philosophy and inductive logic

[andyandy]

We have the following 2 premises;

1) at age X, it is permissible to do Y.

2) in an arbitrarily short period of time, an individual is sufficiently similar to his/her previous self for any changes to his/her self to be negligible


however from these two premises, induction leads to a permissibility to do Y at any age. Such a method does not account for cumulative change, and yet it appears logically pretty sound. The obvious premise to attack is (2) - and to argue that even in an arbitrarily short period of time an individual is sufficiently affected so as to alter the considerations as to the permissibility of Y. However as t (time) gets smaller, this argument gets increasingly strained. One could possibly attack (1) from some kind of libertarian perspective - insofar as it implies a permissive/non-permissive dichotomy dependant upon the state....

but neither seem especially fruitful.....so i wonder how such problems are [and have been] dealt with in philosophy...

cheers

 

[bruto]

...so i wonder how such problems are [and have been] dealt with in philosophy...

Here might be a good place to start.

 

[joobz]

Is this a restatement of Loki's wager?
http://en.wikipedia.org/wiki/Loki's_Wager

If a line needs to be drawn, you find the most logical markers for defining that line and stick to it.

 

[RandFan]

Here might be a good place to start.

Is this a restatement of Loki's wager?
http://en.wikipedia.org/wiki/Loki's_Wager

If a line needs to be drawn, you find the most logical markers for defining that line and stick to it.

I was thinking of a similar point. When does day become night but I wasn't certain if that was the gist of andyandy's argument.

Now I have a better understanding of the paradox. Thanks bruto and joobz.

 

[Tumblehome]

We have the following 2 premises;

1) at age X, it is permissible to do Y.

2) in an arbitrarily short period of time, an individual is sufficiently similar to his/her previous self for any changes to his/her self to be negligible


however from these two premises, induction leads to a permissibility to do Y at any age. Such a method does not account for cumulative change, and yet it appears logically pretty sound. The obvious premise to attack is (2) - and to argue that even in an arbitrarily short period of time an individual is sufficiently affected so as to alter the considerations as to the permissibility of Y. However as t (time) gets smaller, this argument gets increasingly strained. One could possibly attack (1) from some kind of libertarian perspective - insofar as it implies a permissive/non-permissive dichotomy dependant upon the state....

but neither seem especially fruitful.....so i wonder how such problems are [and have been] dealt with in philosophy...

cheers

This is all new to me and I'm not quite sure I understand it; therefore, I'll take a stab at it.

re: 2) I can't agree that the difference can be said to be negligible, no matter how small t becomes. It's very minute, but adding it to all the minutiae before it adds up to something significant.

To use the legal drinking age as an example, there was no obvious increase in my responsibility in the last second before I turned 19. But responsibility is gained over time, of which that last second was a part, and it can't be discounted. If it was discounted, along with all the seconds before it since I was born, then my responsibility--the result of all those seconds--would have to be discounted as well, and I should never get to drink. Legally.

The "heap of wheat" example in the Sorites Paradox link says it makes no difference adding a second grain of wheat to the first because it still doesn't make a heap. But there is a significant difference of 2x. That is hardly negligible. Even the millionth grain of wheat adds something.

As for determining precisely when a heap begins, well, a "heap" is an imprecise quantity, so trying to determine it with precisely measured grains of wheat strikes me as illogical. Same goes for defining the precise moment when I was responsible enough to drink alcohol. It's unmeasurable, so trying to describe it with measured units of time is logically nonsensical.

 

[andyandy]

Here might be a good place to start.

fascinating - thanks!

I didn't realise it was quite such a philosophical battleground

The suggested indeterminate non-classical approach when applied to the very small scale is quite appealing in its physical symmetry - although contextualism does seem [to me] more satisfactory overall....















