Has anyone encountered a formal version of this? I.e. a site for the creation of formal logical arguments. Users can create axioms, assign their confidence to them and structure arguments using them. Users can then see the logical consequences of their beliefs. I think it would make a very interesting format for turning debate into a competitive game, whose results are rigorous, machine readable, arguments.
While I am certainly not against the idea of a tool that can be used to create formal arguments, the proposal has a subtle but radical difference.
DISCLAIMER: I am not a mathematician, and do not fully understand the concepts I attempt to explain in the following.
In his work published as ‘Notes on the Synthesis of Form’, Chris. Alexander developed an algorithm for converting a matrix of relationship strengths between analysed sub-elements of a design problem into a ‘tree-like’ structure. In other words, a hierarchical diagram in which each node can have one connection only, to a higher status node. The number of nodes in each level decreases as one moves upwards, culminating in a single ‘master’ or ‘root’ node.
Following the success the publication of ‘Notes...’ brought, Alexander was employed to work on the development of the metro rail system in San Francisco (the BART), and put his method to work. As a rationalist, he was concerned to find that the results of his work appeared to be failing to fully address the realities of the design problems involved.
His conclusion was that the necessary function of his transformative algorithm which selected the least significant relationship linkages to be broken in order to derive the tree-like diagram was the cause of the problem; some identified real-world relationships were being ignored. And even though these might be ranked lowly, omitting them altogether was destructive.
In it, Alexander contrasts the tree-like diagram with another; the semi-lattice diagram, which, although still hierarchical, allows for connections across branches, as it were, so that overlapping sets of relationships are legal. Semi-lattices, I believe, are not susceptible to formal logical analysis, but nevertheless can be better mapping tools for complex, real-world systems.
My proposal would deliberately allow for semi-lattice linkages. This would allow, to come up with a quick example, a proposition that called for more cycling to link both to a proposition for less carbon emissions and a proposition for congestion reducing transport initiatives.
Tree diagrams are fairly useless in addressing real-world conditions, as these are usually formally complex, with elements occurring in overlapping sets more often than not. As a result, policy documents are not structured like tree diagrams, and do adduce all sorts of linkages, but do this in a totally unstructured manner, and are often functionally weak, while appearing to address everything. As EY says (everywhere); “A theory that can explain everything, prohibits nothing, and so gives us no advice about what to expect.”
My hope for the proposal is that it could bring structured, coherent agreement on sets of principles without the need for total agreement on every aspect of every point.
Has anyone encountered a formal version of this? I.e. a site for the creation of formal logical arguments. Users can create axioms, assign their confidence to them and structure arguments using them. Users can then see the logical consequences of their beliefs. I think it would make a very interesting format for turning debate into a competitive game, whose results are rigorous, machine readable, arguments.
While I am certainly not against the idea of a tool that can be used to create formal arguments, the proposal has a subtle but radical difference.
DISCLAIMER: I am not a mathematician, and do not fully understand the concepts I attempt to explain in the following.
In his work published as ‘Notes on the Synthesis of Form’, Chris. Alexander developed an algorithm for converting a matrix of relationship strengths between analysed sub-elements of a design problem into a ‘tree-like’ structure. In other words, a hierarchical diagram in which each node can have one connection only, to a higher status node. The number of nodes in each level decreases as one moves upwards, culminating in a single ‘master’ or ‘root’ node.
Following the success the publication of ‘Notes...’ brought, Alexander was employed to work on the development of the metro rail system in San Francisco (the BART), and put his method to work. As a rationalist, he was concerned to find that the results of his work appeared to be failing to fully address the realities of the design problems involved.
His conclusion was that the necessary function of his transformative algorithm which selected the least significant relationship linkages to be broken in order to derive the tree-like diagram was the cause of the problem; some identified real-world relationships were being ignored. And even though these might be ranked lowly, omitting them altogether was destructive.
The essay which captures this understanding is published as ‘A City is not a Tree’ - read it here: http://www.rudi.net/pages/8755.
In it, Alexander contrasts the tree-like diagram with another; the semi-lattice diagram, which, although still hierarchical, allows for connections across branches, as it were, so that overlapping sets of relationships are legal. Semi-lattices, I believe, are not susceptible to formal logical analysis, but nevertheless can be better mapping tools for complex, real-world systems.
My proposal would deliberately allow for semi-lattice linkages. This would allow, to come up with a quick example, a proposition that called for more cycling to link both to a proposition for less carbon emissions and a proposition for congestion reducing transport initiatives.
Tree diagrams are fairly useless in addressing real-world conditions, as these are usually formally complex, with elements occurring in overlapping sets more often than not. As a result, policy documents are not structured like tree diagrams, and do adduce all sorts of linkages, but do this in a totally unstructured manner, and are often functionally weak, while appearing to address everything. As EY says (everywhere); “A theory that can explain everything, prohibits nothing, and so gives us no advice about what to expect.”
My hope for the proposal is that it could bring structured, coherent agreement on sets of principles without the need for total agreement on every aspect of every point.