You’re equivocating on the meaning of “true.” I suggest re-reading the main post.

While your right in that i can’t prove that triangles are synthetic, i can prove that maths is not true by definition. Take for example your alien civilisation which you mention, were maths true by definition they would have their own system of maths and physics. Yet, the problem is that they would get things wrong. Using maths we can predict things in the real world (how much weight a bridge can take before calapse, how much fuel we need to drive somewhere etc) but, were you to use a different mathematical system; you would find that your bridges would fall down before you thought so, or that you wouldn’t have enough fuel to drive somewhere. The simple fact that maths is not only true by definition makes it not analytic, so therefore maths must be synthetic.

These two things are linked together by a process called mathematical modeling. We hypothesize the the class of things we’ve grouped together under the name physical triangles has same properties as the abstract triangles which mathematicians invented. Whether this is true or not is a synthetic question. But the properties of the abstract triangles are entirely analytic in any case.

Einstein had unsuccessful experiments of the Solar Eclipse, and as stated before newton didn’t have a unified model to preserve the theory in order to compare against Einstein’s.
Thank god for modern technology!

“There were no experiments to suggest that there was something wrong with gravity as it was currently understood.” Not correct. The reason people were looking for a new theory of gravity is precisely because the body of experiments supporting special relativity strongly suggested that Newton’s theory of gravity was wrong.

It may seem odd that experimental results concerning non-gravitational phenomena could provide evidence against Newton’s theory of gravity. But those relativistic phenomena can, in principle, interact with gravitation, and hence the need for a unified theory.

At first glance, there’s no reason why such a unified theory should preserve Einstein’s theory of relativity and toss out Newton’s gravitation rather than vice-versa. (Indeed, it would be perfectly acceptable to propose a grand theory incompatible with both special relativity and Newtonian gravitation, provided the new model is compatible with the experimental evidence underlying those old models.) The reason people suspected that Newton was wrong is because no one knew how to put together a unified model which both preserved Newton’s theory and accounted for experimental results in relativity and E&M.

The assertion that physical theories should be physically reasonable (e.g. that GR should include Newtonian mechanics as a low-velocity special case) seems especially pedantic. It’s like saying mathematics shouldn’t be considered a priori reasoning since mathematicians check whether their arguments are logically sound.

It’s true that it took a long time to empirically confirm any of the more exotic phenomena predicted by GR. But that’s not the same thing as saying there was no experimental evidence by which to judge it. Scientists put their bets on GR because it was the only relativistic theory of gravity proposed that was compatible with existing evidence. Science doesn’t really pick out True theories; rather, it just gives us the tools to pick the best theory from extant rivals. And GR was effectively the only horse in the race.

Not a priori at all.

In his own context Einstein you know used to devise the intense ‘Thought Experiments’, something so insightful, ideation of which can only be possible in an Einstein’s brain nerves. The slew of scientific developments taking place majorly before/after Relativity era had a different flavor: from Photoelectric effect tests to sprouting of Quantum Physics theories…you name it, all involved observation-research-theory evolution.

However, in only the case of General Relativity, there were NO experimental foundation put forth with the theory. The REAL evidences (1959+), [ not the Eddington one...that was essentially exaggerated! ] came must after theory postulation (1919), and are still coming…
This is where Einstein is marvelous and is rightly acknowledged as. The beauty of a Theory is determined by its life it lives…Newton’s ones lived three centuries. Einstein one has survived one…and counting.

His conviction was so stalwart that he sided against the Quantum worldview altogether and until his death in mid twentieth century he continued his quest for a unified theory. More the nobel prize in 1921 was given for his work on photo-electric effects, ONLY because his theory on relativity cannot be tested and evidenced by that time. Do we need more backing for this a priori thing?

In fact it has been referred that Einstein work on General Relativity during 1914-19 is a period of ‘the greatest intellectual human endeavor by a single brain’
Refer Ronald Clark’s Biography for more.

A great deal of testing and measurement was necessary to arrive at the theory of relativity. The theory was specially constructed to account for experimental results in electromagnetism and, in particular, the results of the Michelson-Morley experiment. The reason Einstein and others had confidence in the theory was because it beautifully accounted for existing experimental data — the theory had empirical support from its conception. If any of them said they were 100% certain the theory was correct, then they were either overconfident, or (more likely) just speaking hyperbolically.

To be blunt: a priori reasoning can only prove things about made-up abstract entities, not real ones; math by itself is indeed quite useless.

But if you still think Einstein proved relativity correct a priori, please do give us the proof; since you have a minor in physics, I don’t think that’s asking too much.

Einstein and his early adherents we certain – *CERTAIN* – that he described reality in his mathematics before any real world confirmations existed. Trust me – I have a minor in physics and was a physics major before I switched to theology. Indeed, his mathematics are so very good that – a priori – if they are wrong, there is something wrong with math.

The critical element is that Einstein need not do any testing or measurements to build a beuatifuly accurate picture of reality through a priori reasoning. all of your attempts to change to focus miss this point – a priori *MUST* be sound or mathematics is useless.

Theologians are trying to piece together a bunch of abstract logic and conclude that the world must work in a particular way (namely, that god must necessarily exist). The entire point of an a priori argument for god is to try to show that god exists without doing any empirical observations. And the only reason anyone attempts to do such a thing is because there is no empirical evidence that god exists.

Lastly, you’re just wrong about Einstein. I’ve never heard a physics professor claim he proved any physical results a priori, or read a relativity textbook which gave anything resembling an a priori proof of the theory’s correctness. If you really think all of us are wrong about this, perhaps you’d be so kind as to show us such a proof.