That is why I provided a proof. — Dfpolis
Do you have a citation for Aristotle? — Dfpolis
I agree that my argument uses insights due to Aristotle, ibn Sina and Aquinas. Still, being old is not a fallacy. Do you have an objection other than the ancient roots of my thought? — Dfpolis
Aquinas wrote for a more philosophically literate audience -- one that knew the distinction between essential and accidental causality. — Dfpolis
Has that caused you any difficulty? — Dfpolis
Contingent facts cannot explain themselves. — Dfpolis
I think you can work that out for yourself. The question is irrelevant to the soundness of my argument. — Dfpolis
Hence also the possession of it [wisdom, universal knowledge of causes and principles] might be justly regarded as beyond human power.
… we must assert that it is necessary that there should be an eternal unmovable substance.
For substances are the first of existing things, and if they are all destructible, all things are destructible.
Further, in virtue of what the numbers, or the soul and the body, or in general the form and the thing, are one-of this no one tells us anything; nor can any one tell, unless he says, as we do, that the mover makes them one.
1) What does contradiction inhere in? — tim wood
Time for you to define existence and being, or to save you some trouble, to correct mine. Allow me to make a division into two classes: mental reality and extra-mental reality. Seven, for example, is a mental reality and not an extra-mental reality, as are all numbers, truth, justice, love, and the American way. — tim wood
Lovecraft's theology does not begin and end with Cthulhu. The ultimate God in his pantheon is Azathoth, the blind idiot God.
Look around you.
Plausible, no? — Theologian
Perhaps Lovecraft derived this idea from the Gnostic's own "idiot" creator God, Yaldabaoth. — Janus
I only wanted to refer to the fact that scientific theories are enumerable. — alcontali
That is probably true for "a science" but not for "science", which is simply any proposition that can be justified by experimental testing. — alcontali
Yes, agreed. I do not think that knowledge is necessarily a "true" belief, with the term "true" as in the correspondence theory of truth. Knowledge as a "justified belief" should be sufficient. — alcontali
Experimental testing always occurs in the real, physical world, of which we do not have the axioms. — alcontali
Therefore, we cannot axiomatically derive that what can be experimentally tested. — alcontali
Math justifies by axiomatic derivation, while science is does that by experimental testing. — alcontali
If a proposition is derived axiomatically from a set of axioms that construct an abstract, Platonic world, you cannot experimentally test it, because that would require the objects to be part of the real world and not the Platonic world in which they have been constructed. — alcontali
The axiomatic method is defined and discussed in numerous places, such as here and here. — alcontali
After Euclid's Elements introduced the axiomatic method, Socrates got the idea that philosophy had to be approached in a similar manner. — alcontali
it was not a good idea for science, as would later become clear from Aristotle's now outdated scientific publications, but it works for mathematics and morality. — alcontali
Axioms can be abstracted from reality — Dfpolis
That is how axioms were originally understood: — alcontali
How does the so-called "axiomatic method" justify its axioms? — Dfpolis
It doesn't. In fact, that is even forbidden, because in that case, they are not axioms. — alcontali
In a knowledge statement P => Q, you can see that Q is justified by P. We do not care how P is justified, or if this is even the case. — alcontali
My preferred approach is to use an analogous definition of truth as adequacy to the needs of a particular discourse. Then, for example, Newtonian physics is true with respect to many engineering needs. — Dfpolis
Recall that the root meaning of "geometry" is "land measure" and many of its axioms are true of real-world geometric relations. — Dfpolis
We also know some of the principles of real-world existence. No real thing can be and not be in one and the same way at one and the same time, and so on. — Dfpolis
We can measure the interior angles of plane triangles and see if the results agree with the prediction that they will sum to two right angles. Then, the result is both axiomatically derived and experimentally confirmed. — Dfpolis
I hate to break it to you, but there is no Platonic world. There is the real world and there are mental constructs that exist in the minds of people living in the real world. — Dfpolis
Historically, most axioms have been abstracted from our experience of reality. — Dfpolis
Those of us trained in the natural sciences do not see unfalsifiable as an advantage, especially given that Godel work ruling out consistency proofs in systems representable in arithmetic. — Dfpolis
As a passing note, the axiomatic method does not work for morality, nor did Aristotle claim that it did. — Dfpolis
