I have Pack Rat and a token copy of Pack Rat in play, so they are both currently 2/2. I target the token with Saw in Half destroying the token and creating 2 more tokens. The Pack Rat card is now a 3/3 because there are 3 Pack Rats in play. What are the tokens' power and toughness? Do the tokens grow when I create more Pack Rats?
With Saw in Half, the tokens' (base) power and toughness will be half the last known (current) power and toughness (C.R. 608.2h, 613.1), each rounded up, of the creature that died, respectively. They won't necessarily be equal to the "number of Rats you control".
This is because, if a copy effect sets a specific power and toughness, the effect doesn't copy any characteristic-defining ability that sets power and toughness (C.R. 707.9d). Pack Rat's first ability is such an ability (C.R. 604.3, 604.3a), so that ability won't carry over to tokens created with Saw in Half (and so won't carry over to other objects that become copies of those tokens, either) (C.R. 707.2, 707.9b, 707.9d). (But compare Pack Rat with Death's Shadow, whose ability is not a characteristic-defining ability and so will carry over as normal.)
Ok, so if I have the 2 Pack Rats, and use Saw in Half on one, I'll have a 3/3 and two 2/2s? Then if I use Pack Rat's activated ability twice, I'll have three 5/5s and two 2/2s?
No, the tokens from Saw in Half will be 1/1s. The creature that died had power/toughness 2/2, that's its last known information about those characteristics. So the two token copies will have 1 as the value for each. What later created tokens have as power/toughness relies on which rat you activate. A normally created Pack Rat will grow with the number of Rats. A sawn in half Rat's activation will give you another 1/1.
So assuming you go for the growing Rat, you'll have 3 5/5s and two 1/1s.
Saw in Half preview image
[180 classic cube]
This is because, if a copy effect sets a specific power and toughness, the effect doesn't copy any characteristic-defining ability that sets power and toughness (C.R. 707.9d). Pack Rat's first ability is such an ability (C.R. 604.3, 604.3a), so that ability won't carry over to tokens created with Saw in Half (and so won't carry over to other objects that become copies of those tokens, either) (C.R. 707.2, 707.9b, 707.9d). (But compare Pack Rat with Death's Shadow, whose ability is not a characteristic-defining ability and so will carry over as normal.)
EDIT (Dec. 30): Correctness edit.
[180 classic cube]
So assuming you go for the growing Rat, you'll have 3 5/5s and two 1/1s.
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