate proofs, hence, mathematics is axiomatic’. I will say this though - something that is logical is not axiomatic, it is self-consistent else it is illogical.

When you’ve defined what 1 and 2 and 3 (and so on) are, as well as what the functions are, you already ‘know’ that 2=1+1 and 2=3-1. To say it is a matter for discussion or discovery is to confuse human ineptness at instant logical reasoning for an epistemological methodology.
 
Regardless of whether or not I have perceived this person, I’m demonstrating the differences between awareness and perception, so don’t try to circumvent the point, which is they are not one in the same. I could say that I am aware of the fact 1+1=2, without ever having to perceive it.
Awareness can simply mean perception. If you are aware of the truth of 1+1=2, then maybe what you’re saying is that you can remember intuitively understanding that 1+1=2. Hence you can remember the comfortable perception of your thought. Which brings us back to the original and unnecessary point that thoughts are experienced.
 
1…where is 2?, I don’t see any 2…1…where is the 2? I still don’t see any 2…still no 2…still no 2…where are you getting this 2? Oh wait! you are adding a quantity of 1 and another quantity of 1…1+1=2. 2!!! knowledge gained.
If you are happy to think that using pre-defined concepts self-consistently is the expansion of knowledge, I am happy to leave this discussion, as that is no threat to empiricism.
 
Your assertion “physical experience is required for knowledge” is a proposition which makes knowledge dependent on experience and thus is a logical contradiction. As all the historical facts have long demonstrated. Further, you have provided no evidence, you have claimed that unrelated observations concerning the physical world are evidence of a theory of knowledge. I have demonstrated several times that you cannot make the leap from something like “I observe water oxidizes iron” to "Therefore physical experience is required for knowledge. As I pointed out, you are trying to defend the strong empirical statement with the weak empirical argument.
What is the value of going through everything point-by-point? Here you show persistent misunderstanding, or deliberate avoidance of the topics at hand, from which countless mistakes could follow.
  1. The assertion is that experience is required for knowledge, not necessarily the materialist interpretation that this experience is physical.
  2. Knowledge can be dependent upon experience without contradiction. Knowledge is reason to believe, experience gives us reason to believe in empiricism.
  3. The knowledge science produces is part of the evidence. You use the example of science to bring in the issue of inductive reasoning, which you then fail to adequately think about. Inductive reasoning is the cement for the non-contradictory nature of this empiricism, by telling us that ‘reason to believe’ rather than certainty is the best we can have.
  4. There is no strong/weak empiricism divide. You don’t even follow what this empiricism is! It is called ‘naive empiricism’, and what you term ‘strong’ empiricism no empiricist would touch with a barge pole, because as is easy to see, it does not support itself. The ‘strong’ fails and the ‘weak’ stands, so you ought to change your description.
How do you explain your failure to address these points?
 
Regarding the discussion I’ve seen here pertaining to math and reality “bending” to it, I disagree with Petey. A statement is “true” in math if it is a definition, logical axiom, mathematical postulate, or a theorem. In other words, everything that is true in math is dependent on its initial assumptions, since the “initial assumptions” are definitions, logical axioms, and postulates and the theorems are defined as those statements that logically follow from the assumptions or other theorems.

That being said, different kinds of math depend on different initial assumptions, and therefore they reach different conclusions. For example, you guys keep tossing around the equation “1+1=2”, but that’s not true in a base 2 number system (in other words, binary). In that case 1+1=10.

And the difference can be more profound that just different sorts of notation. For example, in calculus, the notion of continuity is very important, but continuity doesn’t even exist in discrete mathematics, or so I hear. And you could theoretically invent a sort of math that would serve no practical purpose but nonetheless produce true statements.

The reason we use different kinds of math is because they each serve different purposes. Thus, math is a malleable tool that humans use to explain the world around them. In short, the world isn’t shaped by math; rather, our use of math is inspired by the state of the world.
Math is a science and deals with abstractions. It serves us as a tool, which is thy there are many variants systems and disciplines. It’s in its application that determines it’s utility. If you want to utilize mathematics to create tautological statements, be my guest. However, you’ve then missed its entire point of mathematics. If math is shaped by the world, then you agree with our contention that math can be used to acquire knowledge about the real world.
 
