Outside of social aspects such as evening out the income gap, taxes serve a simple purpose: share the cost of common purchases and thereby obtain savings in scale. For example, if we wish to have a state where people needn't hire private armies to defend our borders and guards to keep our property safe, we gather a sum of money through taxes and hire a common army, police force, legislature process, courts of law, and prison system which exercise a monopoly of violence within our borders. (Incidentally, that is what defines a state.) Currently almost all of that system is paid by income and value added tax as they form an overwhelming majority of our budget's income.
But now consider who has most to lose if the army, police force, law, and criminal system would cease to exist. Rampant theft and vigilantism would follow. Except for our lives, what do we have to lose? Yes, our property! Eventually our society would degrade to stone age where no-one could safely own more than he could carry with him, guard with sight and hearing and run to protect before the thief is gone. So the ones that benefit most of our costly system for maintaining safety and order are the ones who own a lot of properties (land, buildings, valuables, money, shares, promissory notes, whatever). However, property tax pays only a negligible fraction of the costs associated with protecting the properties of people, and it is now being lifted altogether. I don't see the fairness in that.
Estate (inheritance) tax is argued againts by calling it multiple taxation, as the same property is taxed first when the deceased earned it and a second time when it is passed on to the children. However, this argument doesn't hold for two reasons: Firstly, why should property in estates not be taxed when they change hands while essentially all other exchanges of ownership is taxed? Secondly, the one who pays the estate tax is the recipient of the estate, not the deceased, so there's really no double taxation occurring at all!
In my view estate tax can be used to replace property tax simply because everybody dies some day, and whether the taxation is done after death or while living is irrelevant. Therefore now that property tax is removed, estate tax should be sufficiently large to cover a fair share of our common infrastructure that protects property. Nevertheless, in my mind property and estate tax carried by the Finnish state should roughly equal the sum consumed by the interior, defence and justice ministeries, or roughly 5 billion euros.