Philosophical Challenge

Started by james03, November 19, 2024, 08:16:46 AM

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james03

Can an atheist prove that 1 + 1 = 2?

My gut feel is that they can not.  Such a proof must rely on the Transcendentals, and they can't establish them.
"But he that doth not believe, is already judged: because he believeth not in the name of the only begotten Son of God (Jn 3:18)."

"All sorrow leads to the foot of the Cross.  Weep for your sins."

"Although He should kill me, I will trust in Him"

St. Drogo

#1
Bertrand Russell, an atheist, already did so in Principia Mathematica—specifically, he spends 360 pages exhaustively establishing the mathematical and philosophical basis for the equation 1+1=2. I have no clue what transcendentals have to do with that equation—unity is a fascinating constant, but it's not a mathematical transcendental. Are you trying to say that the Peano axioms rely on the existence of God?

Edit:
For the record, I believe that Anselm's argument (which is not an ontological argument) is epistemologically valid, and I suppose that's what you're hinting at here. In that case, you're asking how someone who calls himself an atheist can meaningfully discern the difference between the one and the many, take that distinction as an axiom, and then draw meaningful conclusions therefrom.

Assuming you're referring to transcendental numbers when you wrote "the Transcendentals," atheists and theists alike are more than capable of establishing them and indeed demonstrating that they are infinitely more dense than rationals in our shared axiomatic construction of the number line. That said, you may be interested to learn that Georg Cantor, the father of set theory, corresponded with Pope Leo XIII after his discovery of the transfinites, and that correspondence prompted Leo to pen and issue "Aeterni patris."

St. Drogo

I am immensely curious how you presumably think the sacred sciences prove 1+1=2.

KreKre

However, Kurt Gödel showed that any formal system powerful enough to express Peano's arithmetic must necessarily be incomplete, in the sense that there exist infinitely many statements that can be expressed in that formal system that can neither be proved nor disproved within the system.

In other words, Whitehead's and Russel's attempt to have a complete formal system capable of expressing the entirety of mathematics was doomed to fail from the start.
Christus vincit! Christus regnat! Christus imperat!

james03

QuoteIn that case, you're asking how someone who calls himself an atheist can meaningfully discern the difference between the one and the many, take that distinction as an axiom, and then draw meaningful conclusions therefrom.

I am self taught and sophmoric on philosophy.  I recently read more in depth about the Transcendentals and intuitively sensed that without Unum and Aliquid (One, Something), it would not be possible to prove 1 + 1 = 2.  An atheist can not establish the Transcendentals.

My future interest extends along this line of thought: God -> Transcendentals -> Fundamental Metaphysics (e.g. Identity) and my question is jumping the gun, but intuitively I suspect it is a real problem for atheists.
"But he that doth not believe, is already judged: because he believeth not in the name of the only begotten Son of God (Jn 3:18)."

"All sorrow leads to the foot of the Cross.  Weep for your sins."

"Although He should kill me, I will trust in Him"

james03

Quote from: St. Drogo on November 22, 2024, 09:13:58 AMI am immensely curious how you presumably think the sacred sciences prove 1+1=2.

I call atheists "hitch hikers" who implicitly assume God in their beliefs.
"But he that doth not believe, is already judged: because he believeth not in the name of the only begotten Son of God (Jn 3:18)."

"All sorrow leads to the foot of the Cross.  Weep for your sins."

"Although He should kill me, I will trust in Him"

Michael Wilson

Quote from: St. Drogo on November 22, 2024, 09:13:58 AMI am immensely curious how you presumably think the sacred sciences prove 1+1=2.
I'm curious to know why one could not prove the above; just the principle of "being" and of "identity" should be enough.
"The World Must Conform to Our Lord and not He to it." Rev. Dennis Fahey CSSP

"My brothers, all of you, if you are condemned to see the triumph of evil, never applaud it. Never say to evil: you are good; to decadence: you are progess; to death: you are life. Sanctify yourselves in the times wherein God has placed you; bewail the evils and the disorders which God tolerates; oppose them with the energy of your works and your efforts, your life uncontaminated by error, free from being led astray, in such a way that having lived here below, united with the Spirit of the Lord, you will be admitted to be made but one with Him forever and ever: But he who is joined to the Lord is one in spirit." Cardinal Pie of Potiers

james03

^^^ Yep.  And we can go through an attempted atheist proof that 1 + 1 = 2 to show you need theistic philosophy to do it.

