The meaning of "is"

As a native english speaker, I never really thought about what "is" really meant, but after starting to learn some other languages, I saw how often times, expressions with "is", were often, in the other language, used as expressions with "have". For example: EN: I'm cold. FR: J'ai froid.

This started to make me wonder what "is" actually meant. At first I though that is could just be a synonym to "equals", but that doesn't always work. (E.g. "He is sad". Not, "he equals sad.")

As of now, I have two theories as to what "is" means.

The first is that sometimes "is" can be equated to "equals" (e.g. January 15th is today.) It would be strange to say that January 15th equals today -and that statment would only be true one day of the year-, but technically, I think, that would be a correct logical statment.

The second is that "is" can also mean "the subject of this sentence currently manifests/embodies the abstract concept about to be listed" (e.g. He is sad." would follow this definition.)

What I am wanting to know is whether -and I assume that this list isn't complete- there are other definitions or stipulations concerning what "is" means.

As Wittgenstein put it,

Meaning is one of the words of which one may say that they have odd jobs in our language ... What causes most trouble in philosophy is that we are tempted to describe the use of important "odd-job" words as though they were words with regular functions.

As it happens, only what linguists call lexical words have meanings. Many other words don't have meanings so much as they have uses. They're basically part of the grammatical rebar that's supporting all those meaningful lexical words in the sentence.

They're machinery, these words, and they don't have any meaning. So it's pointless to argue. Words like the and of and there and than; and, most relevantly, be, in all its forms, in many uses.

The overwhelming majority of occurrences of be in English come from one of four constructions:

• auxiliary verb for the Progressive construction: Bill was leaving at 5.
• auxiliary verb for the Passive construction: Bill was shot at 5.
• auxiliary verb for all predicate adjectives: Bill is sick/dead/here/hungry/tall.
• auxiliary verb for all predicate nominals: Bill is a doctor/the man to see/who she mentioned.

Furthermore, even when be is the only verb in the sentence, it still behaves like an auxiliary verb.

• He is going ~ Is he going?
  (auxiliary verb undergoes subject-auxiliary inversion in question)
• This is the one she saw. ~ Is this the one she saw?
  (this be also behaves like an auxiliary)

In fact, no form of be behaves like a real lexical verb, and therefore it has no lexical meaning. Speakers of languages without a copula, about half the people in the world, aren't surprised.

"...there are other definitions or stipulations concerning what "is" means."

The verb is is a tense form of the main (infinitive) verb be. So, if you study the different definitions for be, you would be studying is.

http://www.merriam-webster.com/dictionary/is

http://www.merriam-webster.com/dictionary/be

The Present Tense uses the verb is. The attributes of the Present Tense is that the present tense is used to state facts, show habitual action, but it is not used to state present action. Thus, is is a linking verb by itself, which is otherwise known as a "state-of-being" verb--intransitive, taking no object.

Take is and use it as as a helping verb (a.k.a. auxiliary verb) in verb phrase with a main verb, and you now can get all kinds of meaning, even action, as in the Present Progressive: She is going to college.

It's not a matter of is meaning equal, when you understand that, again used alone, it links one idea with or without a subject complement [predicate adjective/predicate nominative] to another.

The book is on the table. [adverb phrase telling where the book is]

That pen's ink is red. [the predicate adjective red describing the ink as being red]

She is an opera singer. [the predicate nominative singer modified by the adjective [nouns can be adjectives] opera; identifying or explaining that she is an opera singer]

Your statement, "The second is that "is" can also mean "the subject of this sentence currently manifests/embodies the abstract concept about to be listed" (e.g. He is sad." would follow this definition.)" is on cue with is functioning as a state-of-being verb with the purpose of being used as a linking verb:

He is sad.

Subject | linking verb | predicate adjective that answers a question an adjective would ask, "What kind?" What kind of feeling or emotion is he experiencing? That of being sad.

is alone means nothing. It's just a verb with no subject, no other words to help explain its purpose. I say purpose because after studying grammar for so long I began to see that what my textbook on grammar had been telling all the long, indirectly I might add, I had to literally put two an two together, to come up with this:

Every word in a sentence not only functions as a part of speech but also serves a purpose in the sentence.

And is is no exception. It's function is: primarily, present 3d singular of be--Webster's, and its purpose depends on how it is used: linking verb or helping verb. These rules give meaning to the word is. They define is.

Finally, our entire English language is base on a foundation: the eight parts of speech. Some laugh at this as being antiquated, irrelavant to today's linguistic/semantic advancements in grammar. There's only one problem with that, Webster's and all of these guys still use the eight parts of speech http://onelook.com/. And the last I heard is that is is still one of the eight parts of speech, a verb.