*It's always a little disheartening to commit to an idea, and then to discover that you're about 2000 years behind the pace*

 

[andyandy]

Is this a restatement of Loki's wager?
http://en.wikipedia.org/wiki/Loki's_Wager

Loki's Wager is a form of logical fallacy. It is the unreasonable insistence that a concept cannot be defined, and therefore cannot be discussed.

It's difficult to simply dismiss the example as a logical fallacy however - as it's grounded in pretty powerful logical induction.....whilst "unreasonable" seems a rather subjective quantifier upon which to base an argument.....of course this may just be wiki though

 

[andyandy]

re: 2) I can't agree that the difference can be said to be negligible, no matter how small t becomes. It's very minute, but adding it to all the minutiae before it adds up to something significant.

But this requires

at age X, Y is permissable

at age X-a Y is not permissable.

and yet, a can be a measure as small as we like, let's say 10^-100th of a second.....

in a can we be said to cross a permissable/non permissable boundary?

As for determining precisely when a heap begins, well, a "heap" is an imprecise quantity, so trying to determine it with precisely measured grains of wheat strikes me as illogical. Same goes for defining the precise moment when I was responsible enough to drink alcohol. It's unmeasurable, so trying to describe it with measured units of time is logically nonsensical.

the trouble is with a notion of "imprecise quantity" that that one has to abandon descriptors such as "heap" and "bald" altogether - that is accept that they apply to nothing. There is no number of leaves on the ground that would constitue a "heap" - for if there were then we would have a precise quantity with which to ground our induction.

 

[Darat]

....snip...

the trouble is with a notion of "imprecise quantity" that that one has to abandon descriptors such as "heap" and "bald" altogether - that is accept that they apply to nothing. There is no number of leaves on the ground that would constitue a "heap" - for if there were then we would have a precise quantity with which to ground our induction.

Or reintroduce the terms as well defined premises so a "heap" would be defined as "1000 leaves" and bald as "less than 10 active hair follicles per sq cm of skin".

 

[Jekyll]

We have the following 2 premises;

1) at age X, it is permissible to do Y.

2) in an arbitrarily short period of time, an individual is sufficiently similar to his/her previous self for any changes to his/her self to be negligible

You do know this is just a restatement of Zeno's paradox, with extra fuzziness round the edges.

If only there was some branch of mathematics that let us add up increasingly large sets of infinitesimals, in such a way that the answer wasn't 0....

 

[andyandy]

If only there was some branch of mathematics that let us add up increasingly large sets of infinitesimals, in such a way that the answer wasn't 0....

calculus whilst useful in calculations on infinitesimal motion doesn't offer any solution to the OP......

(i assume you were being ironic....it is difficult to tell on a message board )

 

[andyandy]

Or reintroduce the terms as well defined premises so a "heap" would be defined as "1000 leaves" and bald as "less than 10 active hair follicles per sq cm of skin".

hmmm - i guess that is in effect what we do, but it's rather unsatisfactory logically - for we're basing arguments on premises that we can't support or won't when pressed actually be able to define....

 

[fuelair]

This is one of the reasons I do not do philosophy anymore - it is fun to play with but impractical for real purposes. In real life we have two basic ways to go - either a general point where Y behavior/action/ability is acceptable/allowable OR some sort of test/function at which a person demonstrates the ability to do the behavior/action/ability at whatever time they choose. (for point/time feel free to substitute age).

 

[chriswl]

calculus whilst useful in calculations on infinitesimal motion doesn't offer any solution to the OP......

I think calculus is exactly the answer to this problem. As Jekyll said, we need some "mathematics that let us add up increasingly large sets of infinitesimals, in such a way that the answer wasn't 0." That's it.

Or at least it is if you consider the concepts underlying calculus to be firmly grounded logically. Apparently some people are still arguing about this.

The sorites problem is different. It uses discrete quantities.

 

[Darat]

hmmm - i guess that is in effect what we do, but it's rather unsatisfactory logically - for we're basing arguments on premises that we can't support or won't when pressed actually be able to define....

