Fun with logic, Peano and Constructivism!

[Skepdick]

Physical entities are discrete

Which implies that existence is pre-categorized.

and, you are right that language and mathematics are discrete (a very astute and correct observation, by the way). But all physical relationships are analog, which is why no mathematical measurement is ever absolutely exact (except by accident) because measurement is in terms of arbitrary discrete units of measure.

There is no physical infinitesimal (or infinite) which are only the extremes of arbitrary (human invented) units of measure.

Perfectly aware. Human epistemology is discrete. It does not mean ontology is.

I pointed this out elsewhere:

The mind is a Turing machine - a language recogniser, so a central philosophical question becomes thus:

Do we ever really talk about the continuum, or do we only ever talk about finite sequences of symbols that talk about the continuum?

[RCSaunders]

I pointed this out elsewhere ...

See HERE!

[bahman]

Yes, your program is non-deterministic but it is not free.

How do you test for "freedom"?

When I don't use any algorithm to decide. I can just decide discarding all preferences.

How do you falsify "freedom"?

I cannot falsify it. There are time that I don't decide though and do thing according to preference.

No, I am not either thinking of minimising or maximising when I decide freely.
You could do it without a coin. I do it all the time.

You still haven't told me how and why you do it. If you don't know know how; and you don't know why - then why are you so sure you are doing it "freely" ?

I don't know how. I don't care why. I am just free.

There is no distance in integer number.

Then what is subtraction?

Subtracting tells you what is left, not distance, but amount. You have 5 apples, you eat 2, you are left by 3.

No. I was looking for how one can get a consistent mathematical framework that allows us the measurement at the same time explain how one can get continuum from infinitesimal.

What you are really asking is how one can get a "continuum" from discrete elements. The simple answer is - you can't.

Then how do you describe the reality that we experience. It appears continuous.

Mathematics is discrete because language is discrete. On metaphysical level - language is discrete because time is discrete. Humans think in beginnings and ends. Physics is discrete because a "measurement" is an effect on the measurement apparatus caused by the thing being measured.

If physics was "continuous" you can't have things like "causes" and "effects" - you'll just have a function.

Yes. Physics at is core is discrete.

[Skepdick]

When I don't use any algorithm to decide. I can just decide discarding all preferences.

I cannot falsify it. There are time that I don't decide though and do thing according to preference.

So you don't have a theory as to how you do what you do? You don't actually have a conceptual model of yourself?

I don't know how. I don't care why. I am just free.

How do you know that you are free? Ohhh. That's right. You don't

Subtracting tells you what is left, not distance, but amount. You have 5 apples, you eat 2, you are left by 3.

Distances. Amounts - quantities. It's a verb: quantization.

Then how do you describe the reality that we experience. It appears continuous.

Yes. Physics at is core is discrete.

Eh? How does reality appear continuous to a digital physicist?

[bahman]

When I don't use any algorithm to decide. I can just decide discarding all preferences.

I cannot falsify it. There are time that I don't decide though and do thing according to preference.

So you don't have a theory as to how you do what you do.

There is no theory for free decision.

Aren't you even curious to discover a conceptual model of yourself?

You cannot model free decision since it is not functional.

I don't know how. I don't care why. I am just free.

How do you know that you are free? Ohhh. That's right. You don't

Then how do you describe the reality that we experience. It appears continuous.

Yes. Physics at is core is discrete.

Eh? How does reality appear continuous to a digital physicist?

It confuses me. Continuous state is a physical state. How could you take it from a discrete process.