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1. The present formulation of the title question can be improved:

   Taken literally the question supposes the existence of “X” when is starts “Under what circumstances is the observation of X ...”.

   But when assuming the existence of “X” then it makes no sense to question immediately after the existence of “X”.

   A more precise wording seems to me: To observe data and to interpret the data as a certain object.

2. Then your question reads:

Under which circumstances can we derive from observing the data “D” the existence of the object “X”?

3. Example: Under which circumstances do the observed data from the Large Hadron Collider at Cern prove the existence of the Higgs boson? See Higgs boson.

   Apparently the methods are different, depending on the object whose existence is to be proved.

   Sometimes it would count already as a big step to reach an agreement about the observed data, e.g., in your third example concerning God.

1. The present formulation of the title question can be improved:

   Taken literally your question supposes the existence of “X” when is starts “Under what circumstances is the observation of X ...”.

   But when assuming the existence of “X” then it makes no sense to question immediately after the existence of “X”.

   A more precise wording seems to me: To observe data and to interpret them as a certain object.

2. Then your question reads:

Under which circumstances can we derive from observing the data “D” the existence of the object “X”?

3. Example: Under which circumstances do the observed data from the Large Hadron Collider at Cern prove the existence of the Higgs boson? See Higgs boson.

   Apparently the methods are different, depending on the object whose existence is to be proved.

   Sometimes it would count already as a big step to reach an agreement about the observed data, e.g., in your third example concerning God.

1. The present formulation of the title question can be improved:

   Taken literally the question supposes the existence of “X” when is starts “Under what circumstances is the observation of X ...”.

   But when assuming the existence of “X” it makes no sense to question immediately after the existence of “X”.

   A more precise wording seems to me: To observe data and to interpret the data as a certain object.

2. Then your question reads:

Under which circumstances can we derive from observing the data “D” the existence of the object “X”?

3. Example: Under which circumstances do the observed data from the Large Hadron Collider at Cern prove the existence of the Higgs boson? See Higgs boson.

   Apparently the methods are different, depending on the object whose existence is to be proved.

   Sometimes it would count already as a big step to reach an agreement about the observed data, e.g., in your third example concerning God.

1. The present formulation of the title question can be improved:

   Taken literally the question supposes the existence of “X” when is starts “Under what circumstances is the observation of X ...”.

   But when assuming the existence of “X” then it makes no sense to question immediately after the existence of “X”.

   A more precise wording seems to me: To observe data and to interpret the data as a certain object.

2. Then your question reads:

Under which circumstances can we derive from observing the data “D” the existence of the object “X”?

3. Example: Under which circumstances do the observed data from the Large Hadron Collider at Cern prove the existence of the Higgs boson? See Higgs boson.

   Apparently the methods are different, depending on the object whose existence is to be proved.

   Sometimes it would count already as a big step to reach an agreement about the observed data, e.g., in your third example concerning God.

1. The present formulation of the title question can be improved:

   Taken literally the question supposes the existence of “X” when is starts “Under what circumstances is the observation of X ...”.

   But when assuming the existence of “X” it makes no sense to question immediately after the existence of “X”.

   A more precise wording seems to me: To observe data and to interpret the data as a certain object.

2. Then your question reads:

Under which circumstances can we derive from observing the data “D” the existence of the object “X”?

3. Example: Under which circumstances do the observed data from the Large Hadron Collider at Cern prove the existence of the Higgs boson? See Higgs boson.

   Apparently the methods are different, depending on the object whose existence has to be proved.

   Sometimes it would count already as a big step to reach an agreement about the observed data, e.g., in your third example concerning God.

1. The present formulation of the title question can be improved:

   Taken literally the question supposes the existence of “X” when is starts “Under what circumstances is the observation of X ...”.

   But when assuming the existence of “X” it makes no sense to question immediately after the existence of “X”.

   A more precise wording seems to me: To observe data and to interpret the data as a certain object.

2. Then your question reads:

Under which circumstances can we derive from observing the data “D” the existence of the object “X”?

3. Example: Under which circumstances do the observed data from the Large Hadron Collider at Cern prove the existence of the Higgs boson? See Higgs boson.

   Apparently the methods are different, depending on the object whose existence is to be proved.

   Sometimes it would count already as a big step to reach an agreement about the observed data, e.g., in your third example concerning God.