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> The beautiful thing about logic and mathematics is that derivations / proofs can be verified mechanically: if even a dumb computer can follow and verify the r

> The beautiful thing about logic and mathematics is that derivations / proofs can be verified mechanically: if even a dumb computer can follow and verify the reasoning, so can indeed a reasonable person. Even in mathematics and logic you have axioms which cannot be formally proven by mathematics and logic. You do try to minimize the axioms, but they will always be there. So even in the most pure of disciplines, you cannot be 100% "objective". Most real life issues are much messier than logic and mathematics.

Jensson 4y ago
You misunderstand math, the argument in math isn't "these axioms are true", but instead every paper goes "given these axioms, the following result can be derived". Mathematicians can all agree about the second, and then they agree to disagree about the axioms, and therefore reach maximal levels of consensus. If politics was like that instead of the current "try to make the other side seem as different as possible to sway voters" then the world would be a much nicer place. People are too stupid to do that though, when they try they still fall for the fallacies mentioned in the article. Instead of just looking at how the different sides starts with different moral axioms they instead focus on how the derivative results differ and call the other side morally corrupt based on their derivative results being so far from what this side sees as optimal.
- DoctorOetker 4y ago
  I am not sure if you merely wish politics could be like that or if you actually consider a move towards formal verification in society to be actually possible but probably daunting. If the latter you are one of the very few people I have communicated with who can also see the myriad advantages of formal verification in democracy, daily life, or perhaps even courts. Consider things like due process, it may seem like a pedantic thing and overly paranoid to demand we have formally verifiable due process, so that anyone verify due process at home. But its much more than that. Institutional buildings are heavily protected assets, which cost a lot of money to protect. When a fraction of the populace storms such an asset, it costs lives and limbs, it costs a lot of money to permanently guard it, it will cost a lot of money and attention in processing the consequences etc... If the capitol was entirely virtual there would be nothing to storm and all these costs in life, limb, taxpayer dollars and time and attention of both the legal system and the population as audience would have avoided.
prometheus76 4y ago
Trying to point the presuppositions of someone who considers themselves completely objective or rational is a lost cause, I've found. They quickly fall into circular logic, but fail to see the circularity.
- DoctorOetker 4y ago
  The objectivity I claim does not reside in the dogmatic axioms, they are indeed unproven, the objectivity is in the fact that a some theorem provably follows from the axioms. I state nothing less myself when I describe "fundamentalism" as a better moniker: the quest for locally minimal sets of axioms that allow maximal sets of theorems to follow from them without generating mathematical inconsistency.
  - RcouF1uZ4gsC 4y ago
    > the objectivity is in the fact that a some theorem provably follows from the axioms. Actually I don’t think the laws of inference are formally provable.
    - DoctorOetker 4y ago
      The laws of inference are axioms as well. You can see how its done in say MetaMath.
bobthechef 4y ago
Indeed, deduction, while of course important, is downstream from conceptualization. If you begin with muddled concepts, your deductions aren't good for anything. Even a small error in the beginning leads to big errors in the end. And strictly speaking, mechanical deduction is a simulation of deduction that exploits the formal properties of propositions. You cannot analyze the conceptual terms (e.g., predicates) in this fashion because, by definition, the content of those terms are exactly what formalism excludes. Formalism provides us with essentially this: that we can deduce the shape of the (or a) conclusion regardless or for any such terms from the shapes of the premises alone with no concern for the concepts involved.

Jensson 4y ago

You misunderstand math, the argument in math isn't "these axioms are true", but instead every paper goes "given these axioms, the following result can be derived". Mathematicians can all agree about the second, and then they agree to disagree about the axioms, and therefore reach maximal levels of consensus. If politics was like that instead of the current "try to make the other side seem as different as possible to sway voters" then the world would be a much nicer place. People are too stupid to do that though, when they try they still fall for the fallacies mentioned in the article. Instead of just looking at how the different sides starts with different moral axioms they instead focus on how the derivative results differ and call the other side morally corrupt based on their derivative results being so far from what this side sees as optimal.

DoctorOetker 4y ago
I am not sure if you merely wish politics could be like that or if you actually consider a move towards formal verification in society to be actually possible but probably daunting. If the latter you are one of the very few people I have communicated with who can also see the myriad advantages of formal verification in democracy, daily life, or perhaps even courts. Consider things like due process, it may seem like a pedantic thing and overly paranoid to demand we have formally verifiable due process, so that anyone verify due process at home. But its much more than that. Institutional buildings are heavily protected assets, which cost a lot of money to protect. When a fraction of the populace storms such an asset, it costs lives and limbs, it costs a lot of money to permanently guard it, it will cost a lot of money and attention in processing the consequences etc... If the capitol was entirely virtual there would be nothing to storm and all these costs in life, limb, taxpayer dollars and time and attention of both the legal system and the population as audience would have avoided.

prometheus76 4y ago

Trying to point the presuppositions of someone who considers themselves completely objective or rational is a lost cause, I've found. They quickly fall into circular logic, but fail to see the circularity.

DoctorOetker 4y ago
The objectivity I claim does not reside in the dogmatic axioms, they are indeed unproven, the objectivity is in the fact that a some theorem provably follows from the axioms. I state nothing less myself when I describe "fundamentalism" as a better moniker: the quest for locally minimal sets of axioms that allow maximal sets of theorems to follow from them without generating mathematical inconsistency.
- RcouF1uZ4gsC 4y ago
  > the objectivity is in the fact that a some theorem provably follows from the axioms. Actually I don’t think the laws of inference are formally provable.
  - DoctorOetker 4y ago
    The laws of inference are axioms as well. You can see how its done in say MetaMath.

bobthechef 4y ago

Indeed, deduction, while of course important, is downstream from conceptualization. If you begin with muddled concepts, your deductions aren't good for anything. Even a small error in the beginning leads to big errors in the end. And strictly speaking, mechanical deduction is a simulation of deduction that exploits the formal properties of propositions. You cannot analyze the conceptual terms (e.g., predicates) in this fashion because, by definition, the content of those terms are exactly what formalism excludes. Formalism provides us with essentially this: that we can deduce the shape of the (or a) conclusion regardless or for any such terms from the shapes of the premises alone with no concern for the concepts involved.