Well first off I do not know enough about pragmatism (like virtually nothing) to make an informed compare contrast (and it sounds more like the definition of “empiricism” to me), but no, not that we are only able to consider what our senses perceive. We are only able to consider what our minds can conceive. To a highly significant degree there is overlap because our minds our evolved to deal with that which our senses perceive (and the senses we have are tuned how they are because such had salience to our fitness outcomes) but using that cognitive apparatus we can imagine lots that is not in our direct sensory experience. Our systems endogenously create information as well, and not just at the level of immediate sensory perception. We impose pattern recognition, often to our advantage, but sometimes we create patterns out of randomness.
As to the general discussion you are trying to have here, remember that our past discussion had been regarding Spinoza. To him all of reality was one infinite substance and had two “attributes” - “Thought” (which in more modern phrasing can be called “information” which includes “ideas”) and “Extension” (which in more modern phrasing is the physical substance/“stuff”) and both with multiple “modes”. The concept that is key here for this thread is that both are “attributes” of the same thing, at the same time, at all times, and the same thing can be considered at the level of either attribute with equal validity.
Spinoza, as we have previously discussed together, is a pretty heady slog, and he does extend this to the level of the infinite mode as well in which the universe/all of reality is called God (hence he is a pantheist) and in the “Thought” Attribute is considered as the Infinite Intellect and in the “Extension” Attribute is “Motion and Rest” of all stuff. And well if Infinite Intellect can be encompassed by the “Thought” Attribute then I’d think numbers would be! 
MrDibble, you will I am sure disagree with what I more precisely actually said as well as with what you are apparently thinking I said but let me make the distinction anyway.
I tried to phrase carefully and did not say that “you” are the patterns of information processing but that “the properties of ‘you’ feeling whatever you feel, thinking whatever you think, be they numbers or fear or ideal circles, are properties emergent of patterns of information processing.”
The distinction may seem fine to you but it is meaningful.
Indeed “you” are a complete conglomerate of more properties than your thoughts and feelings alone. And the exact manner that you process information indeed includes the impact of your instinctive behaviors (algorithms and rules we are both born with and wired to unavoidably develop in response to inputs that we in almost all circumstances will experience), your memories (that the silliness you linked to says do not exist), and the contributions of your complete body to the information processing, not the brain alone.
Current computers and our minds (which again is inclusive of more than our brains and much more than our conscious minds) are not processing information in the same way. (If anything the analogy-making has generally been more productive going from what we do know of human mind information processing to developing more intelligent machines than from the trying to impose computer processing metaphors onto the function of mind and how it processes information; the former created, for example, AlphaGo.)
Reproducing the exact patterns of human information processing on a different (nonbiological) substrate may never occur (or might). We may never understand which aspects of information processing result those emergent properties. Or Hofstadter may be onto something and eventually we will be able to deduce from an analysis of the patterns of information processing whether an other intelligent behaving entity, be it alien or artificial, is likely also experiencing some similar sort of emergent properties. But those discussions are IMHO immaterial to this one.
