Is half-a-tablet of X a substitute for a tablet of X/2?
This website gives a nice overview, including how the FDA approve drugs that they expect will be spit and some practical issues of pill cutting. 

Yes, half a tablet of (2x dose) is, absent other issues, equivalent to one intact tablet of (1x) dose.  The main exceptions are practical ones.. where the tablet cannot easily be cut; where the dosing is so specific that slight variations of dose (uneven tablet fragments) matter, or where the dose is in a capsule or has some special coating so that cleavage might alter the release of drug into the body.

Yes, dosing scales upwards.  Two pills give twice the total dose of one pill.  

All prescriptions are dispensed with specific dosing regimens (i.e how much you take and when you take them) to ensure the drug reaches effective concentrations in the body. You should not try to 'boost' the drugs effectiveness by taking more drug, or taking drug more frequently than your physician has prescribed.  As noted in the weblink above, it can be tricky to keep track of dosing and timing if your pill bottle contains whole and cut pills.  (i.e what does "take one pill every NN hours" mean ?). 

This is NOT MEDICAL ADVICE . Always consult your physician and/or pharmacist for your particular case.