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Is it possible to give an a priori answer to whether or not an infinite past is possible?

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    Logic has no idea what "infinite" or "past" are, and what their properties are, so no. Logic can not even tell you if it is possible to lift your left hand. You need some physical or metaphysical doctrines to reason about such things, and they are beyond mere logic. – Conifold Jul 14 at 6:48
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    Maybe the correct question is: is it logical possible (i.e. without contradiction) the concept of infinite regress in time ? – Mauro ALLEGRANZA Jul 14 at 11:41
  • @Conifold Correct can mean "well formed" or it can mean "corresponds to reality" and possibly a few other things. If you let mathematics be "part of logic" then, oh yes it does have those concepts. So it would certainly be possible to build a variety of theories about the past in logical systems. And so it would be possible to give well formed answers. You are correct in saying that it isn't possible to know which, if any, corresponds to reality, just by doing math. It's tough to know even including observations. – puppetsock Jul 14 at 19:44
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    @Conifold I've added below what I take to be a traditional sort of answer to this question. That aside, I'm not so confident about the boundaries between metaphysical/physical/logical as tradition seems to be. If my theory asserts 'all green things have color' with other axioms capturing the meanings of terms like 'green' and 'color', I count the models constrained, inferences validated, etc. as constituting a logic, just as most others count models constrained, etc. with axioms governing conjunction, conditional, etc., as constituting a logic. Logic doesn't get connectives for free. – John Beverley Jul 14 at 21:01
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From my epistemic position, there is nothing contradictory about the possibility of an infinite past. So, from my epistemic position, it is possible the past is infinite. If by "give a correct answer using logic" you'll accept answers restricted to epistemic modality, then the correct answer is "yes, it is possible the past is infinite."

If, however, by "give a correct answer using logic" you mean determine - metaphysically speaking - that an infinite past is possible, then the answer seems "no" since this outstrips my epistemic position, and it's neither logically impossible that the past is finite nor does the possibility of an infinite past follow from any logical truths.

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This is one of the antimonies in Kant’s Critique of Pure Reason. It is possible to give reasonable arguments in both directions, so pure reason isn’t able to resolve it “alone”... Kant famously leaves “room” for faith, but empirically there is data (measurements of the cosmic microwave background) that would suggest it is in fact the case that the universe began as a hot dense singularity at a particular point in the past, billions of years ago.

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  • how about the concept of a continuously regenerating universe, and the concept of multiverse? – vidyarthi Jul 14 at 4:46
  • @vidyarthi Since there is no empirical access to these (mathematical/logical) possibilities, it is pointless to muse about them in a scientific context of which Joseph writes here. Logical proofs with empirical input are a minefield. – Philip Klöcking Jul 14 at 11:19
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Is it possible to give a correct answer using logic to whether infinite past is possible or not?

Yes.

There are articles on Wikipedia about Temporal Finitism, the philosophical view of Time and even a statistical mechanics and classical thermodynamics based explanation; which shows that choice of definition can certainly play a part in what the answer would be, and whether such an answer is logical and correct.

My offering is a physics based logical explanation:

References and Definitions:

Prior to our existence we (our universe) had neither dimension, mass, nor time, anything - a state of nothingness. Elsewhere (if it existed) could have those properties, beings in another universe could say we did not exist (that we had no mass, were not located anywhere at any particular distance, up until a particular time). Another's existence is not "our past"; that they had dimensions and time prior to our existence does not impart the property upon us - we could not have had "time" prior to our existence.

Supported by: Wikipedia: The Very Early Universe:

     Prior to 10^−43 seconds after creation:

     "During the earliest moments of cosmic time, the energies and conditions were so extreme that current knowledge can only suggest possibilities, which may turn out to be incorrect. To give one example, eternal inflation theories propose that inflation lasts forever throughout most of the universe, making the notion of "N seconds since Big Bang" ill-defined. Therefore the earliest stages are an active area of research and based on ideas which are still speculative and subject to modification as scientific knowledge improves.

     Although a specific "inflationary epoch" is highlighted at around 10^−32 seconds, observations and theories both suggest that distances between objects in space have been increasing at all times since the moment of the Big Bang, and are still increasing (with the exception of gravitationally bound objects such as galaxies and most clusters, once the rate of expansion had greatly slowed).".

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  • @puppetsock Prior to our existence we have 0 dimensions, once we exist we have a dimension, if we move in any direction our space becomes 2 dimensional, another movement that is not a return to the origin creates the 3rd dimension. That all of that occurs simultaneously, before we have particles (quarks, photons, atoms, etc.) means it occurs prior to the existence of spacetime (and thus time itself). --- Thus going back that far ends time, it's finite. --- The "observations", as you call them, scientifically support the logic of what is proposed. It's easy to answer Y/N, and offer no proof. – Rob Jul 15 at 1:15
  • @puppetsock Another analogy is that time only flows forward and isn't reversible; before "0 time" we do not have negative numbers, 0 is the limit. An example using thermodynamics is that we don't have temperatures below zero Kelvin, we don't have negative Kelvin temperatures. Reference: nature.com/articles/nphys2815#auth-2 – Rob Jul 15 at 1:38

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