The different subjective propositions “he saw the mailman ring the doorbell” and “she heard the mailman ring the doorbell” both reduce to the same objective proposition “the mailman rang the doorbell.” Subjective propositions specify the agent (e.g., “he,” “she”) and the sensory modality (e.g., “saw,” “heard”). Objective propositions, by contrast, specify neither the agent nor the sensory modality.

One of my goals for the notational system that I’m working on is to distinguish between subjective and objective propositions. Subjective propositions, which will be marked as such, will take:

1. One or more agents (e.g., “he,” “she,” “John”)
2. One or more sensory modalities per agent (e.g., his visual modality, her auditory modality)

From the subjective to the objective:

1. More subjective. I both believe that I saw and believe that I heard the mailman ring the doorbell.
2. Less subjective. Thus, I believe that the mailman rang the doorbell.
3. More subjective. You both believe that you saw and believe that you heard the mailman ring the doorbell.
4. Less subjective. Thus, you believe that the mailman rang the doorbell.
5. Objective. Thus, the mailman rang the doorbell.