If they cannot be tested, they are unfalsifiable hypotheses and highly suspect. — Dfpolis
As we have just agreed, the original justification of mathematical axioms was not via deduction from more fundamental assumptions, but via abstraction from reality. — Dfpolis
Why do we care? Because mathematics is a science -- as one organized body of knowledge among many. So, we want its conclusions to be true. In fact, truth is a central issue in Goedel's work. The problem he exposed (which completely undercuts your position) is that there are true theorems that cannot be proven from fixed axiom sets. If mathematics did not deal with truth, this could not be the case. — Dfpolis
Further, if the truth of P is indeterminate, so is the truth of Q if its sole justification is P => Q. — Dfpolis
So, the axiomatic method does not, and cannot, provide us with an exhaustive inventory of mathematical truths. That means that it cannot be the foundation of mathematical truth as you seem to imply. — Dfpolis
On your account, mathematics is no more that a game -- not any different from Dungeons and Dragons, which also has rules that are neither true nor false, but simply to be followed by those playing the game. — Dfpolis
Funding mathematical research would be a scam in which we are paying people to play arbitrary games, with no hope of advancing our knowledge of reality, however theoretical. — Dfpolis
Finally, it mathematics were not true, it would not be applicable to reality. — Dfpolis
Physicists who included mathematical premises in their reasoning, would be relying on claims of questionable or indeterminate truth, making their own conclusions and hypothetical predictions worthless — Dfpolis
On your account, mathematics is no more that a game -- not any different from Dungeons and Dragons, which also has rules that are neither true nor false, but simply to be followed by those playing the game. Funding mathematical research would be a scam in which we are paying people to play arbitrary games, with no hope of advancing our knowledge of reality, however theoretical. — Dfpolis
In science, the observations are the P (justifying statement) and the theory (knowledge statement) is the Q, in P => Q — alcontali
P does not affect the arrow, which is the real knowledge. — alcontali
Mathematics is not justified by experimental testing, and is therefore, not scientific — alcontali
In his lecture, Gödel and the End of Physics, Hawking spent quite a bit of effort justifying his views. For me, it works. — alcontali
While physics can be and has been axiomatized (e.g. quantum theory and quantum field theory) — Dfpolis
If it is physics, it is about the real, physical world, and in that case, you can test it. Therefore, it will not be accepted, as a matter of principle, that it does not get tested. — alcontali
So, a bowl that holds only one apple and one pear cannot be proven to hold two pieces of fruit? — Dfpolis
No. It will undoubtedly be true, but it will not be provable. — alcontali
So, 2 objects and 2 more objects might not yield a total count of 4 objects outside the visible universe? — Dfpolis
Doesn't matter, because you cannot observe it. Therefore, without observations in an experimental testing fashion, such claim about the non-visible universe is unscientific. — alcontali
Mathematics requires you to painstakingly construct the world in which you will derive your mathematical theorems. We did not construct the real, physical world. Therefore, we are not allowed to derive mathematical theorems in it. — alcontali
If God exists (something like the typical ideas of God re the Judeo-Christian God), then either:
(a) God created logic, or it's at least part of His nature, and God could make logic however He'd want to make it--He has control over His own nature,
or
(b) Logic is more fundamental than God, and God can't buck it any more than we can. God must conform to it. It supersedes Him in its regard. — Terrapin Station
What you may regard to be the relationship between thought and reality is simply your thoughts on that relationship. A clear example of why your simplistic bivalent logic fails: — Fooloso4
... the opposite of red is not-red ... — Dfpolis
What is the opposite of red? Is blue the opposite of red? Is green or yellow? — Fooloso4
Using this line of reasoning, we could say that a finite being acting as only an infinite being or as only any other finite being can is also not a possible act. Therefore, finite beings can engage in any possible act. — Theorem
Agreed? — tim wood
The issue is that your distinction between infinite and finite beings is made in terms of an ambiguous definition of "possible acts". — Theorem
Using this line of reasoning, we could say that a finite being acting as only an infinite being or as only any other finite being can is also not a possible act. Therefore, finite beings can engage in any possible act. — Theorem
That is why I provided a proof. — Dfpolis
Call it what you like but it is nothing more than a claim for the existence of a being whose existence you assert but cannot prove or demonstrate exists. — Fooloso4