No it’s not an appeal to authority (why are you both so adamant about authorities!), it’s intellectual honesty. I’m saying that there are complexities about maths and the philosophy of maths that are way beyond what I’m familiar with. These things are very likely dealt with in graduate level teaching and research. Is that something you’re familiar with?
It’s you James that has the issues with authorities. You keep bringing them into the pictures as if by the very mention, they dispel any argument used. You are not an expert in espistemological systems yet you still are debating online with us regarding empiricism at a valid epstimelogical approach. Regardless, your appeal that ‘we are not experts’ therefore ‘we cannot discuss’ the topic at hand is a fairly transparent evasion tactic to deal with questions at hand.
As such, given that neither of us can apparently grapple with logical and non-logical axioms, I’m not going to address this: ‘You need a set of logical axioms to demonstrate proofs, hence, mathematics is axiomatic’. I will say this though - something that is logical is not axiomatic, it is self-consistent else it is illogical.
Do you even know what a non-logical axiom is in mathematics? It’s simply a postulate and nothing more. It’s not some irrational system as you seem imply.
When you’ve defined what 1 and 2 and 3 (and so on) are, as well as what the functions are, you already ‘know’ that 2=1+1 and 2=3-1. To say it is a matter for discussion or discovery is to confuse human ineptness at instant logical reasoning for an epistemological methodology.
The only reason you claim to ‘know’ the answers to these equations is that they are very simple. Complex operations rely upon axioms and their proofs are not predefined. The fact you don’t realize that mathematics is used in many epistemological systems demonstrates a lack of understanding of the applicability of mathematics in knowledge gathering.
 
Awareness can simply mean perception. If you are aware of the truth of 1+1=2, then maybe what you’re saying is that you can remember intuitively understanding that 1+1=2. Hence you can remember the comfortable perception of your thought. Which brings us back to the original and unnecessary point that thoughts are experienced.
By conflating the two concepts, you cloud the matter. Awareness and perception are not the same and to insist that they are only demonstrates that you are being disingenuous about engaging in honest debate. To further elaborate, to conceive and to imagine may seem like they are the same but in reality the two terms are different in meaning. Thoughts are not experiences. If that were the case, what senses are used? This is a question you are trying to avoid answering.
 
If you are happy to think that using pre-defined concepts self-consistently is the expansion of knowledge, I am happy to leave this discussion, as that is no threat to empiricism.
The equation 1+1=2 is not pre-defined, it’s a mathematical operation.
 
… In other words, everything that is true in math is dependent on its initial assumptions, since the “initial assumptions” are definitions, logical axioms…
As well as everything that is not true.
In that case 1+1=10.
The demonstration works regardless of base because it is not demonstrating a mathematical truth, it is demonstrating that we gain knowledge that we did not previously have by performing mathematical functions.
…you could theoretically invent a sort of math that would serve no practical purpose but nonetheless produce true statements.
That’s right, it seems as if truth transcend the universe.
 
If you are happy to think that using pre-defined concepts self-consistently is the expansion of knowledge,
I am happy to point out that you gain knowledge you did not previously have when you conduct mathematical operations.
I am happy to leave this discussion,
It’s not because one obviously gains knowledge that they did not previously have by conducting mathematical operations?
as that is no threat to empiricism.
You were the one claiming mathematics is not evidence for rationalism, if you are withdrawing that claim, it’s fine by me. But nothing can be a threat to empiricism, it died decades ago. The dead have no enemies.🙂
 
