Numbers are useful abstractions with no empirical evidence to back them up. That's my point. Numbers are a way of interacting with the physical world and reproduce certain results, but numbers themselves are abstract and have no physical properties.

As for empiricism, I certainly did not throw it out. It's useful, but not for everything. Say I have three knives in my kitchen drawer: a butter knife, a steak knife, and a chef's knife. Empirically speaking, which knife is the best knife? You can tell me all the physical properties of the knife, and the metallurgy of the knife and the shape and weight of each knife, but which knife is the BEST knife, from an empirical point of view? Empiricism has no answer UNTIL you, a person, say "I want to dice this onion" and empiricism can then arrange the knives in a hierarchical order according to which one will work best. But science has nothing to say about "best" or "worst" until an agent in the world has a purpose for which they want to use something. Then empiricism is a wonderful tool.

Another, shorter example: empiricism can help you build a rocket, but has nothing to say about whether you should aim it at the moon, or at a neighboring country.

And one more, just for fun: the empiricism that was used to detect and classify climate change is the same empiricism that was used to make the internal combustion engine. Empiricism is blind as to intent or motive. Empiricism is a toolset, but has no tools for determining a value hierarchy within the bounds of empiricism itself. Empiricism can only go to work once a person has given it a purpose or goal to work towards.

Oh I think I can see whats happening here - You probably have strong emotional need for things to have purpose and meaning. Sure, if I haven't accepted that pure existence is enough (and depending on the point of view it has none or all the meaning that we want) then exploring pure models in search for purpose would be also what I would do. But since I believe that there are infinite number of abstractions with no real physical properties that can be interpreted as real through your reasoning, from my point of view, empiricism becomes the only real tool (because per Your first example even the best or worst ultimately comes down to preferences that were shaped by physical world).

Let's say your lover writes a poem for you on a piece of paper and gives you the poem. You find it to be quite lovely, and you memorize the poem. Then, in a tragic accident, the cleaning lady throws the paper with the poem written on it into the garbage incinerator.

Does the poem still exist?

The answer depends on what You are trying to prove.

If You define this poem as ordered list of words that can be interpreted trough cultural and local context, then it existed even before it was written down.

If You want to go more realistic way then this poem exists only through my memory (partly as memory and partly as an emotional association) and will disappear with my demise.

You have smuggled in a LOT of things that are not empirical in your response.

"Ordered" - what is the empirical evidence for order? How can one know the difference between randomness and order with only empirical evidence? Order requires a concept of "orderliness" that one is comparing the evidence to.

"Words" - the empirical evidence of a word is a squiggle on a piece of paper. Everything else about a word and its connection to a thing is purely abstract, and not empirically verifiable.

"cultural" - what is the empirical evidence for a culture? What empirical properties does a culture have? Can it be defined merely by its physical characteristics?

"context" - what does this even mean, empirically speaking. We have infinite number of facts. How does empiricism filter relevant and irrelevant facts? What does it even mean for something to be "relevant" empirically?

"existed even before it was written down" - so something existed with no empirical evidence? How can you say it exists then?

"Memory" - what is the empirical evidence for your memory? Can I hook you up to a machine and stimulate your brain in such a way that I could get the words of the poem to read out on the screen?

"emotional association" - what does that even mean empirically?

I could go on, but I have to get back to work. I hope I have helped you clarify your thinking about how "empirical" you actually are(n't), but I've probably just lost you, and for that, I'm sorry. Please forgive my inability to speak more clearly.

> You have smuggled in a LOT of things that are not empirical in your response.

Those are mental models that are useful to me but unfortunately I'm not master at using them. And what is more they are inherently wrong (because they are models and not the real thing - putting aside if anything is real).

I do not believe in them more than I need to. But they are the only way that we can communicate on high level - by establishing common model and that talking about its properties. And then we can empirically test if they really behave as we believe (if we want to, otherwise we can just leave it be and use it as toys and as a way to spend our time waiting for nothingness to take us back).

> Please forgive my inability to speak more clearly.

Likewise - as You may have guessed english is not my native language and those concepts that I speak about are not well developed in my mind - they are merly my intuitions (by which I openly admin that I use things that are not empirically proven - but only because that is the only way that our faulty mind can work - by substituting reality with simplified erroneous abstractions that sometimes work).

>I could go on, but I have to get back to work

Wish You a pleasant work! And thank You for good conversation.

This seems like a facetious word-salad. You asked if a poem that was written then burned, still exists. He answered that the poem exists in his memory. It doesn't make any sense to say, what is empirical evidence for order or culture or context. You can't ask him to redefine literally everything, before you accept his answer.

I agree with your overall comment thread, that you separate empirical stuff like engines rooted in reality, from values like the highest good. You conclude that a way to achieve the highest good is to be religious. But are you sure? It's certainly good for you, your family and the community around you. But is it the highest good for the world? Across all nations, all the wars that have been fought over religion - I'd dispute that it's still the highest good.