Smart contracts are these social protocols that are secured by cryptography and the calculation is done by the node themselves decentrally, everything remaining visible to the whole world. Unlike the current "smart contracts" in ethereum which implement the protocol centrally in a piece of code - the 'protocol' is not decentralised, only the hosting of it.
If a platform can provide multi-signature environment, security and the ability to enforce and execute codes, it is a smart contract platform.
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No, it is an agreement between parties enforced by cryptography, and no third party required.
> In the case of Ethereum, it is enforced by cryptography. No it is enforced by payment to the network, just like aws, but in a worst way, because code is executed wastefully, while still remaining at a central location.
What you are not understanding is that a smart contract is a protocol amongst people. You don't code it anywhere in the blockchain directly. It a a protocol that explains how, if each party runs code independently, assuming everyone as a criminal, still achieves its goal. For eg, multisig is a smart contract, which is a protocol where participants decide what code they'll run (signing) and the wallet layer that makes them meet is a separate layer altogether, not in the blockchain. Sometimes this layer may not even be required, for example in money-laundering or any of the 'hundis'.
Okay, I see your point. This kind of smart contract you describe definitely needs strong cryptography and a blockchain would not be needed. I guess the issue is still about what a smart contract truly is and how it should work. I personally prefer the term self-executing contract as the "smart" seems too sensitive. Regardless of the language or definitions, I am interested in a platform were multisig applications can be executed safely and efficiently.