Identity lost in abstraction:
Identity preserved in concrete:
Impacts on fields:
“Musical idea” metaphor:
Resolving/balancing the tension:
1) Identity lost in abstraction:
a) In set theory, elements of a set lose their individual identity and are interchangeable. The abstract set is what matters, not the particular elements.
b) In categorization, objects are grouped based on broad attributes but specific identities are lost. Individuality is suppressed in favor of abstract categories.
2) Identity preserved in concrete:
a) Objects have unique identities even if they share attributes. A particular table retains its identity whether alone or in a set of tables. Its history and relationships are part of its identity.
b) Living beings have a sense of identity that persists through change. Though my attributes and cells change over time, my identity is preserved through the continuity of my existence. My memories and relationships also help sustain my identity.
3) Impacts on fields:
a) In philosophy, the tension relates to the conflict between nominalism vs. realism or individualism vs. structuralism. The status of abstract objects and categories vs. concrete particulars is debated.
b) In mathematics, the tension relates to the relationship between proof/theory and problem/computation. The identity of a concept in the abstract may differ from how it manifests in a concrete problem or calculation.
c) In social sciences, the tension reflects individual identity vs. group identity or the influence of structure/stereotypes vs. agency/uniqueness. There is debate over how to balance abstract categorization and generalization with recognition of individual differences and realities.
4) “Musical idea” metaphor:
a) A musical theme retains identity through variations, like a tradition retains identity through adaptations. There is a balance of preserving roots while allowing for new expressions. Too much change loses identity, but too rigid preservation limits growth.
b) The metaphor shows how identity can persist as a kind of continuum rather than an absolute. We can recognize the origins of a changed musical theme or tradition, even if it has evolved. Identity is multi-faceted and dynamic, not static.
5) Fundamental uniqueness:
a) Identity stems from something basic about an entity, not just its attributes or characteristics which can change. With a table, its fundamental existence as that particular table is unique, not just its properties.
b) Fundamental uniqueness implies inherent identity prior to comparisons or categories. Identity is not just how something is labeled or grouped but something more primordial about it as an individual entity. Yet it can be difficult to pin down what constitutes this uniqueness.
6) Resolving/balancing the tension:
a) We can recognize both the utility of abstraction/categorization and the limitations of ignoring uniqueness/individuality. Use abstractions where useful but remain aware of what is lost.
b) Examine the relative significance of preserved and lost aspects of identity in different contexts. What is most relevant for a given purpose or in a given domain?
c) Recognize identity as multi-faceted and dynamic rather than absolute. Concrete and abstract perspectives may capture different facets. Total resolution may not be possible and may not even be desirable. Balancing and situating the tension could be an ongoing effort.
[kenneth udut, 3-9-23, Claude AI and ChatGPT going back and forth on interpreting a dream I had in 2017, doing a great job]