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<p>means that every Frenchman is a man, but there are men besides Frenchmen.  Drobisch has used this sign in the same sense.  It will follow from these significations of <math>=\!</math> and <math><\!</math> that the sign <math>-\!\!\!<\!</math> (or <math>\leqq</math>, "as small as") will mean "is".  Thus,</p>

<p>means that every Frenchman is a man, but there are men besides Frenchmen.  Drobisch has used this sign in the same sense.  It will follow from these significations of <math>=\!</math> and <math><\!</math> that the sign <math>-\!\!\!<\!</math> (or <math>\leqq</math>, "as small as") will mean "is".  Thus,</p>

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| align="center" | <math>\mathrm{f} -\!\!\!< \mathrm{m}</math>

| align="center" | <math>\mathrm{f} ~-\!\!\!< \mathrm{m}</math>

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<p>means "every Frenchman is a man", without saying whether there are any other men or not.  So,</p>

<p>means "every Frenchman is a man", without saying whether there are any other men or not.  So,</p>

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| align="center" | <math>\mathit{m} -\!\!\!< \mathit{l}</math>

| align="center" | <math>\mathit{m} ~-\!\!\!< \mathit{l}</math>

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{| width="100%"

{| width="100%"

| width="25%" | &nbsp;

| width="25%" | &nbsp;

| align="center" | <math>\mathrm{f} -\!\!\!< \mathrm{m}</math>

| align="center" | <math>\mathrm{f} ~-\!\!\!< \mathrm{m}</math>

| width="25%" | &nbsp;

| width="25%" | &nbsp;

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| <p>and</p>

| <p>and</p>

| align="center" | <math>\mathrm{m} -\!\!\!< \mathrm{a}</math>

| align="center" | <math>\mathrm{m} ~-\!\!\!< \mathrm{a}</math>

| &nbsp;

| &nbsp;

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| <p>we can infer that</p>

| <p>we can infer that</p>

| align="center" | <math>\mathrm{f} -\!\!\!< \mathrm{a}</math>

| align="center" | <math>\mathrm{f} ~-\!\!\!< \mathrm{a}</math>

| &nbsp;

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The quantifier mapping from terms to their numbers that Peirce signifies by means of the square bracket notation <math>[t]\!</math> has one of its principal uses in providing a basis for the computation of frequencies, probabilities, and all of the other statistical measures that can be constructed from these, and thus in affording what may be called a ''principle of correspondence'' between probability theory and its limiting case in the forms of logic.

The quantifier mapping from terms to their numbers that Peirce signifies by means of the square bracket notation <math>[t]\!</math> has one of its principal uses in providing a basis for the computation of frequencies, probabilities, and all of the other statistical measures that can be constructed from these, and thus in affording what may be called a ''principle of correspondence'' between probability theory and its limiting case in the forms of logic.

This brings us once again to the relativity of contingency and necessity, as one way of approaching necessity is through the avenue of probability, describing necessity as a probability of 1, but the whole apparatus of probability theory only figures in if it is cast against the backdrop of probability space axioms, the reference class of distributions, and the sample space that we cannot help but to abdeuce upon the scene of observations.  Aye, there's the snake eyes.  And with them we can see that there is always an irreducible quantum of facticity to all our necessities.  More plainly spoken, it takes a fairly complex conceptual infrastructure just to begin speaking of probabilities, and this setting can only be set up by means of abductive, fallible, hypothetical, and inherently risky mental acts.

This brings us once again to the relativity of contingency and necessity, as one way of approaching necessity is through the avenue of probability, describing necessity as a probability of 1, but the whole apparatus of probability theory only figures in if it is cast against the backdrop of probability space axioms, the reference class of distributions, and the sample space that we cannot help but to abduce upon the scene of observations.  Aye, there's the snake eyes.  And with them we can see that there is always an irreducible quantum of facticity to all our necessities.  More plainly spoken, it takes a fairly complex conceptual infrastructure just to begin speaking of probabilities, and this setting can only be set up by means of abductive, fallible, hypothetical, and inherently risky mental acts.

Pragmatic thinking is the logic of abduction, which is just another way of saying that it addresses the question:  "What may be hoped?"  We have to face the possibility that it may be just as impossible to speak of "absolute identity" with any hope of making practical philosophical sense as it is to speak of "absolute simultaneity" with any hope of making operational physical sense.

Pragmatic thinking is the logic of abduction, which is just another way of saying that it addresses the question:  "What may be hoped?"  We have to face the possibility that it may be just as impossible to speak of "absolute identity" with any hope of making practical philosophical sense as it is to speak of "absolute simultaneity" with any hope of making operational physical sense.