This is a technical use of the word "dispositional" in the field of psychology, e.g., see Attribution Theory, which explains the difference between dispositional and situational attribution.
Dispositional attribution assigns the cause of behavior to some internal characteristic of a person, rather than to outside forces.
Situational attribution: The process of assigning the cause of behavior to some situation or event outside a person's control rather than to some internal characteristic.
In the sentence you quoted, therefore, the meaning is that "a thought that is only subjectively or privately thought or held to be true" is internal only. Once this same thought is expressed in speech or writing, something changes. At the very least, it is no longer purely internal but available for public discourse. Probably the surrounding sentences may expand on the author's thoughts on what happens to thoughts that undergo this transformation.
You could also apply this idea to questions and answers posted in stack exchange. A question or answer may be privately thought, which is a dispositional psychological structure, but that same thought, when formulated as a written question or answer and the button is pressed to post it .. becomes transformed into something else.