What is the value of going through everything point-by-point? Here you show persistent misunderstanding, or deliberate avoidance of the topics at hand, from which countless mistakes could follow.
Because that is how one advances the conversation, instead of repeating the same refuted arguments, you address each point to it’s conclusion. That is the manner of the intellectual discussions you wish to participate in.
  1. The assertion is that experience is required for knowledge, not necessarily the materialist interpretation that this experience is physical.
Are you now admitting that physical experience is not required for knowledge? If so there is no disagreement on my part with such statement and the immediate matter is settled.
  1. Knowledge can be dependent upon experience without contradiction. Knowledge is reason to believe, experience gives us reason to believe in empiricism.
that is demonstrably incorrect.
knowl·edge Noun/ˈnälij/
  1. Information and skills acquired through experience or education; the theoretical or practical understanding of a subject.
  2. What is known in a particular field or in total; facts and information.
If you cannot make an argument using standard terminology, you really just can’t make the argument.
  1. The knowledge science produces is part of the evidence.
No it doesn’t as I have repeatedly demonstrated, you cannot make that leap.
You use the example of science to bring in the issue of inductive reasoning,
You’re missing the point. It is not solely a problem of induction. You literally cannot make the leap from premises like “I observe water oxidizes iron” to the conclusion “therefore physical experience is required for knowledge”. It’s non-sequitur. The conclusion does not follow from the premises. What you are calling evidence for empiricism is not. The added fact that you cannot induct your way into that proposition, is just icing on the cake.
  1. There is no strong/weak empiricism divide.
There certainly is and has been for a long time. Though you may not regard historical fact as important, it doesn’t just disappear
You don’t even follow what this empiricism is! It is called ‘naive empiricism’,
The fact you think that calling it “naive empiricism” makes it a different beast is just proof that you aren’t very familiar with this subject.
and what you term ‘strong’ empiricism no empiricist would touch with a barge pole, because as is easy to see, it does not support itself.
That is what you proposed at the beginning of the conversation. I told you that was the historical fact and you spent hundreds of posts disagreeing to finally admit it now?:rolleyes:
The ‘strong’ fails and the ‘weak’ stands,
Now you admit there is a strong/weak divide. Further, you have yet to make the weak empirical case because you are still using the strong empirical proposition. Change the proposition and we can talk about weak empiricism.
so you ought to change your description.
Why? Because you don’t like the historical facts?
How do you explain your failure to address these points?
I don’t. I have been addressing your posts point by point for hundreds of posts. I haven’t said anything new in this one either.
 
It’s you James that has the issues with authorities. You keep bringing them into the pictures as if by the very mention, they dispel any argument used. You are not an expert in espistemological systems yet you still are debating online with us regarding empiricism at a valid epstimelogical approach. Regardless, your appeal that ‘we are not experts’ therefore ‘we cannot discuss’ the topic at hand is a fairly transparent evasion tactic to deal with questions at hand.

Do you even know what a non-logical axiom is in mathematics? It’s simply a postulate and nothing more. It’s not some irrational system as you seem imply.

The only reason you claim to ‘know’ the answers to these equations is that they are very simple. Complex operations rely upon axioms and their proofs are not predefined. The fact you don’t realize that mathematics is used in many epistemological systems demonstrates a lack of understanding of the applicability of mathematics in knowledge gathering.
lol actually, I think we have just seen that you do not know what you’re talking about, whereas I just admitted my lack of experience with these matters. I already said that I don’t know what a logical or a non-logical axiom is and that I found these terms on wikipedia. I’m not implying anything irrational! Your rather free interpretation of this point leads you to think that I am asserting that maths is irrational, simply by pointing you towards a fuller understanding of the term ‘axiom’. Given that neither of us understands these terms, we cannot discuss them meaningfully. (Well, I suppose if we can gain knowledge by pure reason, we won’t have to turn to an online encyclopedia, but I doubt that as you know…)

And if you are saying that a concern with authorities is irrelevant to the truth of empiricism, then why are you implying that I should not be arguing my general point because I am not an expert?
 
Warpspeedpetey, what is the definition of knowledge you’re relying upon if not a restatement of empiricism in general terms?
 
Warpspeedpetey, what is the definition of knowledge you’re relying upon if not a restatement of empiricism in general terms?
It’s the definition of the word knowledge. It doesn’t say anything about empiricism.
 
Status
Not open for further replies.
Back
Top