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Though they themselves cannot be directly observed according to the methods of science, we know they are real because we observe their effects.

Anything that has effects that can be observed can be studied by the usual and customary methods of science. That includes most of the phenomena stucied in particle physics and in cosmology. Things that are really constructs based on observed effects, but which cannot be directly observed.

Anything that has effects that can be observed can be studied by the usual and customary methods of science. That includes most of the phenomena studied in particle physics and in cosmology. Things that are really constructs based on observed effects, but which cannot be directly observed.

Then on what basis can science deny the reality of the human soul? Mind, some of the intangible soul's effects are themselves intangible: e.g., love, desire, the seemingly in-built sense of justice, the moral sense, et al. These can produce tangible effects, but usually not of the kind studied by the physical sciences.

Thus it seems to me that the soul cannot be a suitable object for scientific study. So science should just leave the matter to the philosophers and theologians, and stick to what it does best.

Not necessarily -- which explains why medicine, psychology, and sociology -- all of which deal with observable effects -- are not "hard" sciences.

The sneer is left to the interested mathematician.

Cheers! ...oh, and Happy New Year.