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Geometrical Glossary

, (comma) : aaa, bbb as in {2d01 corpus, res extensa} {pp1d03 est, esse} between terms means that they denote the same concept

...^... : see logical opposition

...(... )... : (aaa) bbbb as in {2d04 (idea cognitio) adaequata}, bbb is what is being defined (definiendum), and what is defined is a special type of aaa (aaa: in the example there are two: both idea and and cognitio).

...[space]... : aaa bbb as in {pp1d03 in se^in alio, intrinseca^extrinseca}. This occurs when a term's string ("in se") contains a space. "In se" is a single 5-string term. "In alio" is another single string term denoting the concept complementary to that of "in se", and "intrinseca^extrinseca" denotes the same set of two complementary concepts. In {1d01 causa sui}, "causa sui" is treated as a single 9-string term.

B.H. editor of this web [more]

claimed equivalences: strings that are, in Ethica joined by a [mng eqv] or [prf eqv] connector. The other type is implied equivalences: equivalences not claimed, for which no quote of Ethica can be produced. Most notes pages feature a list of relevant claimed equivalences.

code system: There are bracketed "{}" codes 1. for deductive elements, which include terms formally defined in Ethica (see definiendum) and unbracketed codes for undefined terms called philosopical primitives. The term entry as in the title of the search list "All Entries Order of Appearance in Spinozae Ethica" comprehends all types. [Tutorial].

complement: A complement pair of concepts is a specific type of logical opposition with a specific type of "^" relation: it makes two disjunct ("exclusive") sets in their range (of things they are about, "ideata", locally), together covering their entire range. The logical operator is "NOT". For example "White^NOT-white" (tertium non datur - there is no third possibility). Example in Ethica: "necessarius^contingens" (since "contingent" is defined as "NOT-necessary"). "Necessario^contingens" is exclusive exhaustive: either A or B, never both, tertium non datur. A complement triple, for instance: " >0 ^ =0 ^ <0 " , exhaustively devides its range (some set of numbers) in three disjunct ("exclusive") sets (no fourth possibility, quartum non datur). Hence omitting the =0 predicate, the remaining pair " >0 ^ <0 " is exclusive NON-exhaustive (NON, for an element x=0 conforms neither). Hence ">0 ^ <0 are NOT complements, a term reserved for an exclusive exhaustive set of 2,3, etc concepts. Example in Ethica: bonus^malus (utility>0, utility<0) is exclusive non exhaustive. But (bonus ^ utility=0 ^ malus) is a complement triple. The identification, in each case, of the locally relevant range is vital. In the realm of dynamics (processes in time, duration) many things grow and diminish, so many concepts involve "more^less", hence with "equal" form triple (exclusive exhaustive) complements.

cursive (of linked terms in Ethica): cursive linked terms have a formal definition in Ethica, non-cursive terms are philosophical primitives.

deductive element Only definitions, axioms, postulates, propositions (including their demonstrations) and corollaria are deductive elements. This excludes scholia, explanations, introductions, appendices and titles. Ethica has 443 deductive elements displayed on a grey background. Elements are coded strings. Spinoza linked propositions to their premises in demonstrations, and we follow this exactly in writing web-links. Spinoza himself supplied the exact coding by numbering and classifying in definitions, axioms, propositions etc. The code system: {.d..} (definitio), {.a..} (axioma), {.post..} (postulatum), {.p..} (propositio, including its demonstratio), {.......c} (corrolarium , including its demonstratio), {.L..} (lemma including its demonstratio). Coding protocol: {4p32} is Part IV Proposition 32, {4p32c1} is Part IV Proposition 32 Corollarium 2. Other strings like scholia, explicationes, praefationes and appendices and other non-deductive strings have a white background. They are nowhere linked, not even where Spinoza himself made a reference to them. [Tutorial]

deductive structure: Ethica's deductive structure consist of the deductive elements and their formal proof-relations. The establishment of the proof-relations done by Spinoza and is meticulously copied in the web. [Tutorial]

definiendum a term to be defined. They form part of the deductive elements and are coded accordingly. [Tutorial]

definiens a string defining a term

Elwes: R.H.M. Elwes, translation to the English (1883) as displayed, only as an aid to those less well versed in Latin, in the left cells of the tables of Ethica.html . In a very few vital and totally obvious cases this still very helpful translation has been corrected (corrections not marked). Elwes' integer original is on gutenberg.org.

entry as in the Search List All Entries ...: all deductive elements (that includes defined terms), and all philosophical primitive terms. [Tutorial]

est-definiton Contrary to an intelligo-definition, an est-definition harbours the claim that the definition matches the common notion. E.g. the definition of amor has as its object the Latin dictionary meaning of amor, and is moulded to be congruent to it.

