Thank you for your very kind post.
As you know from the philosophy of science, no hypothesis can ever be proven correct by means of the scientific method. This is because the scientific method procedes by inductive rather than deductive reasoning. It can, however, prove an hypothesis false, merely by finding a single counter-example. So scientific theories are different in character from mathematical theorems. The latter are obtained by deduction.
At present the carbon-dating results do seem to disprove the Shroud's authenticity, and that will eventually have to be addressed by further tests. Many questions still remain. The best scientific inquiry can do is suggest a plausible explanation.
The purpose of relics (Acts 5:14-16 and 19:11-12), as you say, is to point the mind and heart to Him, not to be an end of themselves. The Shroud in particular, if authentic, makes clear just how much Our Lord suffered for us, and that can be a very fruitful meditation for all of us, especially in this season of Lent. We need to remind ourselves of our own role in causing His suffering by our sinfulness, so that we can rejoice fully on Easter in His great mercy and forgiveness.
Relics, as well as our attempts to reason about theological matters, are not substitutes for faith, but may serve to make the leap of faith a bit smaller. In this sense, they can be useful tools for evangelization, especially of skeptics.
If authentic, how could we not be grateful to Our Lord for leaving us this artifact?
“At present the carbon-dating results do seem to disprove the Shroud’s authenticity...”
Thank you for your comments. I did not address carbon-dating in my previous post, though I am aware of the controversy. There is evidence that the intense heat in a fire may have scewed those results. Russian scientists had a piece of linen from the time of Christ and did carbon dating on it before and after exposing it to the intense heat. My understanding is that the heat changed to make it look younger than it was, similar to dating of the shroud. The fabric itself matches weave etc from the first century.
Again, it is not about artifacts, it is about Him. And yes, we do need to remind ourselves of our own role in the need for His death and resurrection.