Indian Logic Forum

Avi Sion · Posted: Tue Jun 20, 2006 8:04 pm Post subject: final remark

Plamen: I first want to add on this final remark that I wanted to do, but could not find my way back into this forum:

I should add that the probability of your possible conclusion вЂњI am in the solar systemвЂќ is 99.999, whereas the probability of my alternatively possible conclusion is 0.001 or less. Drawing an Euler diagram well illustrates this вЂ“ since in one case we have a large area the size of Y, whereas in the other case we have a point (where X, Y, Z intersect).

Nevertheless, even such a low probability number for the alternative is enough to declare the more probable conclusion non-deductive. Deduction means 100 percent probability only. What we can say at the outset, however, is that you proposed вЂњinвЂќ conclusion is the stronger factor вЂ“ i.e. the conclusion we would chose first, until and unless we found evidence to the contrary (i.e. in favour of the second conclusion).

Now, regarding your last comment:

I think we are not using the same meanings of X, Y, Z. Or maybe of ON and IN.

For me, X is a point on the circumference of Y, which is a surface wholly in Z, but not necessarily so wholly in that X falls within Z - X here falls on the circumference of Z, too - i.e. where the two circumferences touch each other.

Thus, X is ON both Y and Z, but IN neither Y nor Z.

This is granting that On is not counted as In (whereas you seem to count an On as an In).

See you later - I want to watch the football!

Avi Sion · Posted: Wed Jun 21, 2006 6:34 am Post subject: More on On and In.

Upon further reflection, in answer to your last comment:

IN means "within the boundaries of" (as e.g. a worm is underground).
The word ON could mean вЂњon top ofвЂќ (implying: outside of, but contiguous to вЂ“ e.g. like a man standing on the planet earth) or вЂњon the surface ofвЂќ (e.g. as a stain is on the surface of a sphere).
In the second sense, ON ought to be counted as a case of IN, in my view. But in the first sense, ON implies NOT IN.

This makes me realize that there is a third alternative conclusion, viz.: вЂњpartly ON and partly INвЂќ вЂ“ as in the case e.g. of a tree which has roots underground and trunk over the ground. Therefore, our syllogism should read:

X is ON Y
Y is IN Z
Therefore, X is вЂњONвЂќ or вЂњINвЂќ or вЂњpartly On & partly INвЂќ Z.

My intent for X, Y, Z is: X is вЂњIвЂќ, Y is вЂњthe EarthвЂќ and Z is вЂњour Solar SystemвЂќ.

Thus, even if вЂњI am on Earth, and Earth is in the Solar SystemвЂќ it does not necessarily follow that вЂњI am in the Solar SystemвЂќ вЂ“ for if Earth happened to be on the very edge of the Solar System (viewed as a bigger sphere with an invisible boundary), I would then be on, and therefore OUTSIDE, the Solar System.

ThatвЂ™s what I meant.

Plamen · Posted: Fri Jun 23, 2006 8:41 am Post subject:

Hi, Avi!

In that particular case, either I will be ON the Solar system, or the Earth will not be entirely WITHIN the boundaries of the Solar system as parts of it will be in conjunction with spaces different from the SS.

But what buffles me more is WHY deduction means 100% probability, which is but 100% certainty. Or the implicate "induction is never 100% probability."

Both case can be easily falsified. Speaking in terms of formal correctness,

All gods are immortal.
Socrates is a god.
Socrates is immortal. (a highly improbable deductive conclusion)

Which leads us to the conclusion that probability is not a pure formal ratio but a category requiring material truthfulness.

As for the falsification of the induction's improbability, it follows from any instance of full induction.

Avi Sion · Posted: Sun Jun 25, 2006 6:08 pm Post subject: mist and smoke

a) concerning the syllogism:

The solar system example is of course not a very good one, since the вЂњboundariesвЂќ of it are very uncertain if not arbitrary. I do not know what a physicist would say about this вЂ“ perhaps the definition of what is within the solar system is a function of the sunвЂ™s power to attract objects (i.e. where gravity towards the sun and gravity away from it are equal).
So that in this case, it so happens that whatever is attracted by the earth (i.e. standing on it) is also within the sunвЂ™s gravitational range, and so would be within the solar system, even if the earth happened to be on the very edge of the solar system.

Logic issues should never be resolved entirely with one example, in any case. We are here concerned with geometry, not physics. And from the purely geometrical point of view, if X is ON Y and Y is IN Z, we cannot deductively infer whether X is ON or IN Z, as already shown.

