Capital letters from P and onwards (P, Q, R, …) denote variable propositions (or whatever truth carrier you prefer).
Capital letters from A and onwards to and not including P (A, B, C, …, O) denote particular propositions.
Non-capital letters from x and onwards (x, y, z) denote variable non-proposition particulars. “t” is also used in relation to time. If further variables are needed they will be chosen backwards from x (v, u, s, …).
Non-capital letters from a and onwards (a, b, c, …) denote non-proposition particulars.
Predicates and relations
Some authors denote predicates1 by a capital letter and a variable letter beginning with F (Fx, Gx, Hx, …). The same authors also often denote relations (with two or more particulars) by a capital letter beginning with R and a variable letter (Rxy, Sxy, Txy, …).
Sometimes I will follow the above pattern but most often I will not. I will use whatever letter best fits the predicate/relation in question. Usually the best fitting letter will be the one that is the first letter of some word that is important in relation to the predicate/relation. E.g. for the predicate expressed by “… is true” I would most likely use T for true. I do this because it makes it easier to remember what the symbolism means, and that is desirable.
Formal english language for reverse translation
I have developed a formal english language (let’s call it FEL1 for “Formal English Language 1”) which I use to translate formalizations back into english. This language is very precise and non-ambiguous though somewhat harder to read than normal english. I use the language mainly for being extremely precise when translating my symbolism back into english, and other at other times for clarity.
The language does not use the “if …, then …” type sentences often found in english because these are ambiguous between many kinds of conditionals (material conditional, logical implication). Similar reasoning apply for “iff” which is not used either.
The table below shows how the symbolism is translated into the language. A similar table is found here.
|Name/group||My preferred symbolization||English translation(s)|
|Implications/conditionals||⇒, →||That P [type] implies that Q|
|Equivalencies||⇔, ↔||That P is [type] equivalent with that Q|
|Negation||¬||It is not the case that P|
|Conjunction||∧||P and Q|
|Disjunction||∨||P or Q|
|Definition||≡||“P” is defined as Q|
|Universal quantification||(∀x)||For all x,|
|Existential quantification||(∃x)||There exists an x such that|
Unique Existential quantification
There exists exactly one x such that
|Possibility||◊||P is [type] possible|
|Necessity||□||P is [type] necessary|
Some additional rules are:
If there is more than one implication in a sentence, add a set of parentheses to make it easier to understand. E.g., P→(P→P) is translated as “That P materially implies (that P materially implies that P).”
Some translations require that a specific type is specified for clarity. Commonly used types are logical, epistemic and physical. The words expressing these are the adverb form, e.g. “logically”, and furthermore e.g. “That P logically implies that Q.”.
My punctuation is sometimes uncommon. This is due to two factors: 1. I am not good at punctuation, no matter the language. I use extra commas (,) for clarity when writing “if …, then …” type sentences. I always write a comma after the antecedent in such sentences, even though it may not be necessary to keep within normal punctuation.
Talking about words/phrases/letters, quoting and special meanings of words/phrases
Talking about words/phrases
For clarity it is useful to use special symbols when talking about words/phrases instead of the concepts/ideas expressed by them. Sometimes and not always I add a short explanatory phrase before the object to make sure there is no confusion about what I am talking about. E.g. “The word “fish”.”. This explanatory phrase is often skipped when it has been used once recently.
When I talk about a word I always use quotation marks (“) around the word/phrase that I am talking about. This is also the case with talking about certain kinds of words/phrases, or in cases where I am unsure/being deliberately vague whether I am talking about a word/phrase, or the idea expressed by the word/phrase.
Talking about letters
I use capital letters to (A, B, C) to talk about letters. E.g. “There are more names beginning with A than with B.”. I may continue to do this with collections of more than one letter. I may switch to using quotation marks, see the preceding paragraph. Generally I use the letter method when the object generally is meaningless. Letters do not mean anything in general, only in specific combinations.
I always use quotation marks (“) for quoting. One at each side marking the beginning and the end of the quote. “[...]” is used to indicate that I have removed some text found in the source. “” indicates that I have changed the conjugation of the embraced words/phrase to make it grammatically correct in the context in which I am using the quote. When quoting I do not insert commas or punctuation marks inside the quotation marks. Such symbols are placed after the quote. Some people do that.
Some people use other symbols for quoting such as apostrophes (‘) or double angle quotation marks (« »). I do not use these symbols for quoting.
Special meanings of words/phrases
I always use apostrophes (‘) for marking that a word/phrase is used with a special meaning, often a non-literal, metaphorical meaning.
Some people use other symbols for this such as quotation marks (“). I do not use these symbols for marking special meanings of words/phrases.
Uncommon spellings, capitalizations (and lack of)
I may use uncommon spellings for words at will. I hold progressive views about language and I may try to change a language by adopting uncommon spellings or uncommon capitalization.
I may drop the digraph PH in favor of the letter F.
I use american spellings for most words that have dual spellings. I prefer spellings that avoid ambiguous letters such as C using instead S and K. E.g. “skeptic” not “sceptic” (cf. the pronunciation and spelling of “scepter” and “sceptic”).
This also extends to lack of capitalizations of words/phrases that it is common to capitalize in english.
- Words referring to languages are commonly written with a beginning capital letter in english. I do not do this. E.g. “I speak english.” not “I speak English.”.
- Words referring to citizens of a specific nation/country are commonly written with a beginning capital letter. I do not do this. “I am danish.” not “I am Danish.”.
Special practices for special contexts
All the patterns mentioned on this page may be overruled by a special case in which I deem that another practice is more desirable.
I am not perfect and I change from time to time
And I may fail to follow my own rules from time to time. Naturally I try to avoid this. Some of my older writings may differ from the rules I mention on this page.
1Single particular relations.