So the atheist says he has one bean, and another bean, and that the total beans are 2 beans, therefore 1 + 1 = 2.  Already he has a problem in admitting "1" and "2", which are dark pixels on a computer screen have meaning.  But we'll let that pass for now.

We could ask why is one bean one?  Couldn't it actually be 5 beans?  And if you actually have one bean and another, when you put them together, does this always end up at 2 beans?

The atheist would reply that this would violate the law of identify and the law of non-contradiction.  You would point out he is hitch hiking using those laws, and ask him to establish them.  He can't.

If he attempts to argue that pixels on a screen actually mean "1", or if there are "laws", he is now an agnostic, and no longer an atheist.  For if the immaterial world exists, then God CAN exist, in which case someone with integrity would have to say at a minimum "I don't know if He exists or not".

This is not some idle discussion, giving young Trad lads interesting topics to woo young Trad Lasses with, this is the basis for the establishment of post-modernism.

"Mr. Modernist, you are correct that God doesn't exist, but how do we know YOU are correct?  What is your foundational principle?".
"But he that doth not believe, is already judged: because he believeth not in the name of the only begotten Son of God (Jn 3:18)."

"All sorrow leads to the foot of the Cross.  Weep for your sins."

"Although He should kill me, I will trust in Him"

TradGranny

#8
Quote from: james03 on November 28, 2024, 10:46:39 AM"Mr. Modernist, you are correct that God doesn't exist, but how do we know YOU are correct?  What is your foundational principle?".

They deny Objective Reality (see Plato's Allegory of the Cave) and cling to Subjective Reality (i.e. Man is the measure of all things. or Each man is his own god).

quick explanation via wikipedia:
Protagoras (/prəʊˈtæɡəˌræs/; Greek: Πρωταγόρας; c. 490 BC – c. 420 BC)[1] was a pre-Socratic Greek philosopher and rhetorical theorist. He is numbered as one of the sophists by Plato. In his dialogue Protagoras, Plato credits him with inventing the role of the professional sophist.

Protagoras is also believed to have created a major controversy during ancient times through his statement that "Of all things the measure is Man, of the things that are, that they are, and of the things that are not, that they are not" which was usually rendered simply as "Man is the measure of all things," interpreted (possibly wrongly, since he disagreed) by Plato to mean that there is no objective truth;
To have courage for whatever comes in life - everything lies in that.
Saint Teresa of Avila

Michael Wilson

Thomistic Common Sense
The Philosophy of Being and The Development of Doctrine.
Rev. Reginald Garigou La Grange O.P.
pg. 200:
QuoteTherefore, we were right to say that there are only three [mutually exclusive] positions that can possibly be held in metaphysics and natural theology:
1) To acknowledge the primacy of being over becoming and deny potency, and then, like it or not, one must return to Parmenides: multiplicity and becoming are illusory. Still, one must explain the illusion,. This represents the position held by pantheists who absorb the world into God and must come to deny the world by denying all multiplicity and all becoming.
2) To acknowledge the primacy of being and acknowledge potency as well. Then, with Aristotle, one must affirm the divine transcendence implied in the concept of Pure Act.
3) To deny the primacy of being, to affirm that of becoming, with Heraclitus. And this is to deny, with Hegel, the objective value of the principle of identity, the fundamental law of thought, and to place absurdity at the very heart of reality. This is the position of the pantheists who absorb God into the world and must come to deny God.

"The World Must Conform to Our Lord and not He to it." Rev. Dennis Fahey CSSP

"My brothers, all of you, if you are condemned to see the triumph of evil, never applaud it. Never say to evil: you are good; to decadence: you are progess; to death: you are life. Sanctify yourselves in the times wherein God has placed you; bewail the evils and the disorders which God tolerates; oppose them with the energy of your works and your efforts, your life uncontaminated by error, free from being led astray, in such a way that having lived here below, united with the Spirit of the Lord, you will be admitted to be made but one with Him forever and ever: But he who is joined to the Lord is one in spirit." Cardinal Pie of Potiers