I would like a more concise way of phrasing what is bracketed in the examples below:
Socrates [said something along the lines of] I'm smart because I know that I don't know much.
Tyler [said something like] success breeds a hidden failure.
If you're being informal:
Socrates was like "I'm smart because I know that I don't know much."
Tyler was all "Success breeds a hidden failure."
In at least my idiolect, "was like" as opposed to "said" is precisely to indicate that the source is being paraphrased.
Like — Oxford Dictionaries
adverb 2. (informal) Used to convey a person's reported attitude or feelings in the form of direct speech (whether or not representing an actual quotation)
"so she comes into the room and she's like ‘Where is everybody?’"
To quote approximately is to paraphrase:
a restatement of a text or passage giving the meaning in another form
In order to use this word, you'd have to restructure your sentences:
To paraphrase Socrates: I'm smart because I know that I don't know much.
To paraphrase Tyler: success breeds a hidden failure.
Instead of going out of your way to make it look like a quote but then disclaim that it's an exact quote, you can indicate that you are paraphrasing what someone else said by avoiding making it look like a quotation in the first place.
For example, if you are talking about something another person said, use the third person to indicate that you are restating what they said, and not directly quoting them. Instead of:
Bob said "I am going to the store."
you can say:
Bob said he was going to the store.
Both convey the same meaning, that Bob intended to go to the store, but the first implies a specific wording was used by Bob, and the second does not.
For your examples, you could write something like:
Socrates said that he was smart because he knew that he didn't know much.
Tyler said that success breeds a hidden failure.
More colloquially, I've heard more or less.
Socrates more or less said I'm smart because I don't know that much.
More or less, Socrates said that I'm smart because I don't know that much.
He said I'm smart because I don't know that much, more or less.
This phrase indicates that you're paraphrasing, or that you're 'reading between the lines', e.g.:
He said "That dress looks fine on you".
More or less, he said I look fat in this dress!
If you're going for down-to-the-syllable succinctness, try out roughly.
Socrates roughly said: I'm smart because I know that I don't know much.
Tyler roughly said: success breeds a hidden failure.
While I agree with some of the answers, an alternative approach is to use words that show your understanding on their stance of role in the idea:
Socrates acknowledged that [he was] smart because [he knew] that [he] don't know much.
Tyler was critical of success [because it] breeds a hidden failure.
Note here that this is fairly formal (third-person past tense) and would come across as more impartial, objective, or academic in a report or article. You might come across as too educated, condescending or patronising if you were to use this in everyday speech or social media.
Here's a phrase you could try:
You could say your paraphrased sentence and add, 'or words to that effect.'
E.g., Socrates said he wasn't smart because he knew he didn't know much, or something to that effect.
Similar to "roughly", you can use "basically" or "essentially"
Socrates basically said I'm smart because I know that I don't know much.
Tyler essentially said that success breeds a hidden failure.
These are both fairly concise and appropriate in a range of situations: they're a little bit informal (particularly "basically") but I have seen these used in academic debates and conferences.
Since we only know the quote approximately, we know the meaning of the quote, and so meant should work.
Socrates meant, "I'm smart because I know that I don't know much."
Tyler meant success breeds a hidden failure.
[WITH OBJECT] 1 Intend to convey or refer to (a particular thing); signify:
‘he was asked to clarify what his remarks meant’
‘Ziana began to understand what her grandfather had meant by those words.’
There are already excellent answers here, but to convey the meaning of the OP, may I suggest
Socrates taught, "I'm smart because I know that I don't know much."
Tyler taught, "Success breeds a hidden failure."
This implies that the words chosen might not be exact, but the meaning is the same. In essence you are quoting his idea, not his words. Ideas, by design, are framed in the language and perspective of the person speaking and not that of the original creator.
Consider "indicated", this sense of which is defined by Merriam-Webster as:
to state or express briefly
Tyler indicated that success breeds a hidden failure.
The simplest solution is not to use quotes. You could use 'that" if you want to emphasize that it's not a direct quote, but it's not necessary.
Tyler said [that] success breeds a hidden failure. Socrates said [that] he was smart because he knew he didn't know much.
If you know what your speaker meant, but don't know the exact words, this should do. If you're not sure of the exact meaning, then you'll have admit that by using some more cumbersome wording. Something along the lines of "something along the lines of."