Here is the argument:

For all we know, A may be the state of B;

What C does is determined by the state of B;

Therefore, for all we know, what C does may be determined by A.

Is the argument valid?

Please keep to one of the following four answers:

No

Yes

I don’t know

The argument doesn’t make sense

Please, don’t comment if you can’t answer the question asked.

EB

Mathematicians who worked on the conception of a method of logic in the 19th century, Frege in particular, were essentially and explicitly motivated by the idea that a proper method of formal logic would help improve the rigour of mathematical proofs, a particular concern at the time, between the two extremes of Abel and Weierstrass. This suggests a view of logic as essentially not arbitrary and therefore as *essentially empirical*.

And in effect, mathematicians working on a method of logic at the time had to rely on the only empirical evidence available to them, i.e. Aristotle’s syllogistic theory, plus what other people since had said on the subject, including other mathematicians, as well as their own personal intuition, as to what formulas could be accepted as logical truths, this in order to work out a method of logical calculus *they could use to improve rigour of proof*.

Today, *on the surface*, we seem to have a very different perspective, whereby logic is more often understood as essentially a mathematical object, like the set of Real numbers is, so that logic is thought of as being the methods of logic themselves that mathematicians have contrived since Frege. In this perspective, logic is no longer seen as an essentially empirical science, but as the motley collection of theories, *seen as arbitrary at least in principle*, that mathematicians are working on as objects of study rather than as methods they could use to improve the rigour of proofs.

Meanwhile, mathematicians themselves still essentially use and effectively rely on their own, intuitive, sense of logic to prove theorems, producing what can be described in effect as semi-formal proofs.

The few examples of formal logic being used to prove theorems today all rely on some variation of Gentzen’s “*natural*” method of proof (conceived between 1929 and 1935), which is essentially a modern generalisation of Aristotle, and a method which effectively relies on the crucial use of so-called rules of inference, which are formulas all essentially taken from the set of formulas long recognised as logical truths in the Aristotelian tradition, save a few exceptions.

So, in effect, all current practice of mathematical proof, be it intuitive or making use of theorem provers, like Isabel in Germany and Coq in France, still literally relies ultimately on the empirical evidence available to mathematicians that some logical truths are *evidently* true. Yet, the fundamentally empirical nature of the logic practised by mathematicians themselves, *today as always since Euclid*, is somewhat airbrushed out of the picture in favour of a more abstract notion of it.

Comments welcome.

EB

Premise 1 - For all we know, somebody’s conscious mind may be the state of a group of neurons in this person’s brain;

Premise 2 - What somebody does is determined by the state of a group of neurons in this person’s brain;

Conclusion - Therefore, for all we know, what somebody does may be determined by the conscious mind of this person.

Everything is admissible as long as it’s what you think is the best expression of the structure of the argument and that you are prepared to argue your view.

Still, I will myself keep away from this thread to let you all try to arrive at a consensus independently of my own view, hopefully through something like a rational debate.

Thank you in advance for your contribution.

EB

EDIT

Apparently I can’t even reply the normal way. So here is my response.

This thread is obviously different from the other one. I’m asking explicitly for a formal expression of the argument. This is obviously to get people to get their acts together and formally prove their point. I already have different people proposing different formal expressions, this in itself should be enough to give you pause for thought. So, instead of your derail, just address the topic at hand and provide whatever formal expression you think best represents the argument as it is worded. Short of that, thank you to abstain from irrelevant comments.

EB

EDIT

I’m pleased to announce I was able to obtain independent confirmation that the argument is valid. I am told it can be couched in the axiomatic S4 of modal logic. Not that I was worried myself, I was even rather embarrassed to ask for the confirmation of something pretty obvious to begin with, but you never know.

There are two specific qualifiers I didn’t expect (beyond necessity and possibility), which are nonetheless required in formal logic to capture the whole semantic of the argument. Good to know.

Still, apparently, it seems there is no metaphysically absolute formal proof that any logical argument is valid. To see that an argument is valid, we all have to rely on our own personal intuitive sense of logic.

Or rely on somebody else we trust, but he himself will have to rely on his own intuition, or possibly on whatever empirical evidence there is as to what people do in this respect.

Still, it’s not all bad. It means anyone here can still enjoy the luxury of being able to deny *mordicus* that the argument is valid, even obviously not valid, even patently not valid. I can’t prove metaphysically, absolutely, that you’re wrong. Good to know, hmm?

EB

To begin, forgiveness seems like a term that can be interpreted in several ways. Does it imply absolution from blame? Does it require repentance of the wrong-doer? Or simply the end of bitterness in the heart of someone who was wronged?

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Rawls’s theory of “justice as fairness” recommends equal basic rights, equality of opportunity, and promoting the interests of the least advantaged members of society. Rawls’s argument for these principles of social justice uses

a thought experiment called the “original position”, in which people select what kind of society they would choose to live under if they did not know which social position they would personally occupy.In his later work Political Liberalism (1993), Rawls turned to the question of how political power could be made legitimate given reasonable disagreement about the nature of the good life.

My broad strokes would be something like this:

- universal healthcare

- affordable, decent housing and food

- meaningful education through high school (including vocational training)

- aid for the disabled

- a shovel for the unemployed (the opportunity for decent pay for a humane day’s work)

- a graduated tax code with no deductions or loopholes

How would you construct such a society?

]]>

Premise 1 - For all we know, somebody’s conscious mind may be the state of a group of neurons in this person’s brain;

Premise 2 - What somebody does is determined by the state of a group of neurons in this person’s brain;

Conclusion - Therefore, for all we know, what somebody does may be determined by the conscious mind of this person.

EB

Thank you to restrict yourself to facts and logic.

EB

Given that we are equal in this regard, there is some rational basis to reason, beginning with the fact of equality on these levels, that the Golden Rule, mercy, compassion, understanding, and equal treatment before the law and in morality have a rational basis. I’m not writing all the steps in this reasoning process, but suffice it to say that the foundation would be equality, and that’s about as far down as we can go. Treatment of our fellow humans can be founded on that premise.

That’s a brief outline of my thoughts. I open the discussion up for criticism.

]]>There is for example a typical distinction which is often made between the methodology in mathematics and science that science should be true of the physical world whereas mathematics doesn’t need to care about it.

Thanks.

EB ]]>

Do you agree with this presentation of this criterion, including with the suggestion that it is not only the main but that it is also the only criterion admissible in empirical sciences like physics.

If you think that there are other criteria necessary to assessing the validity of a theory in empirical sciences, what are they?

EB ]]>

As a motivation introduction, I observe that most educated people take logic to be a branch of mathematics, or perhaps whatever mathematicians study that they call “logic” since broadly the beginning of the 20th century. Yet, the first systematic presentation of what humans understand of logical rules was made by Aristotle and that was something like 2,400 years ago, and as far as I know, most intellectuals since have accepted Aristotle’s presentation as correct. I’m not aware that anything in mathematical logic shows Aristotle was wrong.

Whatever the case, is it possible to study anything if there isn’t something to study? This suggests logic exists somehow somewhere. But where exactly?

Traditionally, philosophers see rules of logic as necessary and a priori, rather than contingent and empirical. Putnam argued they could be empirical, taking the example of Quantum Physics to support this suggestion. Yet, even a priori rules have to come from somewhere unless you think God the merciful help us sort out the necessary from the contingent.

If we all have our own personal sense of logic, why is it most intellectuals agreed with Aristotle’s logic (and I would assume most people here)? But if we all have the same logic, how come?

And where are we supposed to look when we want to produce a method of logic that, somehow, would be correct?

EB ]]>