I disagree that it's logically unsatisfactory (not by the way that logically you should not find it unsatisfactory ) because isn't it just part of logic?

 

[andyandy]

I think calculus is exactly the answer to this problem. As Jekyll said, we need some "mathematics that let us add up increasingly large sets of infinitesimals, in such a way that the answer wasn't 0." That's it.

The problem isn't fundamentally about the sumation of infinietesimals [as in Zeno] but about what point the T/F boundary is crossed within such a sumation. if calculus can provide such an answer, i'd like to see it

The sorites problem is different. It uses discrete quantities.

i'm not sure if the sorites problem is different - t may be continuous, but it's broken up into discrete quantities.

 

[joobz]

consider a jar containing oil and water.

You look at it and can easily say,
"here is the oil phase, here is the water phase"

But if you zoom in, that boundry isn't so distinct. In fact, there is a concentration gradient right at the interface. A domain that's ~20%oil, 80% water, which turns into 50%/50%, which turns into 80/20....
This gradient concentration follows predictible curves and is known as the boundry layer and is kept as grey zone. we don't define the inbetween's as one phase or the other. We define the oil phase as the point where Concentration of oil is equal to the oil concentration in the bulk. This is for convienience.


In your age example, I simply state you have an underling principle as to why you select that certain age and then judge issues in the grey zone based upon that principle.

 

[Jekyll]

The problem isn't fundamentally about the sumation of infinietesimals [as in Zeno] but about what point the T/F boundary is crossed within such a sumation. if calculus can provide such an answer, i'd like to see it

OK I was being a bit glib, but calculus is at least representative of the problem, even if it doesn't hold all the answers. It means that we know we need to get an answer which will be consistent with calculus, even if we haven't made up a reason why yet .

Because I've been working with floating point numbers all day I'll give you a possible answer in terms of them as to what's going on.

We say A and B are exactly the same size if [latex]|A -B|=0[/latex], we say they are approximately the same size if [latex]|A -B|< \epsilon [/latex].

Now the first thing we note is that the idea of approximately equal isn't transitive, so if A is approximately equal to B, and if B is approximately equal to C, A doesn't have to be approximately equal to C.

Now in sequence we,

1)Rewrite the inductive step as:

If A is exactly smaller than a heap A+1 is approximately smaller than a heap.

2)Note that something of size 0 is exactly not a heap but that doesn't imply anything beyond the idea that something of size 1 is approximately smaller than a heap.

3)Give up on philosophical 'paradoxes' and head for the pub.

 

[JoeTheJuggler]

And back to the drinking age question: in some states the age used to be 18, in other 21, and in many countries there is no line drawn. Rather than worrying about at what scale the increment in responsibility is measurable (and therefore, at what age to draw the line), why not conduct empirical studies to see if there are merits to drawing the line at 21 rather than 18 rather than not drawing it at all. In other words, are the negative consequences of drinking better or worse in the various legal situations?

I would be willing to bet that the consequences are the opposite of what these laws intend to accomplish.

I know this doesn't further the discussion of inductive logic, but I think it points out that some questions are MUCH more approachable empirically.

 

[bruto]

And back to the drinking age question: in some states the age used to be 18, in other 21, and in many countries there is no line drawn. Rather than worrying about at what scale the increment in responsibility is measurable (and therefore, at what age to draw the line), why not conduct empirical studies to see if there are merits to drawing the line at 21 rather than 18 rather than not drawing it at all. In other words, are the negative consequences of drinking better or worse in the various legal situations?

I would be willing to bet that the consequences are the opposite of what these laws intend to accomplish.

I know this doesn't further the discussion of inductive logic, but I think it points out that some questions are MUCH more approachable empirically.

I think that if you do some googling, you'll find that since motor vehicle accident statistics are gathered everywhere, and since a number of states within recent years have lowered, then raised again, their minimum drinking ages, a certain amount of empirical evidence does exist, at least with relation to drinking and automobile accidents.

Here is one roundup of such studies.