The Principle of Contingent Causation: The Impossibility of Infinite Regress.

[polymath257]

Can you show your work, totaling it up, and if "nearly all  of it is clearly contingent", what is the small part that isn't contingent, and how do you know ?

If a thing is contingent, it depends for its existence on the existence of something else. 

So for example, life on earth is dependent, directly or indirectly, on the sun.

The sun depends for its existence on the existence of hydrogen.

Please note that you shifted the sense of the word 'dependent' here. The first example is the result of the reactions in the sun producing the light required to drive the chemical reactions of life. Any other G2 star in place of the sun would work equally well. So, in a sense, it is accidental that life is dependent on the sun. it would be more accurate that life depends on the existence of certain sources of energy and the sun is one potential source.

The sun depends on hydrogen in a different sense: it is composed of hydrogen (and helium). But in order to provide the energy for the last step, the sun has to be a certain size, so life is 'dependent' on the sun being a certain size and type of star (unless the energy is provided some other way, like in deep sea vents).

Can you at least agree that your term has shifted meaning between these two examples?

Hydrogen depends for its existence on the existence of sub-atomic particles.

This is in the second sense: being composed of something. We can also allow for dependency on specific arrangements of the composing objects (different molecular isomers, for example).

Hmm...what does the arrangement depend upon?

Sub-atomic particles depend for their existence on the laws of nature being what they are. 

This is a bit different. What does it mean to be a law of nature and in what sense do the subatomic particles depend on those laws? Would you not be able to say directly that the sun depends on those laws? or that life on Earth does?

All of this depends for its existence on the existence of space/time. If there was no space/time, none of this would exist.

That is not at all clear. In what sense does the existence of the laws of nature depend upon spacetime as opposed to the other way around? Or, perhaps, they are mutually dependent. An intriguing possibility for your argument, eh?

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If you know of anything which is NOT dependent for its existence on space/time or the laws of nature, I would be interested to hear about it. 
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Well, the most obvious example would be mathematical objects. Do they depend on the laws of nature or on the existence of spacetime? Of course, it can be asked whether they actually 'exist'. But then, the same could be asked equally validly of the laws of nature. In what sense do they exist and in what sense to things 'depend' upon them?

Plato would suggest Forms as another example. But abstract concepts could be examples even in the absence of platonic philosophy.

For example are the laws of nature descriptive? So, they are simply ways to describe the properties of things in the universe? In that case, the laws and the  properties of things would be co-existent (co-dependent?). But, while the subatomic particles could be said to 'depend' on their properties, it could equally well be said that the properties 'depend' on the subatomic particles.

Whether space/time and the laws of nature are dependent for their existence on some further thing, or whether they "just exist," is the subject of this thread.

I would say that the term 'depends on' is way too vague to be useful and allows, among other things, circular dependency relations through use of different meanings (natural laws depend on math, which depends on humans to  invent it, and they depend on natural laws). There is a vagueness on whether logical dependency and causal dependency are both allowed, and how composition factors into this.

In any case, there is no clear reason why dependency cannot be circular given the different interpretations. And that would allow for the lack of a 'independent source of dependence'. It would be possible all things are dependent, even with only finitely many things. Hence, the  whole argument fails on its own terms.