Si mens duobus affectibus simul affecta semel fuit, ubi postea eorum alterutro afficietur, afficietur etiam altero.
If the mind is affected by two affects at the same time together, when afterward one of the two is affected, the other of the two will also be affected.
DEMONSTRATIO: Si corpus humanum a duobus corporibus simul affectum semel fuit, ubi mens postea eorum alterutrum imaginatur, statim et alterius recordabitur (per propositionem 18 partis II). At mentis imaginationes magis nostri corporis affectus quam corporum externorum naturam indicant (per corollarium II propositionis 16 partis II) : ergo si corpus et consequenter mens (vide definitionem 3 hujus) duobus affectibus semel affecta fuit, ubi postea eorum alterutro afficietur, afficietur etiam altero. Q.E.D.
If the human bod has been affected once by two bodies at the same time, when the mind later imagines one of the two, it records immediately of the other (by IIP18). But imaginations of the mind indicate greater affects of our body than the nature of the external bodies (by IIP16C2): therefore if the body and consequently the mind (see IIID3) has been affected once by two affects, when later it is affected by one of the two of these, it is also affected by the other.
Here Spinoza is describing how our knowledge from our body gradually builds a knowledge of the world around us. Rooted in our body, we make associations based on these impressions. It strikes me (another example of body impact on mind) as the word impressions perfectly describes the process of how memories are developed - it all references the body. Given the variety of tastes that we note in others (as in food or decor or color), this location of memory developing in bodily sensations give rise to enormous differences in experience and, thus knowledge. When someone else mentions an opinion, Spinoza is making clear that these memories are a long ways from 2+2 =4.
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