Editing Abstraction (section)

===Physicality===
{{Further|History of accounting#Ancient history}}
A physical object (a possible referent of a concept or word) is considered ''concrete'' (not abstract) if it is a ''particular individual'' that occupies a particular place and time. However, in the secondary sense of the term 'abstraction', this physical object can carry materially abstracting processes. For example, record-keeping aids throughout the [[Fertile Crescent]] included calculi (clay spheres, cones, etc.) which represented counts of items, probably livestock or grains, sealed in containers. According to {{harvnb|Schmandt-Besserat|1981}}, these clay containers contained tokens, the total of which were the count of objects being transferred. The containers thus served as something of a [[bill of lading]] or an accounts book. In order to avoid breaking open the containers for the count, marks were placed on the outside of the containers. These physical marks, in other words, acted as material abstractions of a materially abstract process of accounting, using conceptual abstractions (numbers) to communicate its meaning.<ref>Eventually ([http://www.laits.utexas.edu/ghazal/Chap1/dsb/chapter1.html Schmandt-Besserat estimates it took 4000 years] {{webarchive |url=https://web.archive.org/web/20120130084757/http://www.laits.utexas.edu/ghazal/Chap1/dsb/chapter1.html |date=January 30, 2012 }}) the marks on the outside of the containers were all that were needed to convey the count. The clay containers evolved into clay tablets with marks for the count.
</ref><ref>{{cite book|first=Eleanor|last=Robson|author-link=Eleanor Robson|year=2008|title=Mathematics in Ancient Iraq|publisher=Princeton University Press |isbn=978-0-691-09182-2}}. p. 5: these calculi were in use in Iraq for primitive accounting systems as early as 3200–3000 BCE, with commodity-specific counting representation systems. Balanced accounting was in use by 3000–2350 BCE, and a [[sexagesimal number system]] was in use 2350–2000 BCE.</ref>

Abstract things are sometimes defined as those things that do not exist in [[reality]] or exist only as sensory experiences, like the color [[red]]. That definition, however, suffers from the difficulty of deciding which things are real (i.e. which things exist in reality). For example, it is difficult to agree to whether concepts like ''God'', ''the number three'', and ''goodness'' are real, abstract, or both.

An approach to resolving such difficulty is to use ''[[predicate (grammar)|predicates]]'' as a general term for whether things are variously real, abstract, concrete, or of a particular property (e.g., ''good''). Questions about the properties of things are then [[proposition]]s about predicates, which propositions remain to be evaluated by the investigator. In the ''graph 1'' [[#Simplification and ordering|below]], the graphical relationships like the arrows joining boxes and ellipses might denote predicates.