frequency: see usage frequency.

geomap: Example: click {2p07 ordo et connexio}. A geomap of a deductive element shows, in the left column, the deductive elements and philosophical primitive terms referred to in that element, and, in the right column, the deductive elements referring to the deductive element central in the geomap you are viewing. In the geomaps the usage frequency is the number of entries in the right column (specified in the header). Clicking on an element in one of the columns moves that element to the centre of the map. Colour coding in the geomaps: .d..... (definitio), .a...... (axioma), .post..... (postulatum), .p...... (propositio), .p.....c. (corrolarium), .L...... (lemma), pp......... (philosophical primitive). [Tutorial]

geometrical: in Ethica referred to as: "ordine geometrico". In Spinoza Ethica the paradigm of geometrics are Euclid's Elements (about 300 BC), a powerful and comprehensive axiomatic exposition of geometrical propositions still a standard text in Spinoza's time. This "geometrical order" is adopted in this web to analyse of Ethica. In terms of some modern near-equivalents: a formal, logical or structural analysis of Ethica as an axiomatic deductive structure . Thus there is no evaluation of the tenability, truth or adequacy of Ethica's definitions and axioms. They are considered as given data. The web's note pages serve to provide a selection of main loci relevant to the meanings and uses of philosophical primitives and definitions. The aim of the notes pages is restricted to help clarifying exactly what is claimed in Ethica to follow (sequitur) from what. Thus this web provides all necessary preparations for evaluating the formal correctness of those claims, in other words: this web pretends to take clarification and structural analysis exactly to the point where the meaning of the demonstrations is sufficiently clear to start evaluating their soundness.

implied equivalences: equivalent strings for the equivalence of which no quote of Ethica can be produced. The other type is claimed equivalences.

intelligo-definition Contrary to an est-definition, an intelligo-definition is designed to be a philosophical innovation and hence may be entirely different from any common notion associated with the term defined.

logical opposition aaa^bbb (read: "aaa" as opposed to "bbb") as in {1d07 liber^necessarius} between concepts means that their relation only involves formal logical operators and relations, and no other philosophical concept. There are many types of logical oppositions, such as contrary, inverse and complementary pairs. If in Ethica there are concepts aaa^bbb and aaa^ccc, the two different meanings of aaa will be denoted by adding its ^-term in the contexts in brackets superscript: aaa(^bbb) and aaa(^ccc) respectively. Example: since we have {1d07 liber^necessarius} and pp4p67 liberus^servus, the two types of freedom are called "liber(^necessarius)" (free as opposed to necessary) and "liber(^servus) " (a free man as opposed to a slave) respectively.

mantra: a string of more than one word frequently occurring in the deductive structure.

NOT : aaa NOT bbb as in : this alerts the reader that a string bbb occurs, similar to aaa but with different meaning. Example: {pp1d02 cogito NOT cognitio}

notes page every one of the 76 defined and 55 philosophical primitive terms has its own notes page, containing salient passages using a term, truncated but linked to the source, with in bold the reason why selected and displayed. Notes pages of primitive terms start with "pp" then give the deductive element where the term first occurs, e.g. pp1d02 cogitare, cogitatio NOT cognitio.html . Notes pages of formally defined terms can be found by clicking, in the "all entries" or "terms alphabetical" view "[notes]" displayed behind the term) [More]

...pp... philosophical primitive

philosophical primitive: a non-trivial philosophical concept which has no formal definition in Ethica (find the list through the geometrical report). Coding: pp1d02 res, where {1d02} is the first locus of the occurrence of res. The pp-codes are not on a grey background and not in "{}" for such is reserved to deductive elements. Philosophical Primitives have geomaps, where the left column has zero entries by definition. [Tutorial]

preoccurrence an occurrence of a formally defined term (by default in the deductive structure only) above the location of its definition. See also usage frequency.

search list: Web index page. Ethica Help-Web has two: (A) All Entries Order of Appearance in Spinozae Ethica . This lists all deductive elements (on grey background) and preceded by those, alle philosophical primitive terms that first appear in them (on white background). (B) All terms alphabetical. You can switch between them left-top.

terminal elements deductive elements with zero usage frequency. This means that they are not used in any other deductive element. Hence their purpose is to serve as a conclusion of the deduction. Most of them are propositions, but there are terminal axioms, postulates and definitions as well (find all terminal elements through the geometrical report, under "Items in order of usage frequencies").

usage frequency of a deductive element or a philosophical primitive: the number of deductive elements in which it occurs. The geomaps show the usage frequency as the number of entries in the right column (specified in the header).