Why French writers say 'je ne sais' without 'pas'
You learned early on that French negation has two parts: ne before the verb and pas after it. In formal and literary French, though, four verbs can be negated with ne alone: pouvoir, savoir, oser and cesser. A novelist writes je n'ose y penser or elle ne cesse de sourire, and the sentence is fully negative even though pas never appears.
This catches English speakers in two ways. When reading, the lone ne is easy to miss, so you may read a negative sentence as positive. It can also look like the expletive ne of avant qu'il ne parte, which carries no negative meaning at all. Here the ne really does mean not. It is simply a more elegant, more old-fashioned way of saying it, much like English dare not or know not.
The pattern is almost always the same. You have ne, then one of the four verbs, then an infinitive. With cesser the infinitive comes after de. With savoir you can also have an indirect question introduced by si, où, que or quoi. Adding pas is never wrong: je n'ose pas and je n'ose mean the same thing. Leaving it out mainly changes the register, which becomes more formal, more written and slightly literary.
The rule of thumb for English speakers: treat the pas-less version as something to recognise in books, letters, speeches and journalism, and to use sparingly in your own formal writing. In conversation, people say je sais pas. They drop the ne, which is the exact opposite of this pattern.
Pouvoir followed by an infinitive is the most common case in formal prose. You will also meet the old first-person form je ne puis, which sounds deliberately literary.
Savoir in the sense of to know drops pas mostly before an indirect question or a question word followed by an infinitive. In the sense of to be able to, it appears above all in the conditional je ne saurais, a polite and formal way of saying I couldn't.
Oser plus an infinitive works just like English dare not.
Ne cesser de plus an infinitive means to keep doing something, often with a note of insistence or exasperation.
The pattern does not spread to other verbs. Je ne veux venir or il ne mange viande are simply wrong. They need pas.
Even with the four verbs, keep pas when there is no infinitive or question after them. Je ne sais pas la réponse needs pas, and so does a bare je ne peux pas on its own. The lone je ne sais without a complement survives only in fixed set phrases.
Some of those set phrases are worth knowing because they are frozen and appear even in everyday French: un je-ne-sais-quoi (an indefinable something), je ne sais qui (someone or other) and je ne sais combien (who knows how many). The very common n'importe quoi and n'importe où come from the same old pattern with the verb importer.
Finally, do not confuse this with ne ... que. Je ne peux que vous remercier means I can only thank you, not I cannot thank you.
In formal written French, pouvoir, savoir, oser and cesser can be negated with ne alone when they are followed by an infinitive or, for savoir, by a question word or si. The meaning is fully negative, and adding pas is always correct too. Learn to spot the lone ne when reading, use it only in polished writing, and never extend it to other verbs.