The Contradiction of Math/Geometry

[Eodnhoj7]

1+1=2 and the triangle both apply to an infinite number of things thus are paradoxically indefinite truths.

[Magnolia5275]

I don't understand. Can you explain this better?

[mickthinks]

Me neither. Where's the contradiction, Eod? What paradox?

[Agent Smith]

Me neither. Where's the contradiction, Eod? What paradox?

I thought you were a Mike ... on a ... bike! Absit iniuria

[alan1000]

1+1=2 and the triangle both apply to an infinite number of things thus are paradoxically indefinite truths.

The argument actually cuts the other way. Each individual triangle may be regarded as an "indefinite" truth, ie an incomplete or poor definition of "triangle", because there are many other kinds of triangle which may differ greatly from it in appearance. But the mathematical concept of "triangle" is capable of precise definition and cannot be confused with any other geometrical form.

But let's get pedantic, in a probably futile attempt to stem the flood of dipstick and yoyo content which seems to be inundating the philosophy forums in the Trump era, and which moderators apparently lack the intellectual courage or integrity to control.

First of all, a "triangle" is not actually "true" or "false". It's a definition.

Secondly, the truth of 1 + 1 = 2 is not dependent upon the existence of "things" in any empirical sense. It follows necessarily from the structure of the inductive number line, the axioms of arithmetic, and the axioms of arithmetical logic. There is no way it can be falsified. You can't get much more definite than that.

[Eodnhoj7]

I don't understand. Can you explain this better?

1+1=2 and the triangle are both definite truths. However they can equate to an infinite number of things thus these definite truths are simultaneously indefinite.

[Eodnhoj7]

1+1=2 and the triangle both apply to an infinite number of things thus are paradoxically indefinite truths.

The argument actually cuts the other way. Each individual triangle may be regarded as an "indefinite" truth, ie an incomplete or poor definition of "triangle", because there are many other kinds of triangle which may differ greatly from it in appearance. But the mathematical concept of "triangle" is capable of precise definition and cannot be confused with any other geometrical form.

But let's get pedantic, in a probably futile attempt to stem the flood of dipstick and yoyo content which seems to be inundating the philosophy forums in the Trump era, and which moderators apparently lack the intellectual courage or integrity to control.

First of all, a "triangle" is not actually "true" or "false". It's a definition.

Secondly, the truth of 1 + 1 = 2 is not dependent upon the existence of "things" in any empirical sense. It follows necessarily from the structure of the inductive number line, the axioms of arithmetic, and the axioms of arithmetical logic. There is no way it can be falsified. You can't get much more definite than that.

1. Considering there are infinite number of triangles, even "perfect" triangles, the triangles definitive nature is indefinite.

2. The definitive nature of the triangle is indefinite because of its infinite states. I never said it was true or false...but that is another point to witness. A thing defined is a thing that exists, either abstractly, empirically or both. As such the definition has a truth value in the respect it exists. This is considering existence can be argued as truth.

3. All numbers are dependent upon the act of counting and as such are inseparable from the senses, be it abstract sense or empirical sense. Numbers are inseparable from forms. The most universal form is the loop considering it applies to all shapes when the shape is traced out, even the line itself as the repetition of points.

4. 1+1=2 is dependent upon the act of teaching. Without teaching it would not exist. As such mathematics is a perspective which is formed and as a perspective is falsified. It may be taught that 1+1=3; the one, the other one and the set of numbers as one.

5. 1+1=2 follows the same argument as point 2. Considering it is definite yet its definitive state results in it meaning an infinite number of things it becomes paradoxically indefinite at the same time. In other terms the presence of definition paradoxically becomes indefinite, truth value results in a false value. Dually 1+1=2 may be falsified under this condition: a point is added to a point and these points becomes one point.

6. The axioms of arithmetic are justified by the proofs which follow from them. The proofs are justified by the axioms which compose them. It is circular.

[alan1000]

A triangle is definable as a plane figure bounded by 3 straight lines which intersect so as to form 3 angles and 3 vertices.

A circle is a line enclosing an area within which there is a point which is equidistant from every point in the line.

These are essentially the Euclidean definitions. In what way would you amend them to make them more "definite" and precise?

[alan1000]

1+1=2 is dependent upon the act of teaching.

Does God exist only because some people tell other people that he exists? Of course not. I doubt that God exists but, if he/she/it does, it is presumably in some absolute and self-sufficient sense, and not merely because some people are saying to others, "God exists".

1 + 1 = 2 is dependent upon the definition of the natural number progression as 0123456789, the successor function S(), and the additive operator +. This was discovered - and began to be taught - in the 19th C, but that doesn't mean it wasn't true before that.

[Agent Smith]

Finished!

Lemme see!

Like it?

Where's the muffin?

If I tell you, you'll never forgive yourself.

Ok, ok. Where's the chocolate?

If I tell you, you'll never forgive me.

Oh! I suppose there's no point asking where the wine is.

It's behind the vase.

[Impenitent]

one exists on the surface of a sphere...

-Imp

[Eodnhoj7]

A triangle is definable as a plane figure bounded by 3 straight lines which intersect so as to form 3 angles and 3 vertices.

A circle is a line enclosing an area within which there is a point which is equidistant from every point in the line.

These are essentially the Euclidean definitions. In what way would you amend them to make them more "definite" and precise?

They have a dual indefinite nature.

The fact that the shapes are infinite in applicability....they represent an infinite number of things and have an infinite number of expressions in the empirical world. Dually they have an infinite number of sizes thus the same shape differs from itself.

[Eodnhoj7]

1+1=2 is dependent upon the act of teaching.

Does God exist only because some people tell other people that he exists? Of course not. I doubt that God exists but, if he/she/it does, it is presumably in some absolute and self-sufficient sense, and not merely because some people are saying to others, "God exists".

1 + 1 = 2 is dependent upon the definition of the natural number progression as 0123456789, the successor function S(), and the additive operator +. This was discovered - and began to be taught - in the 19th C, but that doesn't mean it wasn't true before that.

1. In claiming God may or may not exist one must be first taught the concept of God.

2. The 'successor function' and the 'additive operator' are functions of language thus are created in certain respects. One cannot argue the difference between 'discovery' and 'creation' without ending in paradox: The concept of 'creation' was 'discovered', the concept of 'discovered' was 'created'. Discovery and creation share the same nature of 'actualization in perception' and as such cannot be separated in their entirety.

3. If the observation of the relation of the number line/successor function/additive operator where not taught prior to the 19th century then people where unaware of it and as such it had no existence as a concept before then....and it is a concept.