Do you have a citation for Aristotle? — Dfpolis
No. — Fooloso4
Claiming that a being is the cause of being leaves unexplained the existence of that being. — Fooloso4
Claiming that there is self-explaining being is not to provide a discursive explanation. — Fooloso4
You simply posit what you cannot explain or demonstrate. It is just kicking the can. — Fooloso4
Aquinas wrote for a more philosophically literate audience -- one that knew the distinction between essential and accidental causality. — Dfpolis
You should not underestimate your own audience. There may be some here who do not know the difference but some who do. — Fooloso4
Positing a necessary being or, facts as you would have it, explains nothing. It is a misuse of the term explanation. I think you might know this and that is why you called you assertion a fact. — Fooloso4
While there are some who still attempt to defend Aquinas' argument others, including theologians, have rightly moved on. Your argument fares no better than his. — Fooloso4
Goes to show how barren theology has become, when modern arguments for God are nothing more than restated millennium-old syllogisms — Maw
Infinite being can effect any possible act either directly, or by indirection. — Dfpolis
because it is not possible to instantiate a contradiction. — Dfpolis
So, I simply deny both horns of your supposed disjunction. God is unqualified being. The beings of experience depend on God. Humans develop logic to think about being in a rational way. So, the order of precedence here is God -> created being (including humans) -> logic (created by humans). — Dfpolis
When you have rebutted my argument, you may claim this. Without pointing out a false premise or a logical misstep, this remains your unsupported belief. — Dfpolis
Then you should not claim the authority of Aristotle. — Dfpolis
This mischaracterizes the argument. — Dfpolis
Third, in my proof infinite being does not stand as unexplained, but as self-explaining and precisely because it is infinite being, so that what it is entails that it is. — Dfpolis
I made it clear in the OP that I was not talking about discursive explanations, but about dynamical ones. — Dfpolis
Infinite being [who] can act in all possible ways in all possible places at all possible times. — Dfpolis
Premise 2: Whatever exists is either finite or infinite. — Dfpolis
Premise 6: A finite being cannot explain its own existence. — Dfpolis
But, being human does not imply that I exist. If it did, no human could cease existing. — Dfpolis
There is no case in physics, or in any other science, in which observations logically imply a theory. Observations are particulars, while theories make universal claims. — Dfpolis
The portion of mathematics following from propositions abstracted from nature, or testable by observation (e.g. the parallel postulate), is scientific. The portion deriving from unfalsifiable hypotheses (e.g. the axiom of choice) is clearly not scientific, for it violates the accepted canons. — Dfpolis
our capacity to investigate those foundations shows that being an axiom does not preclude justification — Dfpolis
We can prove it by (1) noting that apples and pears are both fruit, (2) that they are also both units, and (3) applying ordinary arithmetic via the dictum de omni. Feel free to rebut this. — Dfpolis
This is irrational and inconsistent. You claim that mathematics need not be justified by observation. I hope you would agree that it is a mathematical truth that 2 + 2 = 4. — Dfpolis
They merely work out the implications of axioms that may or may not be justified by our experience of the real world. — Dfpolis
If the axioms are justified — Dfpolis
If the axioms are unfalsifiable hypotheses, those applying them are merely playing complex mental games. They are entitled to play their favorite games, but they can hardly expect society to support their play. — Dfpolis
Clearly, we may not believe (accept) what we know, which would be impossible if knowledge were a species of belief. — Dfpolis
If you know it, it means that you can justify it. So, why would you not believe it? — alcontali
If we only need begin with unjustified axioms, we can start with any assumptions and prove anything. — Dfpolis
No. A system becomes trivialist because it contains a contradiction, for example — alcontali
Math does not justify axioms by experimental testing. In fact, Math does not justify axioms at all. If you justify axioms by experimental testing, then it is simply not math. In that case, you are doing something else. — alcontali
I personally do not believe that a good physicist could ever be a good mathematician, nor the other way around. — alcontali
Concerning the coherence theory of truth, I agree with Bertrand Russell's objections: — alcontali
Therefore, I cannot agree with "Newtonian physics is true with respect to" — alcontali
Entanglement allows for simultaneous being and not being in the real world. — alcontali
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