One thing worth adding in this regard: the Euler diagram above shows the domains in question as circles, which have one point in common вЂ“ but we should not take this literally. Even that is a specific example, used as illustration. Y could equally well be a square or some other shape, as indeed could Z be, so that there are any number of intersection points.

b) concerning the induction-deduction issue:

The ultimate truth is: all knowledge is inductive, since all knowledge requires SOME SORT of experiential input from somewhere or other to take shape at all.

Deductive logic is simply the ordering of such knowledge with reference to the laws of thought (identity, non-contradiction and excluding the middle). Deduction is impossible without some data to deduce other data FROM. Even in the most extreme cases of deduction, namely treatment of paradoxes, the conclusion proceeds from a premise. For example: вЂњIf I say that knowledge is impossible, I am claiming this as possible knowledge, therefore knowledge cannot be impossibleвЂќ. This is as near as we can get to вЂњpurely deductiveвЂќ knowledge вЂ“ yet we could not do this without having first induced a concept of вЂњknowledgeвЂќ and a concept of вЂњpossibilityвЂќ, and so forth вЂ“ so even here, some experience is needed. All the more so, when we have more hypothetical premises, as in cases of astronomy for instance.

Granting this reflection, it is easy to see the foolishness of KantвЂ™s вЂњanalytic вЂ“ synthetic dichotomyвЂќ, or similarly the work of logicians who assume there is such a thing as вЂњpurely deductive logical systemsвЂќ. Such philosophers and logicians do not stop to ask how THEY got their knowledge out of nowhere apparently.

Granting that all knowledge is inductive вЂ“ i.e. ultimately based on some experience (whether sensory, mental or intuitive), and therefore on some generalization and/or adduction from the experiential data вЂ“ we can still institute a deduction vs. induction distinction, somewhat conventionally, by stating:

When the conclusion from some given premise(s) is the ONLY one, we shall call the inference DEduction; but when there are TWO OR MORE possible conclusions, we shall it INduction (in a more specific sense of the term). A single conclusion has 100% certainty, because it is alone; whereas multiple conclusions have to share the 100%, and so they each have less than that much (though usually varying amounts).

This is both useful and in accord with common usage.

c) concerning mist and smoke

To return to the original example of confusion of mist and smoke: if I see something that is вЂњmisty or smokeyвЂќ looking, I would be foolish to call it mist, or for that matter call it smoke, because that apparent data is not sufficient by itself for me to draw either conclusion. I have to get more data вЂ“ e.g. look and see if there is a fire or a body of water underneath, or make a chemical analysis of the matter at hand, or use whatever means I can devise so as to narrow down the possibilities, by eliminating all but one of them. This is inductive logic.

If I eventually eliminate all possibilities except one, the remainder can be called a 100% probability obtained by a prolonged inductive process. Or we can view it as a deductive conclusion, drawn not from one isolated datum (the first misty-smokey appearance), but from a complex of data (including e.g. chemical analysis).

With this in mind, you can understand my objection to the Indian philosophers who seem to attack ordinary human knowledge, simply on the basis that I cannot draw an IMMEDIATE conclusion of mist or smoke! They are setting a standard they themselves cannot keep up to (i.e. how do they immediately know what is mist or what is smoke, enough to criticize others?). They are merely revealing their own ignorance of the complexities of induction.

PS вЂ“ I will later look at your http://nyaya.darsana.org/topic75.html comments, so as to complete this discussion (which is taking much more of my time than I intended to giveвЂ¦).

Mukund Dhaygude

Dear Sir, the best work that has been posted on Gangesa is that of Cornelius Goekoop in 1967 published by D Reidel. He gives us western and eastern representations of Gangesa's works i.e Tatvacintamani. He worked on Computational aspects of Navya Nyaya.

Mukund Dhaygude · Posted: Wed Oct 18, 2006 9:35 am Post subject: Set theoretic approach

The inclusive or exclusive set theoretic approaches are good for certain class of problems. We need to convert the problem to such set theoretic representation and then apply principles of inclusion or exclusion. Very often it will lead us to boolean logics and computer solvability of the problem will increase.

Mukund Dhaygude

I think induction and deduction as mathematico-logical processes are simply inverse processes and probability is something different.

Plamen · Posted: Wed Oct 18, 2006 9:57 am Post subject:

Probability is a sidewalk characteristic of all inductive knowledge, except for the cases of full induction.

Deductive is the logic that does not pay attention to the way its general assumptions (in the form of hetu-vakya) have been reached. It just takes them for granted. Then, when something goes wrong, it starts looking for argumental seemingness (hetvabhasa).

Mukund Dhaygude

Dear Friends, I guess J F Sowa's works has been illuminating in this area.